the positioning of the coach and the transformative agency of teachers
TRANSCRIPT
The positioning of the coach and the transformative agency of
teachers: The problem of constituting joint meaning in an
“underperforming” secondary mathematics department
Sol DiMaggio
Submitted in partial fulfilment of the requirements of the degree of Doctor of Education
(with coursework component)
July 2013
Melbourne Graduate School of Education
The University of Melbourne
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Abstract
The Victorian State Department of Education and Early Childhood Development (DEECD)
instituted a coaching program (2007-2010) to improve teaching in primary and secondary
schools. The DEECD policy platform of school improvement through teacher-trained coaches
saw the employment of Teaching and Learning Coaches (henceforth “coach”) employed from
2007 to support mathematics and science instruction. Eleven numeracy coaches were deployed
across the western metropolitan region of Melbourne in 2008 and placed in schools that were
identified as “underperforming” based on student performance data. This research focuses on
two school sites in which a coach worked at each on a weekly rotational basis in an onsite
professional development program to improve teaching practice using a sanctioned generic
mathematics lesson structure. The coaching program in this study involved the teachers of
mathematics, the appointment of school-based coaches from among them, and administrators in
the targeted “underperforming” secondary schools, with the intention of changing the prima
facie unproductive, culturally specific, mathematics teaching practices in those schools. This
thesis examines how mathematics teachers in targeted “underperforming” schools reported how
they were influenced, by working with a coach.
The research is founded on the theoretical belief that there is nothing else to social life but
symbolic exchanges and the joint construction and management of meaning, including the
meaning of bits of stuff including things we control and things that we don’t, but are expected to
use to “remake” ourselves. To become relevant in the teachers’ life spaces the coaching stuff,
including the coach herself, had to be interpreted to play a part in a human narrative.
Interpretations require grammars that are historically and culturally local. The thesis presents
fine-grained descriptive analyses of the semiotic interactions and the psychological positioning
of mathematics teachers in the accounts of their experiences of the coaching program. The
recommended practices put by the coach were resisted where they were seen not to serve the
teachers’ personal identity formation in the local moral order of their school. The teachers’
social activity with the coach shows they live in a double social order. One component consists
of the social arrangements for maintaining their teaching lives in their teaching environment,
which was difficult by virtue of the educational disadvantage of the community, they served and
their own poor training and professional isolation. This is the practical order and the teachers
had their local proper place in that order. The other component consisted of the social
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arrangements for creating honour and status. This is an expressive order. The material world of
privileged strategies, tactics, student test performance data and other elements of the program of
improvement brought by the coach can be understood in their full human significance only if
their roles in both these orders are identified. As to the teachers’ social motivation around these
material things, the accounts of the teachers present a strong case for the priority of the
expressive over the practical in their social action. The new lesson structure the coach
introduced can become a social object only within the dynamic frame of the teachers’ storylines.
It is this most ephemeral and “invisible” product of the teachers’ action that is really real, the
narratives that are realized in the social orders in their school.
The elaboration of a more comprehensive theory of mentoring / coaching practices based on this
approach to constructing a new constitutive order involves a study of the social objects as
created in and through constitutive practices. This draws on a distinction between constitutive
orders of the rules of maths teaching, which are prospective doings, and sayings constructed
around social objects, and institutional orders of maths teaching, which are retrospective and
depend on “accounts” and justifications. It is essential that constitutive orders of practice are
collaborations. Taking all this into account requires thinking of meaning making as one of
communication or interaction, or as Harré argues, taking conversation as real or causal. To
make sense of, or claim meaning in, the teachers’ constitutively ordered conversational
sequences about their interactions with the coach, in the use of social objects, their self
organising practices or language games, is to explore their orientation to a constitutive rule and
their exhibition of it to others.
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Declaration
This is to certify that
i) the thesis comprises only my original work towards the degree of Doctor of Education,
ii) due acknowledgement has been made in the text to all other material used,
iii) the thesis is approximately 55,000 words in length, exclusive of tables, maps,
bibliographies and appendices.
Signed: _________________________________ Date: _________________________
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Acknowledgements
The author expresses sincere gratitude to the following people who provided generous support
and encouragement throughout the research and writing of the thesis:
Foremost, I would like to express my heartfelt appreciation to my supervisor Dr. Rod
Fawns for the continuous support, tireless enthusiasm, and immense knowledge. His
guidance assisted me greatly throughout the time of research and writing of this thesis.
I could not have imagined having a better advisor and mentor for my D.Ed. study;
The academics and researchers, otherwise known as the “Ginger Group” who provided
constructive feedback and moral support throughout the period of this research;
All the direct participants in the study, in particular the teachers who granted me entry
into their teaching world by generously sharing their views openly in the hope that it
would contribute to a better understanding of teacher professional practice;
My patient and encouraging wife Christine and daughter Carla whose love and support
were essential for the completion of my work.
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Table of Contents
Chapter 1: Coaching for school reform ---------------------------------------------------------------1
Orientation ---------------------------------------------------------------------------------------------- 1
The problem for centrally directed educational reform: From the inside and underneath --- 1
A program for changing: DEECD’s sanctioned lesson structure to be presented by the
coach ---------------------------------------------------------------------------------------------------- 4
Teacher meaning making towards self-improvement in a coaching program ----------------- 6
The teacher as hero ------------------------------------------------------------------------------------- 8
To teach mathematics is to labour existentially --------------------------------------------------- 10
Rationale for this research ---------------------------------------------------------------------------- 11
Research questions ------------------------------------------------------------------------------------ 12
The research context ---------------------------------------------------------------------------------- 12
Acquiring teacher skills and knowledge ------------------------------------------------------------ 13
Introduction to the theoretical framework ---------------------------------------------------------- 14
Chapter 2: Discursive practice; for, as and of meaning making ---------------------------------17
Introduction -------------------------------------------------------------------------------------------- 17
Purpose and approach to the study ------------------------------------------------------------------ 18
The social milieu: The institutional paradigm of professional development ----------------- 18
Professional development as a constitutive process for change --------------------------------- 19
Coaching as a policy model for transforming teaching practice -------------------------------- 20
The Japanese Lesson Study: A narrative constitutive model of professional development 22
The situational grammar of professional identity formation ------------------------------------- 24
Organisational learning and the ideal world of the Lesson Study in a community of practice 29
Towards a model of coaching as a transformational discourse ---------------------------------- 33
Signing in conversation with the coach ------------------------------------------------------------- 37
Emotion in the analysis of the teachers’ narrative of the coaching intervention -------------- 40
The coach as myth bearer: The mythopoesis of a new lesson structure in the improvement
of mathematics teaching ------------------------------------------------------------------------------- 41
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The discursive psychological positioning of the coach and her message in teachers’
storylines of their practice ---------------------------------------------------------------------------- 43
Locating the person of the teacher in their storyline ---------------------------------------------- 45
“My kids just don’t get algebra, I’ve tried everything and they just don’t get it” ------------ 46
Narrative research for understanding the sense making of teachers ----------------------------- 47
Summary ------------------------------------------------------------------------------------------------ 48
Chapter 3: Language and self-monitoring, the basic particulars of personhood ------------50
Introduction -------------------------------------------------------------------------------------------- 50
Discursive accounts ----------------------------------------------------------------------------------- 51
Conversational perspective taking ------------------------------------------------------------------ 53
Overview of the study --------------------------------------------------------------------------------- 54
1. Subject selection ------------------------------------------------------------------------------- 55
2. The school research sites --------------------------------------------------------------------- 56
3. Data sources ------------------------------------------------------------------------------------ 56
4. Steps in the research (2008 to 2010) -------------------------------------------------------- 57
5. Data collection methods ---------------------------------------------------------------------- 58
5.1 Surveys ------------------------------------------------------------------------------------ 58
5.2 Interviewees ------------------------------------------------------------------------------ 59
5.3 Observations ------------------------------------------------------------------------------ 59
5.4 Artefacts ----------------------------------------------------------------------------------- 59
5.5 Presentation of narrative functions of discursive episodes ------------------------ 60
5.4 Data analysis ----------------------------------------------------------------------------- 63
The scope of this research ---------------------------------------------------------------------------- 64
Pilot interview with Sally ----------------------------------------------------------------------------- 66
Issues of trustworthiness and other limitations in this study ------------------------------------- 75
Thesis structure ---------------------------------------------------------------------------------------- 76
Chapter 4: Lambertia College --------------------------------------------------------------------------77
Samantha, the Regional Coach ------------------------------------------------------------------------ 78
Maria Oslava, Principal of Lambertia College ------------------------------------------------------ 80
Tony Roma, Lambertia College ----------------------------------------------------------------------- 81
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Tony’s self / identity analysis ------------------------------------------------------------------------- 83
Samantha’s response ------------------------------------------------------------------------------------ 100
Chapter 5: Grallina College -----------------------------------------------------------------------------101
Samantha, the Regional Coach ---------------------------------------------------------------------- 103
Sonia Peterson, Principal of Grallina College ----------------------------------------------------- 104
Mandy Fitzpatrick, Grallina College ---------------------------------------------------------------- 105
Samantha response ------------------------------------------------------------------------------------ 134
Chapter 6: The causal power of discourses of reproduction and transformation -----------132
Chapter 7: The positioning of the coach and the transformative agency of teachers: The
problem of constituting joint meaning in an “underperforming” secondary
mathematics department ------------------------------------------------------------------141
How can shared meaning be constructed between the coach and teachers? ------------------- 141
What should pass as research in the phenomenological sociology of teaching and learning?
-------------------------------------------------------------------------------------------------------------- 144
What is worthwhile about this research? ----------------------------------------------------------- 147
References ---------------------------------------------------------------------------------------------------155
Appendices
Appendix 1: Maths Lesson Structure
Appendix 2: Whole school survey
Appendix 3: Survey structure
Appendix 4: Survey results – Lambertia College
Appendix 5: Survey results – Grallina College
Appendix 6: Interview schedule - Coach
Appendix 7: Interview schedule - Principal
Appendix 8: Vladimir Propp’s Theory
Appendix 9: Josh Ryan
Appendix 10: Sarah Farqua
Appendix 11: Pete Milios
Appendix 12: Ray Bush
Appendix 13: Liz Taylor
Appendix 14: Jon Adams
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List of Tables and Figures
Table 1: Teacher identity after Gee (2000-2001) ---------------------------------------------------28
Table 2: Application of Vladimir Propp’s (1928/1968) theory of the “fairy tale” to the
teacher narratives offered in this study ----------------------------------------------------65
Table 3: The Scope of the Research - Ontological and Phenomenological Dimensions of
Social Activity after Nellhaus (1998, p. 19) ----------------------------------------------65
Table 4: Sally’s discursive identity formation after Gee (2000-2001) and Bullough (2005) -66
Table 5: Tony’s discursive identity formation after Gee (2000-2001) and Bullough (2005)---83
Table 6: Mandy’s discursive identity formation after Gee (2000-2001) and Bullough (2005)-107
Figure 1: Lesson Study cycle (Lewis, Perry, Murata, 2006, p. 4) ---------------------------------23
Figure 2: The discursive psychological model of professional identity formation and
concurrent reform of organisational structures proposed in this study after Harré
(1993) ------------------------------------------------------------------------------------------25
Figure 3: Transformational model of social activity / person connection, after Harvey (2002)
and Bhaskar (1994) --------------------------------------------------------------------------33
Figure 4: Transformational model emphasizing a historical rhythm and the agent dependent
nature of the social transformation process after Harvey (2002) and Bhaskar (1994)
----------------------------------------------------------------------------------------------------35
Figure 5: Transformational model emphasizing time dependence in a community of practice
----------------------------------------------------------------------------------------------------35
Figure 6: Transformational model of social activity in the coaching episode using Simmel’s
(1968) account of human agency as mutual self-cultivation and cultural production
in a community context after Harvey (2002) and Bhaskar (1994) --------------------36
Figure 7: Mediational triangle after Vygotsky -------------------------------------------------------38
Figure 8: Semiotic triad after Peirce ------------------------------------------------------------------39
Figure 9: Mutually determining triad in a conversational episode --------------------------------43
Figure 10: Model of social transformative action in a community of practice --------------------137
Figure 11: Collaborative mentorship as an enabling condition -------------------------------------138
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Glossary
Agency Agency is defined by Harvey “…as embodied intentional causality or
process…” in the sense that human beings have the power to do as they
please without any form of conscious or unconscious influence (2002, p.
172).
Coach Prepares a candidate for examination or other performative assessment.
Community of
practice
A community of practice is defined by Wenger & Snyder as “groups of
people informally bound together by shared experience and passion for
a joint enterprise.” (2000, p. 137). A “…relatively stable community of
face-to-face interaction between members working in close proximity to
one another, in which identity formation through participation and the
negotiation of meaning are central to learning and knowledge
generation” (Amin & Roberts, 2008, p. 355).
Constitutive order
and Institutional
order
Rawls argues that make sense / sense making is encouraged through
reflexive moments of communication between people where there is an
emphasis on cooperation and moral equity (2011). Meaning emerges as
a result of a mutual orientation towards “… constitutive use practices:
constitutive rules, “use” conventions or background expectations.”
(Rawls, 2011, p. 397). Meaning making is thus prospective rather than
retrospective as is the case with an institutional order where formal roles
and practices dictate peoples’ actions and where social thought is
stultified.
Conversation A conversation is “… an ordered sequence of meaningful exchanges
having, more often then not, some upshot or end defined by local rules
and customs” (Harré, 1999, p. 52).
Culture “[The]… set of values, beliefs, and meanings, together with the artefacts
of their expression and transmission (such as myths, symbols,
metaphors, rituals and ritual objects), that are created, inherited, shared,
and transmitted within one group of people; that, in part, distinguish that
group from others; and by which the patterns of collective action unique
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to that group are acquired, maintained, changed and put to use.” (Cook
& Yannow, 1996, p. 15).
Digilearn Digilearn is a Department of Education and Early Childhood
Development (DEECD) online resource
Ethogenic The ethogenic approach focuses on speech acts which accompany
everyday human action, mediated in a community of practice, to
describe how an individual becomes the kind of person his language,
tradition, tacit, explicit and social knowledge tell him/her what she/he is.
Identity Palmer defines identity as “…an evolving nexus, a moving intersection
of the inner and outer forces that make me who I am” (1998, p.13) that
others recognise as a certain “kind of person” performing in a given
context (Gee, 2000-2001).
Key Learning
Areas (KLA)
A Key Learning Area (KLA) is a subject discipline / department.
Mathematics is one of 8 KLA’s in the DEECD curriculum
Japanese Lesson
Study
The Lesson Study involves the observation of classroom practice by a
group of teachers who collect data over the course of a number of
teaching and learning episodes. The data collected is referred to as the
“research lessons” and consists of non-judgmental accounts of teaching
and of student learning. Teachers who observed the lesson then
collaboratively analyse, reflect upon and document teaching and
learning as an approach to making improvements within the contexts of
teaching (Lewis, Perry and Murata, 2006).
DEECD’s
Mathematics
Lesson Structure
A framework for the teaching of mathematics consisting of four
instructional component parts. These were:
(i) a “warm-up” activity to engage students;
(ii) teacher introduction of the topic;
(iii) student participation in activities based around the topic, and
(iv) students review their learning by means of a “reflective”
activity.
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Mentor Provides wise and trusted counsel.
“Past-present” Composed of artefacts and utterances which are alleged in our everyday
discursive practice to have survived from the past and been recognised
in terms of their worth in current engagements and as such influences
decisions made and shapes teacher agency in the process.
Position The term “position” refers to “positioning theory” to describe the
process in which social actors take on identities within discourse as they
position others or let themselves be positioned by others (Davies and
Harré, 1990; Harré and van Langenhove, 1999).
Practice Practice represents habits and norms that teachers use and reference in
going about their day-to-day tasks.
Professional
Learning Team
(PLT)
A Professional Learning Team is a discourse community established to
encourage site-based teacher collaboration of improvement to teaching
practice.
Regional Coach A Teacher employed and trained as a Teaching and Learning Coach by
the Western Metropolitan Regional Office of the Department of
Education and Early Childhood Development. The Regional Coach was
deployed in schools that were deemed by the DEECD as requiring
assistance.
Smart testing The “Smart testing” program for teachers. It is a self-initiated tool of
diagnosis of specific student learning attainment.
Structure Porpora (1989) views structure as enduring and as persistent patterns of
collective behavior as built up, reproduced and transformed over time
through conversational encounters.
The Mathematics
Developmental
Continuum P – 10
The Mathematics Developmental Continuum P – 10 is a DEECD
developed Internet based resource that provides indicators and
descriptive tests for classroom teachers of student progress on a learning
continuum. The continuum highlights understandings required by
students in order to progress through the Victorian Essential Learning
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Standards for the mathematics.
Ultranet The Ultranet is an online system for Victorian government schools that
provides a secure site for students, parents and teachers accessing the
Internet and in the protection of information. It also aims to provide
collaborative learning ‘spaces’ for students and teachers as well as an
opportunity for parents to view their child’s progress.
Umwelt An individual’s internationalized model of the world.
V.I.T. Victorian Institute of Teaching is a statutory authority to regulate the
teaching profession established by an Act of the Victorian Parliament in
2001. Graduate teachers are required to undertake a structured
induction program.
1
1
Coaching for school reform
Orientation
At the time of writing this thesis I was a Humanities teacher in a government Preparatory to
Year 12 College in the socially disadvantaged Western Metropolitan Region of Melbourne. I
have been and continue to be employed as a government secondary school teacher having been
so for approximately twenty-four years. In 2005 I was contracted as a Teaching and Learning
Coach (henceforth “coach”) for three years across a cluster of two secondary and two primary
government schools. As a coach I experienced, first hand, how the practice of teaching
mathematics had not changed from when I was taught mathematics as a student. The same
practice prevailed, that is, of a teacher demonstrating some new manipulations on the board
followed by practice. The questions posed to elicit student participation and the briefest correct
answer in the first phase inadequately addressed the learning needs of students but rather
promoted apprehension and inhibited intellectual risk taking. Individual competition for
teacher’s approval was the prime motivational theory. I observed a shallow teaching syndrome,
which could be characterised as teaching procedures without reasoning. Challenged by the
expectations of my role within the DEECD and my positioning by the teachers I coached, I
commenced research into coaching for school reform soon after my contract ended.
The problem for centrally directed educational reform: From the inside and
underneath
Interest in school effectiveness and improvement, in recent years, has been fuelled by
challenges facing developed countries. In the 1990s mounting international challenges
associated with the rapid growth of technological innovation, migration, increasing economic
globalisation… all required the implementation of government policies to deal with the
complexities, uncertainties and fears that emerged (Matthews, Moorman & Nushe, 2007). One
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government response in these countries has been to seek greater productivity and accountability
for teaching practices. To this end, the education policy course moved in the direction of a
“standards based agenda” (Harris, 2003; Levin, 1998). The “effective school” or perhaps the
“underperforming school” has become the unit of analysis at the centre of policy research in
which performance on educational outcomes are sought on statewide normative testing of
student learning in mathematics, English and science. More recently the reform agenda has
been publically framed in terms of improving the “organisational capacity” of schools to cope
with future contingencies through a prescription of curriculum, assessment, and leadership
coupled to a framework of accountability as presented through the use of student performance
data and institutional bench marking at different year levels (Elmore, 2007). Other performance
data on teachers, students and parents attitudes towards “underperforming” schools has become
the focused shame or guilt responses, but as Elmore (2007) observes a corresponding
investment in human resources to overcome revealed educational disadvantage, in teachers and
their organisational capacity at the level of the subject department level is required but has been
typically neglected.
The improvement of organisational capacity in the “standards based reform” agenda in
Victorian schools may be traced back to 2003 when the Schools Innovation and Excellence
initiative was introduced to provide support for leadership and planning at the level of the
school and across clusters of schools (DEECD, 2009). The Leading School Fund was another
initiative administered by the DEECD (2013) between 2003-2008 to focus on supporting
teachers more directly in the classroom. This shift in policy was attributable to proponents such
as Hattie (2003) who argued that increasing teacher capacity had a flow on effect on improving
student achievement, and Elmore (2007) who suggested that teachers in Victorian schools
should “… be exposed to coaching and mentoring others as early as possible in their careers”
(p. 7). The Teaching and Learning Coach program in Victorian schools was thus born,
concerned with building teacher capacity to respond to the local context, the local conditions
and responsive to student needs (DEECD, 2010a). The initiative was introduced in 2007 and
employed coaches across the state to effect improvement to student outcomes in literacy,
mathematics, and to a lesser degree science and literacy targeted at Koorie students (DEECD,
2010a). Coaches were also deployed to assist with the implementation of the Ultranet, another
Victorian government initiative that promoted online learning for teachers, students and parents
(DEECD, 2010b).
The Teaching and Learning Coach program was a professional development approach that was
encouraged, centrally managed, and imposed from “head office” in the form of a coach (2010a).
3
A coach was a classroom teacher, trained up to promote institutional regeneration through a
centrally administered program of change. This mandated professional development program
was positioned within the school and encouraged teachers to apply state supported approaches
to curriculum, pedagogy and assessment. The coaching program hoped to apply the principles
of adult learning drawn principally from Schon’s (1996) rational reflective practice to the
improvement of their pedagogical content knowledge. To facilitate the organizational
restructuring and to sustain changed practices in schools and in mathematics departments, the
Western Regional Office of the DEECD encouraged key staff members in schools to attend
periodic regional meetings facilitated by consultants to guide planning and delivery of
professional development. Key staff members included a representative from the school’s
leadership team, the mathematics department head and a teacher who would assume the
responsibility for becoming the school-based coach once the Regional Coach had left. The role
of the school-based coach was to take over the responsibilities of the Regional Coach thereby
ensuring practices introduced by the Regional Coach would be sustained and thereby embedded
and embodied within the school culture.
It was envisioned by the DEECD that at the school level, Professional Learning Team (PLT)
meetings would be established to review school performance data that essentially focused
conversations on reviewing practice in order to improve student outcomes. Teachers attending
the PLT meetings were encouraged to share experiences of pedagogical approaches to the
teaching of mathematics as informed by the new sanctioned Mathematics Lesson Structure
(discussed below) (DEECD, 2011).1 For example, the coach would share resources in the
form of “warm-up” activities that consisted of games or problem solving activities all of which
encouraged students to learn using a “manipulable approach”, the focus of which was to
engender a richer learning experience. The coach would introduce activities at the PLT meeting
and encourage teachers to implement and to report their experience back to their colleagues at
the next PLT meeting. Teachers were also encouraged to involve the coach in demonstrating
pedagogical approaches with their class. The re-conception of mathematics teaching was
through the PLT which was directed by the coach and sanctioned by the school’s leadership;
directly connected to the DEECD to effect change as the state mandated quasi leaders of
“underperforming schools”. It was expected that the school-based coach would continue this
on-site professional development approach confirming the establishment of instructional
leadership in “underperforming schools”.
1 Refer Appendix 1
4
Between 2008 and 2011 eleven mathematics coaches were deployed across the Western
Metropolitan Region of Melbourne in “underperforming schools” to assist in the improvement
of student performance on nation-wide mandated testing. The introduction of a sanctioned
Mathematics Lesson Structure was the working agenda that the leadership team in each school
was expected to support as part of the coaching program. This institutional authority and the
appointment of school-based coaches with local experience was designated to enhance the
moral authority of the coaching program among teachers targeted to improve their teaching
practice. Once this was achieved, the Regional Coach would then be deployed to another
school. The policy can be seen to resemble a conventional centrally directed approach to
professional development but led by local teachers as change agents. Smylie and Perry (1998)
expressed a concern about the bureaucratic assumption professional development programs
designed by policy makers could efficiently resolve the complex issues of lifting the status of
“underperforming schools”. For promoting change through a coaching program is complex
given that a change in the practical order (maintenance of appropriate role behaviour) that
serves system maintenance does not necessarily equate to change in the expressive order
(honour and reputation) in the social act of teaching where the latter often takes priority over the
former. A bureaucratically controlled coaching program Harris (2003) warned, could be viewed
as just another way of sedimenting control over the process of teaching, creating more teacher
resistance in the process. Despite this, the coaching policy introduced by the Labor government
was an attempt at improving student outcomes in “underperforming” schools and as such cannot
be judged on simple grounds. The funding for the coaching program was not sustained with the
election of a conservative government in 2010 and the coaching program was terminated at the
end of the 2011 academic year.
A program for changing: DEECD’s sanctioned lesson structure to be presented by
the coach
The sanctioned Mathematics Lesson Structure is a move away from the old professional
development paradigm to one that puts the focus back on students (DEECD, 2011). The
Mathematics Lesson Structure consists in restructuring the mathematics lesson into four
instructional component parts. These component parts included:
(i) A “warm-up” activity in the form of a game to motivate and engage students to
think mathematically.
(ii) A brief introduction to the topic.
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(iii) Students would spend the bulk of the lesson completing an activity or a series of
activities to demonstrate their mathematical understanding.
(iv) Finally, students would review their learning by means of a “reflective” type
activity.
In order to facilitate this new approach for professional development in teaching mathematics
the coach would meet with a teacher of mathematics to review their lesson prior to visiting the
class in which the lesson would take place. During the lesson, the coach would actively assist
both teacher and students in the class and debrief with the teacher at the conclusion of the
lesson.
Initially a Melbourne based mathematics consultant contracted by the DEECD introduced the
lesson structure to coaches and teachers. The consultant experienced success with the
sanctioned lesson structure in individual schools and believed that it could be a useful approach
to system wide improvement in the teaching of mathematics, with the ultimate aim being to
improve the teaching and learning of mathematics so that students would become more
numerate. Further, the goals associated with the implementation of the lesson structure were: to
engage and involve teachers with challenges in the teaching and learning of mathematics, to
engage students with their mathematics learning, to build teachers mathematical knowledge,
pedagogy and pedagogical content knowledge and to improve the planning of mathematics units
/ content thereby making it consistent across the subject department. Whilst research (Clarke,
2003; Mesiti, Clarke, & Lobato, 2003) existed in lesson structures worldwide, the Mathematics
Lesson Structure as outlined above did not come directly from any recommended model.
Instead it resulted from a combination of research findings and anecdotal knowledge around
what constituted effective teaching of mathematics. The Mathematics Lesson Structure was
essentially developed by Regional Coaches, in consultation with a mathematics education
consultant and took into consideration research that was based on the Japanese Lesson Structure
(Shimizu, 2003; Stigler & Hiebert, 2000; Takahashi & Yoshida, 2004). The Mathematics
Lesson Structure also had its basis in pedagogy that promoted deeper thinking and student
reflection. The Mathematics Lesson Structure was promoted by coaches, the maths consultant,
at regional network meetings and posted on the Ultranet.
6
Teacher meaning making towards self-improvement in a coaching program
I sought to explore in this research the “life world” of maths teachers in “underperforming
schools”. The “life world” is the individual teacher’s province of meaning and of meaning
making. It is in this world that teachers develop habits and beliefs expressed through intentional
acts of what it means to be a teacher of mathematics in a time and place (Schutz as cited in
Heiskala, 2011). Further, Schutz argues, that to explore a teacher’s meaning making is to
analyse the structures of their “life world” in order to experience how subjectivity is involved in
the construction of social meaning, social actions and situations (as cited in Heiskala, 2011).
The experience of the “life world” is a process of typification one that assists the actor to
understand the world and people. Objects in the “life world” of the teacher assist them to act
out being a teacher in the discursive practice of maths teaching. The textbook, electronic
whiteboard, calculators, algorithms and the like are all signs that index physical objects in the
teaching environment that have embedded experiences and meaning and where corresponding
affordances are transmitted by means of teacher narratives. Teacher actions are embedded in
discursive practices, habits and beliefs. Their repertoire of maxims and recipes not only
emanate from typified objects found in a classroom but are also found in their actions,
situations, personalities… that they naturally index in the course of their meaning making.
Meaning making is a system of relevance, which is made the more applicable with respect to
teaching angles in Year 7 when teachers view the practice or experience through the perspective
and connotative knowledge of other teachers. The importance of which was illuminated in a
study reported by Paige, Chartres and Kenyon (2008) in which they describe a professional
development program based on oral history and how it improved the quality of the educational
practice of teacher-learners for it provided “…numerous opportunities for teachers to reflect on
their practice, to be involved in the ongoing sequential professional development relevant to
their needs and to be involved in action research in their classroom” (p. 526). Approaches such
as the one quoted here typify the cultural, historical and biographically conditioned perspectives
of other members of a subject department as a community of practice where meaning is
constituted by way of conversation and acts of reflexivity (Heiskala, 2011). Everyday teacher
action is therefore embedded for better or worse in a cultural environment and a product of
cultural evolution.
Charles Sanders Peirce argues that the actor / agent is but a product of a cultural evolution
where the basis of actions is in the anticipated outcomes of that action. The fact that things
happen according to certain habits, results in an actor realising their potentiality in following a
7
general law of action (Hartshorne, Weiss & Burks (Eds). (1931–1958), Vol. 2, p. 148). For
Peirce, meanings are essentially habits of action for “… what a thing means is simply what
habits it involves…” (Hartshorne et al. (1931-1958), Vol. 5, p. 400). Therefore anything
perceived in our environment, such as a calculator come to be interpreted by habits of action,
which as a meaning, constitutes beliefs. Habits are therefore what provide generalities in all
phenomena and constitute the intelligible and continuous structure of the world. Based on an
actor’s biography they will express different degrees of doubt, habits of interpretation, until a
hypothesis is confirmed. Peirce employed the Aristotelian idea of “esse in futuro” to capture a
potential mode of being rather than one that is actual. Laws of nature and human potentialities
have their “esse in futuro”, in that, full justification is expressed through explanatory future-
based outcomes for it is in future circumstances where the degree of confidence in a hypothesis
is settled. That is, confidence in a hypothesis is not settled until future performances eliminate
doubt and reconfirm the epistemic authority of the hypothesis in question. The actor / agent
realises doubt-resistant beliefs of everyday knowledge and of veritable belief through inquiry
(knowledge and truth) by way of a constitutive approach to meaning making, one where habits
are geared towards this purpose (Gabbay, Hartmann & Woods (Eds.) 2011; Heiskala, 2011;
Rawls, 2011).
Constitutive meaning making, Rawls argues (2011), is the possibility of shared meaning as an
active process of “mutual attention” at a local level that creates or constitutes “social objects”
referencing the shared practices of the group that is constituting them. Limited opportunities
exist in schools particularly disadvantaged schools, for teachers to reflect with others on their
professional identity. For whilst teachers exercise individual discretion and judgment in
complex teaching and learning situations, they do so in relative isolation from central authority
and resources. Deliberation on psychological and psychosocial agency associated with teaching
and learning is therefore limited. Social determinism in gross forms reinforces passive fatalism,
avoids any challenge to the privacy code in staffrooms and persists as a property of everyday
discourse. The way in which teachers learn is therefore not adequately attended to because the
person of the teacher is hardly ever heard (Harré, 1999). The effective implementation of
improved teaching and learning practice is felt to be the responsibility either of the teachers
themselves or the state as their employer. The failure of one is readily attributed to the other.
What it means to learn to know something is generally understood to encompass not only the
products of learning but also the very process by which higher forms are established (Vygotsky
as cited in Wertsch, 1985).
8
Robertson (2009) argues that a hierarchically positioned school leadership is embedded in a
culture of dependence and any bottom up appreciation of professional self-improvement
through collegial partnership in a community of practice is politically suspect in the staffroom
and rarely evident in practice. Particularly in larger secondary schools, privacy persists as a
guiding mantra in relation to teaching practice. The coach brings a message from “head office”
that it in principle operates outside the teachers’ habitus, which has produced persistent failure
in classroom learning and notionally independent of current school and leadership. Independent
of the local institutional order the coach is nevertheless positioned by the state to challenge
teaching, and perhaps also viewed as coaching the principal. Whilst the idea may have intuitive
plausibility it does not take into account the effect that the political play from “head office” of
changing the locus of responsibility for professional development has on professional interests,
ideologies, and institutional norms as they relate to teachers and principals alike.
The coaching program was positioned within a school system to challenge the leadership of
both school administrators and classroom teachers to shift from one paradigm perceived to have
failed as measured by student test data to another hopefully more successful paradigm
developed with the coach. This study analyses teachers’ discursive acts in the moment of being
coached in the government program to better describe structure and agency in improving
teacher practice. Taylor (2002) and Woods (1994) argued improvement in social practices is
the fundamental validating purpose in social science research. It is not the purpose of this thesis
to attempt to evaluate the coaching program per say, but rather to understand its positioning of
the teachers, the coach, and the semiosis surrounding the actions of the coach in transforming
the teaching of mathematics in two “underperforming” schools.
The teacher as hero
For the teachers in this study, their life’s work as maths teachers seems to them to have been
defined for them, by cultural tradition, as the didactic presentation of a mathematical topic
interpreted logically, but neither with social immediacy nor energy, from a prescribed textbook.
Siskin (1994) studied the micro-cultures of the subject disciplines in academic schools. The
subject department, she argued is the dominant social organizational structure in the academic
secondary school. The mathematics teachers, she observed, typically use an interrogative
approach that seeks to show how the correct answer is achieved with minimal student
interaction by following standard logical steps but does not show how students may proceed
from where they are. This lonely figure of the mathematics teacher at the whiteboard typically
9
presents a couple of worked examples of the required mathematical transformations before
students are instructed to complete problems as practice, from the chapter in the prescribed
textbook. There seems never to be enough time to ensure every student has understood the
logical process. The teachers see their basic social responsibility is to cover all topics in the
requisite time. Because there are so many topics to cover, confusion arises for the student who
feels mentally inadequate and apprehensive. Siskin observes the discipline of mathematics
addresses mathematical thinking as logical structure and mathematics education as logical
training that is asocial. That is, teachers feel they are expected to teach and students to learn in
a formal sequenced way.
Students who are unable to complete what is expected, disabled from moving onto the next
topic forms the prescription for failure. In this paradigm, students are easily identified by the
teacher and by data as failures – as not having what it takes to succeed in mathematics. This
problem is further compounded when students are expected to sit state mandated tests that
socially construct failure, failure in students, failure of teachers and the school as a unit of
production. Further problems associated with mathematics education are related to the low
student self-efficacy in mathematics, which is strategically correlated with socio-cultural
expectation or the socio-economic status of the student’s home address (McConney & Perry,
2010). In addition, a more severe problem for mathematics education is that teachers are
typically less academically equipped than in any other areas of the school curriculum and as
such, exercise less pedagogical freedom (Darling-Hammond & Youngs, 2002). Each of these
problems was identified in the two study schools. In an attempt to intervene to rescue as many
students as possible, all students in many schools including the two study schools are
mathematically tested and set in levels of innate personal competence where students are
grouped for passive instruction at different rates (Zevenbergen, 2001).
Cultural tradition can be felt to define the “life world” of a teacher. On the one hand, the
dominant western tradition portrayed in the popular film “Stand and Deliver”, where Jaime
Escalante a maths teacher at Garfield High, located in a Hispanic neighborhood in East Los
Angeles California believed that his students could attain amazing learning feats against all
social injustice and personal difficulty. Whilst other teachers at Garfield High labelled students
as “no-hopers”, Escalante’s unconventional teaching methods achieved an impossible result for
his students. The moral order for teaching, founded on the rational grammar of student
achievement of predetermined goals, is described by Nussbaum (1986) in the Fragility of
Goodness, as
10
“[t]he accidental circumstances of life become mere appearances, while ultimate
reality exists in the ideals visible only to human reason. Once transcended through
reason, temporal appearances no longer have the power to excite emotions, which,
according to this tradition, blind humanity from sustaining conceptions of
goodness… worthy knowledge as that which can be entertained by human
reason…” (as cited in Wood, 1992, p. 539).
An existential perspective illuminates another classical tradition, of teacher as tragic hero. In
this tradition, the mundane everyday life of the lone teacher who strives day after day with the
chasm between their hopes and intentions, and the daily grind. Their persistence in bringing the
most to bear in the face of the ongoing and of potent contingencies and structural impositions
defines their heroism. As Nussbaum describes,
“[t]he Greek tragedians, however, offered a counter tradition, [t]hey took a
dimmer… view of the power of human reason in that they acknowledged… the
inescapable nature of fate… portray[ing] the detached, rational character as guilty
of hubris, a tragic flaw.” (as cited in Wood, 1992, p. 539).
To teach mathematics is to labour existentially
An existentialist lens seems useful in unpacking the politics of the everyday life of the teacher
and of teaching. Sartre (1960) contrasted a “divine view of the world” with that of a human
view where there is no “divine” standpoint. He argues in the divine view that when “God”
thought about creation; creating the world and human nature, she / he had in mind what to
create. This represents the essence and then God created everything by giving existence to
essence. Therefore, God or political authority prescribes a belief in the fact that “essence
precedes existence”. To Sartre, “existence precedes essence” (2007). This distinction for
Sartre, whilst important is not as important as the fact that there really is no ultimate authority
(for defining best teaching practice in the world) and therefore there is no purpose, value or
possibility of “following” such rules. Student performance against prescribed global
mathematics standards may be seen here as a metaphor for ultimate authority in a godly
appraisal of a teacher’s professional worth or standing. Living in this instance becomes
“absurd” meaning unreasonable or ridiculous.
11
In The Myth of Sisyphus, Camus (1942/1975) offers the ancient Greek mythical figure
condemned to eternal labour, of continually rolling a stone up a hill. He is condemned eternally
to this punishment in a never-ending exercise of futility. Camus proposes Sisyphus’s plight is
an allegory to the “everyday” life of many people. We wake in the morning, have breakfast, go
to work, teach mathematics to difficult classes of students who dismissively reject and resist
learning, go home, wake in the morning… and repeat the practice day after day. To rise each
day, to fight a battle you know you cannot win, dishonoured for your failure, to do this with a
sense of humour, and concern for the future of your students and even as a sense of duty is to
face the “absurd” in a spirit of true heroism. The personal persistence of teachers requires
serious study, rather than pity or scorn. Camus proposes that like Sisyphus, we are freely
conscious, we nevertheless push on in what comes to be known as a plight of essential
hopelessness, a living private hell. For Camus, resignation from teaching is not the
existentialist’s response, rather the existential response is to make life endurable by deciding
that it is meaningful by seeking it in collective endeavour and resistance as a collective
narrative.
For Camus, Sisyphus characterizes the spirit of revolt from meaningless necessity; Sisyphus is
therefore a source of life instruction. The “absurd” expectation is an unavoidable indeed
defining characteristic of the human condition. The only response to it is a full, resolute and
courageous persistence. The Sisyphian spirit of defiance is a spirit of opposition against any
perceived unfairness, oppression or indignity in the human condition. Camus can be seen to
propose that, like Sisyphus, the mathematics teachers in this situation accept their essential
isolation, the “absurd” nature of their existence, seek collective agency, which is a confrontation
with the world that goes on regardless. To live one’s life as a teacher of mathematics in this
situation, one must exercise the freedom to create a life as a teacher, that is, to find what is
authentic and meaningful for one’s self. This existential approach, Camus argues, allows
Sisyphus to be occupied and fulfilled with what he is doing.
Rationale for this research
The published research on “coaching” towards teacher self-improvement to date evaluates the
coaching paradigm without reflecting on teacher ontologies or studying their discursive
repositioning particularly as it informs changes to their professional identities. The research
reported here does not attempt to evaluate the effectiveness of DEECD’s coaching program as a
professional development strategy for improving student learning outcomes. It explores the
12
practice of teaching situated in a time and place, where a re-trained teacher is positioned with
them in a familiar role as a coach, as somebody who knows whilst others, notably the teachers
of mathematics in “non performing schools”, don’t.
Research questions
1. How can shared meaning be constructed between the coach and teachers?
2. What should pass as research in the phenomenological sociology of teaching and
learning?
The research context
Siskin (1994) observed that the subject department is typically the most important social and
political organisational unit in academic secondary schools. In her sociological study of subject
departments in “academic” secondary schools in the USA, Siskin argues mathematics is
distinguishable from other subject departments, in two particulars: mathematical knowledge is
conceived as cumulative and presented in a linear fashion from the simple to the complex, and
student achievement is regarded as a social index of intelligence and students are ranked in a
hierarchical order based on ability. Teachers that demonstrate the perceived subject-based
competency are positioned accordingly, often teaching at the senior end of the school.
Consistent with Siskin’s observations, inadequate professional development opportunities was a
concern for the teachers of mathematics in this study. Whilst Lambertia had a conventional
academic structure it had no staffroom arrangement for mathematics teachers. Mathematic
teachers at Lambertia whilst supporting each other demonstrated a resistance to the broader
curriculum direction the administration required. They saw this as impinging on their practice.
Grallina on the other hand had a cross-curricular emphasis and no mathematics staffroom.
Whilst experienced teachers at Grallina relied on broader collegiate relationships for assistance
the novice teachers welcomed the coach perhaps out of necessity to achieve the “security” and
opportunity for professional self “discovery” that the institutional order at Grallina did not
adequately afford. Teacher conversations were limited in both schools largely disengaging
teachers from opportunities to develop conceptual understanding of practice and professional
identity formation in the process.
13
Harré (2009) suggests that teaching mathematics can be explored as a conversational practice
where teachers share a social responsibility of promulgating the positive myth of mathematics
education with each other and their students. A myth in this curricular context, after Leonard
(1983), is not an untruth but rather a “known unknown” embodying the mystery of “good”
teaching, of “making a difference” and creating opportunities that afford students and teachers
reimagination of their everyday classroom experiences. Teachers in acting according to what it
meant to them to teach mathematics at Grallina or Lambertia enacted the “illusion” of the
existence of mathematics as a discipline discourse. A body of knowledge shared by teachers
represented in the flux of discursive practices, gave rise to the respective institutional structures
described differently in maths departments at each site. Teachers’ discursive practices were
studied for their “accounts” of their personal positioning, institutional practices and societal
rhetoric as mathematics teachers.
Acquiring teacher skills and knowledge
A report commissioned by the Australian Council of Deans of Science (Harris & Jensz, 2006)
found that state secondary schools are increasingly forced to deploy under-qualified teachers to
teach mathematics. The report found that one in twelve practicing maths teachers had studied
no mathematics at university. At least 45% of teachers of junior mathematics in Australia had
not studied mathematics to third year undergraduate university level (Harris & Jensz, 2006).
Green, Machin, Murphy and Zhu (2010) found that better academically qualified teachers who
had pedagogical training in their discipline were more likely to be employed in the private
school system. As can be seen in the biographical accounts, many of the mathematics teachers
who participated in this study were positioned out of necessity in their schools to teach maths
outside their field of expertise and without the necessary training in mathematical pedagogy.
This was problematic particularly amongst the novice teachers. For whilst they brought new
pedagogical principles and strategies from their teacher training program and were afforded a
more experienced colleague as “mentor” to assist them, learning to teach in these contexts was
not secured by “following rules”. Rather their teacher practice was shaped by local rules to
meet the specific local exigencies and contingencies of the classroom. An instructional
approach to the mandated curriculum emerged from private rather than resources shared among
the teachers in these schools. The narrative construction of teacher identity was strongly
embedded and embodied in duty and responsibility to get through the state mandated curriculum
in the time required, using limited resources against all student resistance and disinterest; a
14
storyline of self-justification, of honour against feelings of inevitable and perspectival failure.
In the face of concerns about the quality of mathematics teaching in state schools, the motive of
the DEECD’s (2010a) coaching program was to redefine classroom teaching in order to engage
students and improve learning outcomes. As Lambert (1990) a prominent mathematics educator
argues, teachers must redefine the meaning of knowing mathematics to challenge traditional
approaches to teaching. In her autobiographical study she challenged students in her class to
think mathematically to encourage and engage them to generate a strategy and argue for its
legitimacy, one where “the problem is not the question and the answer is not the solution”
(Lambert, 1990, p.40). The re-inventing of new types of teacher-student interaction requires
new ways of pedagogical thinking. This ontological redefinition of the meaning of mathematics
teaching was recognised as a key element of the coach’s agenda but established teachers
dismissed it as unreal or simply absurd, disempowering in the face of the existing specific local
exigencies and contingencies in their respective classrooms. The narrative reasoning required in
teaching mathematical modelling as Lambert (1990) argues is therefore subject to many
influences, where both formal and informal learning is required and where subjective constructs
are juxtaposed against professional expectations and standards. The processes involved in
constituting a different executive relationship between student, teacher and mathematical
knowledge were not expressed in any established teacher’s “account”.
Like Lambert (1990), Shulman & Shulman (2004) contend that teacher-education programs
should emphasise social mediation in the subject department that challenges traditional forms of
teaching and learning. They see the development of professional teaching skills or
mathematical reasoning as an individual learning process, enabled by a multitude of factors that
include: practical experience and participation in a community of practice, access to a vision of
the purpose of mathematics education, a philosophy of learning and teaching, and a positive
proactive view of teacher professional learning. The Regional Coach potentially offered such
access but her institutional positioning by teachers outside their local moral order blocked
access to her vision, training and experience in mathematics teaching.
Introduction to the theoretical framework
A teacher’s practice forms part of a repertoire that is representative of the teacher’s habitus
(after Bourdieu, 1977). The acts and actions (doings and sayings) of the teacher are socially
learned behaviours and dispositions acquired through professional training and everyday life in
15
schools, first as a student and then later as a teacher working in a subject department. A
teacher’s doings and sayings constitute the way in which they come to act intelligibly in
different circumstances. Segal (1998) argues teacher’s explicit beliefs and ideals are not
generated independently but strongly influenced by specific local exigencies and contingencies
of the classroom. Teacher identity is constituted in their doings and sayings shared everyday, in
part inherited from past practice, accountable in the local moral order in various discursive
circles in their school and recursively references the greater culture of what constitutes
mathematics education in the academic but more powerful social milieu of state schooling. The
teacher of mathematics is a social product of the dichotomous relationship of nurturance and
appraisal one weighted more recently by the latter to which the teacher of mathematics is
“thrown” into as well as a producer of that society (Segal, 1998).
Harré (1993) argues that the distinction between a “shame culture” and a “guilt culture” can be
used to identify emotional structures characteristic of a practical and expressive order (p. 202).
It is in this interplay, between the practical and the expressive where the public and collective
aspects of life are produced. Applying this to the institutional narrative of the “underperforming
school” causes anxiety and stress for it employs an underlying emotional structure of guilt or
shame as the basis of moral judgment. Teachers and the schools in which they teach in this
emotional system, formalized by the DEECD are found guilty of their indiscretion, of creating
failure, of “underperformance” and publically shamed through the publication of student
performance data. This temporal dimension illustrates a social psychology of the expressive
order one that is based on honour and morality, one that is compounded further for the specific
and local exigencies and contingencies of the classroom to which the teacher must respond
cannot be easily heard in “head office”. Yet for the classroom teacher to survive in the
classroom is to replace the curricular purpose with whatever it takes to maintain order, this is
the primary emotional universal teachers must attend to for it expresses an honourable position
with their colleagues in the subject department and with the broader school community. Segal
(1998) argues that in the face of classroom contingencies, teachers adopt an instrumentalist
approach to their teaching practice, one that does not express their beliefs about what good
teaching encompasses but rather one that allows them to maintain their appropriate place in the
local order of honour by coping with the situatedness of their position. Segal argues that this
somewhat disengaged instrumentalist approach has been arrived at as a consequence of being in
the world of the mathematics “classroom”. The exigencies and contingencies of “existence” in
the maths classroom can construct and reconstruct the habitus and teacher identity denying
ideals that constitute the “essence” of teaching mathematics.
16
Crossley (2001) argues that a teacher’s habitus is therefore an active biography of past actions
and practices that shape and reshapes their current perceptions and actions thereby contributing
to the social construction and reconstruction of their social world. In an analogy with playing a
game of chess, the player demonstrates competency through learnt dispositions, know how,
schemas and the like, all of which facilitates the competent pursuit of a specific goal acquired
from the structured social contexts of the past that comes to be realised tacitly. For the socially
isolated teachers their practice comes from the incorporated habits predisposing them to
continue with a particular form of practice thereby regenerating practice shaping teacher identity
in the process. Bentley (1987) argues human experience with objective constraints begins early
in life mediated by the adult world; rules of honour, sexual division of labour, language
learning… all of which provides the basis that constitutes tacit understanding of what comes to
be known as the grammar of life. Dispositions, Bentley further argues are inscribed through
specific and local exigencies and contingencies and can only be altered with great difficulty
through objective conditions and subsequent life experiences of the actor all of which generate
changes in the structure of the habitus. This all assumes that human actors act privately, have
no social agency to enact purposeful activity and are more or less ignorant of the forces that act
upon them, independent of what they may believe. Rather than subscribe to a socially
determinist individualist perspective, this theses is guided by Giddens (1984), Harvey (2002)
and others who address the duality of agency and structure as recursively related.
Giddens (1984) and Harvey (2002) argue that human actions take place in a continuity of time
and space and in the context of a pre-existing social structure. Accordingly, all human action is
partly predetermined given the rules at the time the action takes place. Rules are not concrete
but rather maintained and changed by human action through reflexive capacities of the human
actor in the continuity of their practice. Reflexivity in this study refers to the monitoring of the
ongoing purposeful social life of an actor who is able to recount and elaborate discursively the
embedded set of processes (routinization) used in a particular time and place. In doing so, the
teacher as social actor is provided with the necessary ontological security sustained through
daily activities of social life providing a sense of equilibrium in his / her waking life towards the
construction of a moral concern as a maths teacher. The practice theories of Bourdieu (1977),
Giddens (1984) and others present a response to the debate surrounding structure and agency in
the social sciences including education research, as well as attending to the problems as they
relate to the limitations of representational concepts of teacher knowledge and also to the way in
which individuals and organisations learn (Miettinen, 2006).
17
2
Discursive Practice; For, as, and of meaning making
“… practices are indissoluble blends of speech and action, what we can do is quite
tightly related to what sort of plans we can make, what sort of instructions we can give
ourselves and others, what sort of catalogues we have to hand, and so on.”
(Harré, 1997, p. 174)
Introduction
Coaching studied here is a centrally initiated approach to instructional improvement and can be
contrasted with another contemporary approach such as the Japanese peer based Lesson Study,
(Lewis, Perry, Murata, 2006) which has attracted local interest. This research employs a
discursive psychological approach to investigate teachers’ discursive practice in a coaching
program. Their discussion alludes to their social actions emanating from the interplay between
their agency and social structures that influence their practice. Agency and structure are
recursively related. It is argued that it is in the dynamic interface of private and public
discourses of teaching that teachers’ identities emerge through positions they and others take up
in the discourses of their professional practice. As social actors they are agents in a social and
cultural history in which they go about reproducing or transforming their social world in
everyday discursive practice. The social order of mathematics teaching in the two study schools
that is investigated here is achieved through teacher use of a catalogue of tools, artefacts and
signs that are inscribed with meaning that assist them to navigate and negotiate change,
maintaining and transforming institutional structures in the process. This, it is argued can be
explored primarily through studying an actor’s discursive practice, their discursive positioning
in working day conversations, institutional practices and societal rhetoric. The focus of this
research was to gain a better understanding of teachers’ social order and identity formation in
the context of attempted institutional change in mathematics teaching.
18
Purpose and approach to the study
This study explores the discursive practices of secondary school teachers of mathematics
participating in a government programme to enhance the organisational capacity of teachers to
achieve cognitive academic targets in their mathematics classes. In doing so the study explores
how teachers may move from receiving “good advice” to a committed grammar. This literature
review firstly locates coaching as an on-site professional development program in the existential
context of mathematics teaching. A critical realist portrayal of the attempt to transform the
behaviour of the targeted teachers requires their accounts of the social ontological relations
between the actualities of agency and possibilities in structures in their particular communities
of practice. This microanalysis of the process of personal professional identity formation in
teachers’ discursive practice is skeptically opposed to the view that behavioural change can be
studied as somehow naturally flowing from the application of a particular social stimulus. After
Miettinen (2006), Deweyan pragmatism and Vygotsky’s activity theory are in this study
synthesized within current practice theory to illuminate the discursive signing acts and actions
of secondary school teachers of mathematics as they interact with a coach within the local moral
order of their practice communities. Positioning theory developed by Harré and Van
Langenhove (1999) together with Peirce’s theory of signs are both used as analytical tools in
this discursive psychological study. Both allowed the researcher to locate the teacher within his
or her own storyline illuminating processes of professional identity formation.
The social milieu: The institutional paradigm of professional development
A dominant organisational learning paradigm has drawn upon the corporate world and assumes
that with external accountability comes a corresponding improvement in student achievement
(Newman, King & Rigdon, 1997). Current policies of educational reform have increased
pressure on schools to account for student outcomes against mandated standards. Education
policy directed from the centre shifts accountability to the school level, the place where
education is delivered and where school personnel are appraised. The Victorian government
schools in this study are accountable for student achievement on periodic numeracy and literacy
tests throughout the compulsory years of schooling as are schools in other jurisdictions in
Australia and elsewhere around the world. Data collected from the school site brings public
rewards for success, and state intervention in those schools that consistently underperform
(Ablemann and Elmore, 1999). Early research on systematic reform of teacher practice
articulates a leadership driven professional development approach based on an assumption of
19
inadequate and ineffectual middle level leadership in regard to teaching and learning strategies
in some subject departments (Siskin, 1994). Education policies that attend to aging
organisational capacities in schools have seen the introduction of an intervention strategy
amongst others that comes in the form of a coach or surrogate leader.
The coach embodies the state’s on-site professional development program; a program aimed at
transforming the local culture of failure. This is primarily achieved with the use of state
comparative school data (“league tables”) that is used to justify the introduction of a new
teaching regime in the form of an emergent storyline introduced by the coach. The professional
development of the mathematics teacher is designed within social rules defined by the needs of
all schools to improve student attainment in mathematics, that is, a new actor is invited onto the
school stage in the form of a coach to help the mathematics teachers meet new state policy
settings for the school.
Professional development as a constitutive process for change
Professional development is conventionally viewed as crucial in promoting change in teacher
behaviours (Guskey, 1994). Teacher professional development up until recently has largely
consisted of attending a workshop, usually with teachers from other schools and away from
their classroom or school site. Whilst this has cost effective features, it is now regarded as
relatively ineffective as the sole means of delivering professional development (Forbes, as cited
in Lindimore, 2006). Guskey also argues that it is ineffectual because it doesn’t recognise the
significance of context that is internal to a school structure. Whilst Gusky and others perceive
these structures as relatively determinative, Shulman (1986) and Siskin (1994) argue for the
significance of practice cultures of subject departments and specialised teacher-content
knowledge. Whilst Samantha the Regional Coach coach in this study is a skilled and
experienced teacher and further trained in subject content knowledge, new theories of teaching
and learning in mathematics, and works along-side teachers in context (on-site) to effect change,
the coach is expected to educate each teacher towards a new commitment to changing their
habituated practices. Darling-Hammond and McLaughlin (1995) support, in principle, coaching
programs on the grounds that they can teach and serve the need to strengthen existing skills in
experienced teachers while developing and transferring new skills into classroom practice.
Teachers may then benefit from working alongside a coach who may draw from a number of
coaching models as presented by Knight (2008) to improve teacher practice.
20
Coaching as a policy model for transforming teaching practice
The idea of a coach references images of a sporting coach, a “life” coach or even a leadership
coach. The sign of a coach indexes
“… a commitment to improve, a coach who observes and interprets the
learner’s knowledge and abilities at any time, who makes adjustments to the
teaching at any time and who provides feedback that encourages the learner to
continually strive for higher goals or levels of achievement” (Munro, 1999,
p.2).
A coach is this and more. A coach is a person who has skills and knowledge, is able to
articulate those skills and consequently viewed by others as the one that knows, whilst others
don’t. In schools there are a number of such “roles”. For example, a student welfare counselor
is positioned to deal with teenage issues; a career counselor is positioned as one who introduces
students to the range of post-secondary vocational options…. While the role, duties,
responsibility and hence identity of a school’s student welfare and career counselor have long
been established, created by others before them as with all the other positions of responsibility,
the coaching “role” researched here facilitates a new form of teacher development. Teacher
development as funded directly from government as a form of emergency service in poorly
performing schools by reforming and supplementing established instructional approaches to
teaching and learning in those schools.
It follows that the role of the coach in the DEECD paradigm of educational reform may be
viewed as a “change agent” tied to performance improvement, indexed to student achievement
policy measures. The policy may be criticized as identifying the teacher as a passive learner or
patient in the process of educational reform. The treatment comes in the form of a coach armed
with embodied attributes in subject knowledge and professional skills that will improve
mathematics-teaching practice. While the impulse to effect or mediate change comes in the
form of data, where data “shows” that something has to be done and that doing something to
improve the data is necessary and urgent; support materials, packages of recommended practice
have also been developed by the DEECD to support change. One recommended practice is to
employ the online materials. First amongst these is the Mathematics Developmental Continuum
P-10 (DEECD, 2006). The Continuum is a tool developed to equip the individual teacher with
21
substantive skills in introducing, diagnosing and treating student difficulties in teaching each
topic in the state’s school mathematics curriculum.
“The Mathematics Developmental Continuum P-10 provides evidence based
indicators of progress, linked to powerful teaching strategies, aligned to the
progression points and the standards for the Mathematics Domain of the
Victorian Essential Learning Standards.
Indicators of progress are points on the learning continuum that highlight
critical understandings required by students in order to progress through the
standards.
The Mathematics Developmental Continuum P – 10 will assist teachers to:
• deepen understandings of the Mathematics domain,
• enhance teaching skills to enable purposeful teaching,
• identify the range of student learning levels within their Mathematics
classes,
• monitor individual student progress towards achievement of the
Victorian Essential Learning Standards in Mathematics, and
• develop a shared language to describe and discuss student progress.”
(DEECD, 2006).
Whilst applying a treatment in the form of the Mathematics Developmental Continuum P-10 by
the coach forms part of the role of the coach here, exploring a teacher’s position within a subject
department, on the other hand, in the way that it is shaped and defined by relationships with
students and colleagues remains unexamined by researchers and policy makers alike. The
subject department, Siskin (1994) contends is often the most significant organisational unit in
the work of secondary schools following an academic curriculum. In the absence of effective
collegial relations, teachers are immersed in a persistent culture of privacy. Capobianco (1994)
suggests isolation protects teachers from judgment and criticism where on-job learning is
primarily achieved through trial and error from a tradition of teacher autonomy and as a result
change whilst not impossible is difficult to enact. He observes the private practice of teaching is
“professionally” embedded into all aspects of education and any movement is viewed as
problematic. For example, having to work with a coach could likely be taken to be a public
judgment that a teacher’s performance is deficient and a sign of incompetence. Another
challenge faced by teachers and coaches alike is the stance taken by each with respect to
22
teaching and learning practices. Boxley (2006) argues that if viewpoints are too far apart
openness to suggestions through professional dialogue and a willingness to take a risk may be
thwarted, placing more pressure on the pedagogical knowledge and interpersonal skills of the
coach, which in turn may affect the relationship. A final concern is that teacher resistance may
emerge to being coached, where there is a lack of time (funding) to develop supportive
relationships, where coaches who do not allow mistakes or suggest quick solutions that do not
fix complex situations, and of personal problems that remain unexamined (Levinson, 1996).
This research does not approach structural intervention in the form of the coach and the
epistemic authority and agency of the mathematics teachers as separate but rather treats the
unresolved dualism of structure and agency in their interaction as one of theoretical and
professional interest. To this end another well-documented model of school-based professional
development is presented to clarify features of the coaching model studied in this research.
The Japanese Lesson Study: A narrative constitutive model of professional
development
A professional development that claims to value teachers and teaching is outlined in Figure 1. It
is known as the Lesson Study (APEC, 2009). The Lesson Study has operated in Japanese
elementary schools for the past century and appears to embody features that some researchers
have come to realise as effective in changing teacher practice. The Lesson Study uses concrete
materials to focus on a particular area of study taking into account contexts of teaching and the
experiences of teachers and operates within a collegiate network of support. In doing so, the
Lesson Study avoids many features noted as shortcomings in the dominant professional
development paradigm that operates in Victorian schools, shortcomings that are “… short-term,
fragmented, externally administered, and insensitive to the local context and individual needs of
teachers” (APEC, 2009).
23
While the Japanese Lesson Study model harnesses local organizational capacity and resources,
the coach offers external incentives and expertise. Both models assume the strength of the
other. The first essentially embraces a societal ontology while the latter operates as an
individualist ontology. The teachers in this study work in schools where they probably feel they
could assume the worst of both professional development models; humiliating individual
professional redemption as teachers of mathematics through a coach from “head-office” and
unresourced and poorly coordinated collective self-help. This embodiment of pre-existing
“realities” stultifies rather than liberates teacher agency. The person of the mathematics teacher
operates within a community of practice that is structurally constricted and historically set, as
“the way things are done around here.” Postill (2008) observes that this forms the accepted way
in which the agent operates for it coordinates what is intelligible and warrantable and becomes
permanently internalized as the social order in the personal identity of the teacher.
1. STUDY CURRICULUM & FORMULATE GOALS
Consider long-term goals for student learning and development. Study curriculum and standards, identify topic of interest.
4. REFLECT
Formal lesson colloquium in which observers:
• Share data from lesson • Use the data to illuminate
student learning, disciplinary content, lesson and unit design, and broader issues in teaching-learning
Documentation that consolidates and carries forward new learning. A new set of questions posed for the next cycle of the Lesson Study.
Figure 1. Lesson Study cycle (Lewis, Perry, Murata, 2006, p. 4)
3. CONDUCT RESEARCH
Consider long-term goals for student learning and development. Study curriculum and standards, identify topic of interest.
2. PLAN
Select or revise research lesson
Write instruction plan that includes:
• Long-term goals • Anticipated student
thinking • Data collection plan • Model of learning trajectory • Rationale for chosen
approach
24
The situational grammar of professional identity formation
Gee (2000-2001) defines identity as “being recognized as a certain ‘kind of person’ in a given
context… [where]… all people have multiple identities connected not to their ‘internal states’
but to their performance in society” (p. 99). For example, a teacher of mathematics
demonstrates an identity in their classroom through how they position themselves and are
positioned psychologically, socially and social psychologically by students, curriculum, other
teachers, and parents. All of which makes an impact on a social actor’s identity. As Garvais
and Jovchelovitch put it,
“[t]he sense of oneself and the sense of belonging to a collective are both
shaped by the knowledge, traditions, values and practices one shares with
members of [different] communit[ies]” (as cited in Howarth, 2001, p.231).
Identity is what makes us who we believe we are, makes us individual and gives us a sense that
we are different to others. Mead (1934) and Davies (1989) argue that identities are constituted
and reconstituted through “I / Me” discursive practices in which we find ourselves and
participate in. For whilst an individual may feel that they alone contribute to their identity
formation the respective communities to which they aspire socially shape their identity. Identity
therefore is neither static nor determinate, but rather responsive to the many discourses open for
the social actor to engage in. Identity is thus “… an evolving nexus, a moving intersection of
the inner and outer forces that make me who I am” (Palmer, 1998, p. 13).
This dynamic interface Davies and Harré (1990) argue between the private and the public
psychological space is evident during episodes of social interaction. It is here where an
individual expresses or hides aspects of their identity in line with what is warrantable and
normative behaviour in a sociohistorical context. Unlike a theatre performer who has
memorized their lines to a familiar script they have performed a number of times over, a social
actor is presented in every day conversations with a narrative universe in which they respond by
evoking different narrative forms expressed through internal dialogue. This dialogue brings to
the fore elements of their biography encapsulated as symbolic representations of past and
present experiences. Identity is therefore a narrative social position or positions that an
individual chooses to accept or reject in a particular sociohistorical moment. In this way, a
teacher positions themselves within the local moral order defining who they are through the way
in which they orientate themselves to their work as expressed in the justificatory “accounts”
they provide.
25
Figure 2 schematizes the social construction of professional identity formation and restructuring
of the subject department as a prospective interactive process between the private and public
domains of discursive practices. This process is not assumed to be linear and will not follow the
sequence outlined in the schema if there is no sustained local conversation about teaching
practice. Whilst entry is at any point, I commence with the top left quadrant where a teacher as
a member of a community of practice is afforded an opportunity through a semiotically
mediated social process to share their narrative of practice in a public forum. Their narrative of
practice is an expression of their consciousness, that is, “… the subjective reflection of material
reality by animate matter” and as such reveals their intentionality and their position as a teacher
within the local moral order of the subject department (Wertsch, 1985, p. 187). This public
accounting encourages teachers to share their teaching practice, the aim of their labour that their
respective efforts are directed towards. Wertsch suggests that teacher’s professional identity is
revealed in their disclosure of the range of psychological tools and social relations used to enact
everyday tasks. In this way, an individual achieves a higher mental function as a product of
recasting their professional identity (1985).
Figure 2. The discursive psychological model of professional identity formation and concurrent reform of organisational structures proposed in this study after Harré (1993)
MANIFESTATION
Public (Subject department)
Collective Accountive Individual
TRANSFORMATION
Private (A teacher’s own life space)
Presentation
Public stance taken by a teacher in conversation with colleagues.
Conventionalization
Conventionalization of public stance and acceptance and inclusion in conversation among teachers in their “role” as teachers and later as colleagues in conversation.
Appropriation of cultural elements
Elements of conversations with colleagues or significant other(s) in the subject department; private coherence of practice.
Internalization
Individual constructs of personal schema. Process of gaining control over external sign forms.
26
An example by which a mathematics teacher takes a public stance allowing for the presentation
of students’ work for discussion in the subject department may commence with the utterance
“My kids just don’t get algebra, I’ve tried everything and they just don’t get it”. The ensuing
publication of artefacts in this way invites members of the subject department in their “role” as
teachers to socially reconstruct teaching practice that is perhaps later incorporated into
conversations with each other. The publication of a teacher’s “speaking personality”, “speaking
consciousness” is not an outright transferral of what was once a privately held belief about
teaching into one that is now accepted collectively. Rather, it is through conversation that the
community comes to conventionalize ideas of teaching practice. Taking a public stance in this
way assists teachers to gain control over and mastery of external sign forms. This is primarily
achieved through the dialogical organisation of questions and answers that semiotically
mediates access to a higher mental function both for the individual and for the community of
practice. The process allows an individual engaged in discourse to internalize higher mental
processes that involve the transformation of social phenomena into individual psychological
phenomena as expressed through an inner voice. Consciousness is therefore a product of
dialectic, it is not a direct transferral, but a process where the internal plane is formed and
reformed through semiotic mediation. In taking a public stance, participants present their
improved self-positioning inviting others in the community of practice to challenge their own.
This public accounting introduces a committed grammar that shapes the habits of mind, as well
as reshaping personal professional identity. The schema above illustrates how cultural elements
in a subject department and in a school may be formed at the interface of public and private
domains reshaping not only the identity of participants but also the subject department as a
community of practice.
Davies and Harré (1990) argue, “… what individuals do publicly and privately is intentional
[and] what individuals are to themselves and [to] others is a result of interpersonal interactions
developed over a lifetime [of commitment to shared problem solving].” (as cited in Phillips,
Fawns & Hayes 2002, p.243). Individuals’ construct and reconstruct their social reality,
consciously and unconsciously in episodes of discourses and is reflective of an agent’s
biographical journey. It is in conversation, Harré and Van Langenhove (1999) content those
interpersonal relations and belief systems framed within stable institutional narratives guide
human social and psychological phenomena (as cited in Phillips, Fawns & Hayes, 2002). They
argue private and communal thinking bring change as represented by actions first, followed by
discussion of improvement to practice. A social actor’s identity is first formed in the social,
through conversations with others and strengthened reflexively with internal dialogue in
discursive circles. It is here where a moral sense is recognised and maintained by way of
27
agreement and or struggle for this provides a framework that encourages practice grounded in a
sense of authenticity (Bullough, 2005). Analogous in some way to a game of chess, that is,
whilst actors must accept the rules by which the game is played out, an actor can produce
creative agential performances that emerge from the practice of play. In doing so, each player is
positioned and positions the other. It is in this way, through the recursive nature of structure
and agency that identity emerges from a dialectical interplay, where new practices emerge. This
is depended upon the tacit acquisition of the principles of the “game” and the effortless
performance of rule following without recognition that rules are actually being followed
(Mutch, 2004). The concurrent identity formation and organisational restructuring in a subject
department is therefore an ethogenic process mediated by artefacts developed for the
improvement of practice. In addition, a significant other who leads this must not only be
granted moral authority by the group but must also have the moral capacity to position others in
the local moral order.
The coach as a significant other in institutional and constitutive discourse circles provide the
necessary impetus for building a sense of community that promotes a commitment to the
program of pedagogical reform. Bullough (2005) argues that teacher self-knowledge about
being a teacher and of teaching mathematics in this study is not only important to their
professional identity formation but also important in relation to the educational outcomes of
students. It is in this context, that identity as an analytic tool, may afford an understanding of
how a subject department functions through the way in which individuals act out and recognize
certain identities in context (Gee, 2000-2001). Gee summarizes four identities outlined in Table
1 (2000-2001, pp. 100-101) to show how the study of identity may assist and is associated in the
discursive exploration of educational theory and practice.
Insight into the conversational processes of identity formation is likely to be important in
negotiating among coaches, mentors, and colleagues shared meanings constitutive of a
situational grammar in the local moral order of improving practice. In recognizing and
responding to the acts and actions of a maths teaching colleague with the performance as a
certain “kind of agency” or of different “kinds” of agency, others may influence personal
identity reformation in the reflexive moment. Bullough (2005) applies Gee’s (2000-2001)
identity construct to explore how a teacher may progress from one identity to that of another. In
doing so, he argues for the importance of attending to teacher identity formation through
“structural collaboration” in a subject department as a community of practice. For as Gee
argues,
28
“… identity formation is not a passive but a dynamic affair, that involves a
giving and a withholding which simultaneously alters oneself and one’s context,
with the result that alternative identities may form… by which an individual
confirms or problematizes who she/he is/becomes” (2005, p. 146).
A “community of practice” here provides an emotional space, a nurturing environment of risk
taking. For it is only in such an environment of positive emotional support and social
influences where an individual may have their identity and the identity of their respective
community of practice reshaped by a significant other. The schema as presented in Figure 2
above perhaps best demonstrates this possibility.
Process Power Source of power
Nature-Identity “[W]hat we are primarily because of our ‘natures’”, that is, a state of being that is not chosen. For example, being a tall person.
developed from
forces
in nature
Institutional-Identity Sustained in institutional discourse circles “[W]hat we are primarily because of the positions we occupy in society”. For example, a teacher acts in accordance to rights, duties and obligations as outlined in legislation….
authorized by
authorities
within the school or government school system
Discourse-Identity Developed in the conversational moment at the intersection of purpose and necessity “[W]hat we are primarily because of our individual accomplishments as they are interactionally recognized by others”. For example, an individual responds accordingly to another’s disposition or agency.
recognised in
the discourse / dialogue
among colleagues in the hiatus between institutional and constitutive orders of the school
Affinity-Identity Sustained in a constitutive discursive circle “[W]hat we are because of the experiences we have had within certain sorts of ‘affinity groups’”. For example, a person joins a community of practice and as such is recognised by others outside of this group as a certain kind of person.
shared in
the practice
of “affinity groups” that are project based, e.g., a Lesson Study group in the maths department
Table 1. Teacher identity formation after Gee (2000-2001)
29
Organisational learning and the ideal world of the Lesson Study in a community of
practice
The cognitive and cultural practice that promotes organisational learning, as embodied in the
Lesson Study program, may be viewed through the paradigm of a community of practice. The
cognitive perspective is one approach to organizational learning. This perspective takes
organisational learning to be a cognitive activity (Cook & Yanow, 1996). The assumption is
that organisations learn in the same way an individual learns and therefore the results of
organisational action are representative of how individuals learn. This cultural perspective, on
the other hand, postulates that when a group of individuals act collectively, learning takes place,
since shared practice involves shared meaning as represented in shared cultural artefacts and
therefore an activity of the organisation rather than that of the individual. The cultural
perspective on organisational learning does not rest with the individual but is reflected through a
group of individuals working collaboratively as a community of practice. Easterby-Smith &
Lyles (2003) understands organisational learning as the acquisition, conversion, and creation of
knowledge aimed at facilitating the attainment of organisational goals. Argyris and Schön
(1996) argue that an organisation comprises a collective of individuals whose behaviour is
governed by often-implicit rules, that is, the recognizable collective is politically formed and
therefore organised to act. The rules govern the myriad acts of engagement that forms a
cooperative system. When individuals come together to act, based on the operating rules, then
it could be said that they are learning both on an individual level and also at an organisational
level. For example, an individual learns when she / he engages in a form of inquiry, that is, a
rational and controllable process, and as a result there is an outcome, the outcome could be as
simple as acquiring new information on behalf of the organization.
A community of practice concerned with social learning and knowledge generation expressed in
the way in which it shares historical and social-cultural artefacts. In this sense participants in a
community of practice will not only draw from physical artefacts, such as, paper, pencils,
computer… to complete a task or find a solution to a problem but also draw on the
competencies of others both within and outside of their immediate work environment, without
realizing that they do so (Sole & Edmonson, 2002; Brown & Duguid, 1991). The Lesson Study
can be seen to afford exploration of teachers’ tacit knowledge through shared activity to
uncover elements of practice that improves teaching for all members of a community of
practice. Advocates argue this is achieved when shared practices and competencies held by
community members are recast either consciously or unconsciously to represent a constitutive
approach to organisational learning. Shared activity also relies on shared artefacts. Moreland
30
(1999) and Wenger (1998) argue that denied access is a denial of pedagogical knowledge and
therefore denied an opportunity to learn. Access to the community of practice and to a full
range of resources facilitates development of “transactive memory”, or knowledge of what
others know. This transactive, trusting turn-taking knowledge is what Rawls (2011) argues
constitutes shared social meaning and a constitutive order of practice.
This concept of “transactive memory” is employed in Lave’s case study of the Yukatec Mayan
midwives (as cited in Resnick, Levine, & Teasley (Eds.), 1991). The case study describes the
Yukatec apprenticeship in midwifery and shows how learning in practice takes place as it
socializes change in behaviour and in identity to enable participants to become full members of
a community of midwives. Jordan (1989) argues that learning is given a structure through
participation in an ongoing activity one where participants are made aware of the existence of
what is to be learned and secondly, where learning, that is, knowledge and skill is improvised in
practice. Whilst the disposition to want to learn is important there is no one individual that is
responsible for inculcating knowledge and skill into a community of newcomers, but rather, it is
this cultural perspective of situated learning that “invites” new and existing members to
participate. Resnick, Levine, & Teasley (Eds.) (1991), conclude that learning takes shape
through participation in a community that not only has a shared broad repertoire as expressed
through a history but is also guided by the older members of the community.
Cook and Yanow (1996) view the learning of teachers and students as situated in a social,
historical and cultural context. Learning from this perspective takes place as a consequence of a
community of individuals acting collectively. The community functions, mediated by a culture
of story telling to share stories both from within and from outside of the group to deal with a
problem that the current espoused theory cannot. This view characterizes the socio-cultural
perspective of organisational learning as a collective situated activity rather than one where an
individual can learn for the entire organization. This socio-cultural perspective stresses the
construction and reconstruction of reality through tacit knowledge, identity formation and
shared meaning. These are the ways in which organisational learning is created, sustained and
changed. Values, beliefs and feelings are transmitted to new members using cultural artefacts
such as metaphors, ceremonies, stories, language…. In the case of the Lesson Study, teachers
are assumed to be “… persons-in-the world participating in the practices of a socio-cultural
community” (Haneda, 2006, p. 808). Lave and Wenger (1991) describe this view of learning as
“legitimate peripheral participation”. They describe engagement in social practice as entailing
learning as an integral constituent. Newcomers to teaching acquire skills by engaging in the
practice both in and outside of the classroom moving from novice to expert as knowledge and
31
skills are mastered particular to the community of practice. Learning and identity formation
come from an individual’s “legitimate peripheral participation” through their membership in a
community of practice, rather than from an individual’s cognitive conceptualization of learning
as an individual achievement. Learning based on “legitimate peripheral participation” involves
becoming an insider, enculturated, immersed in a culture behaving as one would as a member of
a community. Brown & Duguid (1991) argue that because learning is socially mediated and
locates knowledge in the context in which it has meaning, it is therefore built out of materials at
hand and related to structuring resources of prevailing conditions of the space, time and place.
This socio-cultural approach in a community of practice captures both how individuals learn
and how organisations learn. Weick & Westley further contend that
“… cultural artefacts and practices preserve past learning; cultural awareness
and criticism may provide occasion for cultural change; organisations have
multiple cultures which allows for ongoing comparison and review of what any
one culture fails to see; and culture underscores that the object of mass learning
is intersubjective meaning.” (as cited in Bood, 2001, p.84).
From the socio-cultural perspective, it is this intersubjectivity, this common understanding
between individuals that opens the path to describe how an organisation learns. A community
of practice engaged in the Lesson Study notionally demonstrates how organizational learning is
achieved through a shared cultural perspective.
Advocates argue that the Lesson Study as a professional development model achieves this
intersubjectivity as a system of socially shared cognition. Evers & Lakomski (2000) see, the
Lesson Study group as a cognitive entity that operates in a culturally mediated process to
distribute and process information using multiple strategies. Whilst the Lesson Study embodies
the structures that allows for communal participation, each individual teacher that attends the
Lesson Study brings with them a different way of thinking reflected through a cultural paradigm
linked to their biography. Intersubjectivity is mediated through communal dialogue. It is
through discourse that teachers reconcile cognitive differences through a social sense of
belonging to a community of like-minded individuals who share the same cultural concerns.
They argue that participants in a Lesson Study may neutralize any sense of bias, self-promotion
or self justification that arises in the dialectical discourse of inquiry as in step 4 in Figure 1
above, thereby making a decentralized approach to professional development preferable to one
that is hierarchically managed.
32
This individually decentralized feature is a social constructivist view of knowledge and
cognition as represented in the cultural historical work of Vygotsky (1978). Vygotsky (1978)
describes knowledge as something that is not passed from one person to another but constructed
through collaborative efforts with either a common objective or by means of a dialogical
dialectical process undertaken through a discourse community. Knowledge in this sense is
distributed / diffused in three forms. There is explicit knowledge in the form of espoused
theory, there is tacit knowledge, that is, knowledge that cannot be readily articulated but rather
understood in an intuitive sense, and finally there is knowledge that is embedded in practice.
Hutchins & Klausen argue that if knowledge is distributed then cognition must also be
distributed for cognition relies on distributed access to not only information but also shared
understanding amongst participants (as cited in Plaskoff, 2003).
From Plaskoff’s (2003) and Bruner’s (1986) perspective a community of practice that utilizes
the Lesson Structure approach, operates as a cognitive space. Harré and Van Langhove (1999)
would see this cognitive space as a normative or moral space. It is within this cognitive space
that individuals share and shape their environment. It is in this normative space of “good
mathematics teaching” that an individual’s cognitive capacity comes into play using cognitive
artefacts (strategies, tactics, texts, lesson structures, test results…) both past and present. It is
through a process of inquiry that an individual can reconcile doubt, correct error… to solve a
problem. Garbis & Artman (1998) argue an individual recognizes artefacts as embodied
systems; “neuronal” systems that exist outside of the immediate cognitive head of an individual,
analogous to a nebulous constellation floating freely occasionally bumping into and shaping not
only their own cognitive identity but also that of others in a never-ending pattern. This
speculation drawn from cognitive science imagines an intricate multi-dimensional network of
cognition that is coordinated through a socio-cultural system. The positive influence of socio-
cultural capacities in the ideal world framed by the Lesson Study model may equally produce
the negative outcomes that should be expected where such capacities are absent. The current
study commences from the critical social realist assumptions of Bhaskar (1989) and Harré
(1993) that local structure and agency should be conceived as mutually constructed and
teachers’ everyday discursive practices afford an explanation of the social orders that influence
their social actions.
The two contemporary models of school based professional development, the Coach and the
Lesson Study introduced above are characterized respectively as a “top down” entity in the
institutional order and “bottom up” entity in the constitutive order, however, such
characterizations of power relations are grossly simplistic. The agency-structure dualism has to
33
be transcended to liberate agency from the constrictions of structure without being drawn into
methodological individualism. Bhaskar (1994) usefully brings the two together offering a
transformational model of social action that provides a more robust theoretical platform for the
concurrent transformation of teacher identity and social organisation in schools.
Towards a model of coaching as a transformational discourse
Bhaskar (1994) asks whether there is in fact a “law” of society and of human behaviour?
“Critical naturalism”, Bhaskar’s response to this question espouses the “… self-determining
moment of human agency and the irreducibility of social institutions” (Harvey, 2002, p. 166).
Harvey shows how Bhaskar brings together sociologies as represented by the work of Max
Weber, Emile Durkheim and Peter Berger in formalizing a schema that describes both how
social objects are the result of human behaviour and how social objects have a life of their own,
external to and coercing the individual. On the left side of Figure 3 we find the irreducible triad
of “Underperforming” School 1 ⇒ Socialization ⇒ Individual, where on the right side we find
the reverse of Emile Durkheim’s sociology represented as Individual ⇒ Reproduction /
Transformation ⇒ “Performing” School 2 (Harvey, 2002, p. 167). Whilst the arrows represent
causal flow, the dashed lines that connect the two sociologies suggest that “Society creates
Man” and also that “Man creates Society”. This dialectically structured model of production
and reproduction is captured as a sociological whole and is social constructionist in form.
Figure 3. Transformational model of social activity / person connection, after Harvey (2002) and Bhaskar (1994)
“UNDERPERFORMING”
SCHOOL 1
“PERFORMING”
SCHOOL 2
SOCIALIZATION
INDIVIDUAL TEACHER
REPRODUCTION
OR TRANSFORMATION
INDIVIDUAL TEACHER
34
Harvey’s transformational model of social activity after Bhaskar can be applied to the social
episode of coaching. Figure 3 is a representation for identifying societal reproduction in both its
reproductive and transformational moment. To this, Bhaskar introduces the concepts of human
agency and social structure to the debate where structure and agency are dialectically entwined
to form the coaching episode (Harvey, 2002). For as Bhaskar argues,
“[s]ociety is… both the condition and outcome of human agency… and human
agency both the production and reproduction (or transformation) of society (the
duality of agency)…. At the heart of this conception of…[agency as material
causation]… is the idea of human agency or praxis as transformative negation
of the given (think of cooking a meal, mending a bike); and at the same time as
both enabled and constrained by and reproductive or transformative of the very
conditions of praxis, so that these conditions are activity-dependent or
autopoietic, conceptualized (concept-dependent but not concept exhausted) and
geo-historically dependent (and thus themselves possible objects of
transformation)” (Bhaskar, 1994, pp. 92-93).
Social life therefore does not exist in isolation but rather exists as part of a network of Marxist
social relations mediated by what Bhaskar (1994) calls positioned-practice which provides for
the dialectical linkage between agency and structure (Harvey, 2002). Bhaskar’s (1994)
representation in Figure 4 causally connects the two halves as mediated by “istory”, that is, the
personal story provided by a teacher of mathematics about themselves with respect to being
coached, and “biography”. The schema shows an irreversible timeline that demonstrates how
individual behaviour is constantly renewed through a social psychology of ongoing and ever-
present social pressures (Harvey, 2002). According to Figure 4 a teacher’s biographical self-
identity shifts from one moment (T1 = Time 1) to another moment (T2). Similarly, the subscript
notation used for society also denotes a shift in a historically evolutionary moment. The TMSA
is now a representation of an “…irreversible historical flow of material processes and
institutional shifts” (Harvey, 2002, p. 178). This may also be represented diagrammatically as
in Figure 5 where individuals are interconnected to each other in a subject department as a
community of practice. This single strand is that of the subject department (routine) and comes
to represent the tacit and ever-present knowledge / practice of what comes to be known
collectively as intelligible and warrantable mathematics teaching moving inexorably through
time and space (noted as moving from T1 to T2) occasionally bumping into formal systemic
directives such as with the case of the coach program, off site workshops conferences and the
like.
35
It is Bhaskar’s philosophical conception of transformational social action that Harvey (2002)
argues should be further examined through a social psychological lens in order to illuminate
how human agency develops within the interactional nexus prevalent in a community of
practice. Harvey (2002) provides a social psychological rendering of the TMSA by
Figure 4. Transformational model emphasizing a historical rhythm and the agent dependent nature of the social transformation process after Harvey (2002) and Bhaskar (1994)
“UNDERPERFORMING” SCHOOL
T1 ISTORY
“PERFORMING” SCHOOL T2
SOCIAL REPRODUCTION OR TRANSFORMATION
SOCIALIZATION AND
SOCIAL CONTROL
TEACHER T1 AS PRODUCT OF
SOCIAL INTERACTION BIOGRAPHY
TEACHER T2 AS SOCIALLY LOCATED AUTONOMOUS AGENT
Figure 5. Transformational model emphasizing time dependence in a community of practice
T2
Subject department T1 T2
Individual
Community of practice
T1
36
incorporating the idea of the dialectic of self-cultivation as proposed by Georg Simmel (1968).
The dialectic of self-cultivation casts light on how an actor appropriates various cultural
artefacts / symbolic representations that afford her / him an opportunity to achieve a position
within the local moral order of the subject department. It is in the subject department as a
community of practice where teachers of mathematics, unless otherwise challenged by means of
conversational transactions, produce and reproduce mathematics teaching that remains
relatively unchanged. For the subject department is where teacher agency operates from, where
social identity is formed and mediating artefacts / symbols are located in order to effect the
production and reproduction of a particular social reality. A coaching program, as a social
relationship may have the capacity, through conversation to promulgate through practical and
symbolic representations an imaginative world-view that may present unrealized aspects of a
teacher’s personal or professional life, casting an ontological light on the world of possibilities.
A social relationship led by a significant other who has both the moral authority and capacity
bestowed upon them by the community of practice is important to the improvement of practice
(Harvey, 2002). Harvey suggests this aspect is represented as a nexus at the centre of Figure 6
where the dialectics of self-cultivation, history, currently accessible resources, and biography
interact in the context of a community of maths teachers in a subject department as a
community of practice (2002). In terms of causal powers Harvey argues that the critical realist
model
Figure 6. Transformational model of social activity in the coaching episode using Simmel’s (1968) account of human agency as mutual self-cultivation and cultural production in a community context after Harvey (2002) and Bhaskar (1994).
“UNDERPERFORMING” SCHOOL T1
SOCIALIZATION AND SOCIAL CONTROL
TEACHER AS PRODUCT OF SOCIAL
INTERACTION
“PERFORMING” SCHOOL T2
SOCIAL REPRODUCTION OR TRANSFORMATION
TEACHER AGENCY: THE SELF-
CULTIVATED EXPRESSION OF
COMMUNAL POWERS
HISTORICALLY ACCESSIBLE
CULTURAL FORMS
ACTUAL OR ANTICIPATED MEMBERSHIP IN A CONCRETE
COMMUNITY
DIALECTICS OF CULTURAL
REPRODUCTION AND SELF-CULTIVATION
37
“[t]he community is both the ever present condition (material cause) and the
continually reproduced outcome of self-cultivation (efficient cause), just as self-
cultivation is both the conscious production of self and the reproduction of the
communal conditions of future self-production” (2002, p. 188).
Recapitulating, the process ontology of personal identity formation of the mathematics teacher
in social episodes with the coach is the focus of this research. The skilled performance by a
teacher or teachers is taken to be a psychological process or phenomenon. This performance is
skilled if it is intentional, though not necessarily conscious, that is, directed to some end and is
subject to assessment of right and wrong for it is normatively constrained. A useful metaphor
for the interpersonal flow of “skilled action” of mathematics teachers is taken in this study
employing language philosophy after Austin (1961) and Harré (1983) to be their everyday
conversation in the context of coaching. The teacher’s conversation is taken to be a kind of
ultimate reality or cause. Their decision-making is a conversation, while introducing a
mathematics lesson using the coach’s “warm-up” strategy is conversation like.
Signing in conversation with the coach
A symbolic interactionist perspective provides an insight into the teacher’s perceptual and
connotative knowledge, in particular, how actors interpret their environment. For example,
Harré (1999) argues, humans act towards objects that have meaning for them; the meaning
ascribed to objects have been negotiated through social interaction and come to be interpreted
when required in daily situations of human experience. To understand a teacher’s meaning
making is to understand how they make use of language, symbols and signs. This
acknowledges the teacher as an efficacious agent in a symbolic world. The actor agent
constructs culture through collective meaning making referring to these meanings in order to
make sense of their world thereby guiding their behaviour. To understand how the teachers
construct and interpret meaning in their organisation of social life is to examine ordinary talk
through conversations, particularly in the way symbols and signs are used.
Deweyan pragmatism, and activity theory as presented by Vygotsky both regard practical
activity in the form of bodily actions, routines and habits as the starting point for studying
human behaviour and the relationship between thought and objects in how humans transform
their world. Dewey (1910/1997) regarded thinking and reflecting as important elements in
reorganizing the world. His instrumentalist view describes how thought functions to
experiment, through the use of cognitive objects, concepts, and models, with the purpose of
38
serving future projects. Vygotsky (1978) on the other hand developed the concept of mediation
as presented in Figure 7. For example, during socialization a parent reads to their child
occasionally indexing pictures / objects in a book, pointing to embellish its meaning. Similarly
a teacher points to a picture of a mathematical symbol such as a graph to describe an everyday
process or experience of defining mathematical relationships between say distance and time to
show space. The child / student is encouraged to replicate this culturally mediated action
whenever and wherever he / she comes in contact with the symbol, culturally reinforcing the
sign in subsequent conversations. The conversation encompasses not only interpersonal
exchanges but extends to all semiotic transactions including gestures and activities. The
relation between the teacher, student, subjects and object representation is therefore mediated by
cultural means. Tools such as words, objects, and performances are historically loaded with
past meanings and associated activity and the use of these culturally mediated psychological
signs constitutes the foundation in the development of higher order psychological functioning in
the mathematics teacher’s conversations with their students.
The triad presented as Figure 8 shows how the Sign / Representamen is used as a tool to
mediate the social construction of knowledge and understanding that leads to action. Tools like
material objects act like prosthetic extensions of our embodied being that assist an actor / agent
to achieve their goals. Signs are embedded within communal understanding; a historically
mediated message that transcends time and space. Charles Peirce argued that there is no
Figure 7. Meditational triangle after Vygotsky
Mediational Means Tools: Symbols, books, writing,
pointing, speaking, conversation, gesture….
Object/Motive à Outcome(s) Improved cultural agency
Subjects Individual, dyads, groups
39
knowledge without signs and signing (Hartshorne, Weiss, & Burks, (Eds.), 1931–1958). In
Figure 8 the Peircian semiotic triangle frames coaching as the sign system that indexes
improvement to teaching. Coach intervention as a social object is both Immediate and
Dynamical. The Immediate Object indexes professional improvement; this is the internal
transitive and episteminological dimension of knowledge. A relationship exists between the
immediate object and the dynamical object, one that may not be readily foreseeable but never
the less exists, one that encapsulates the transitive and intransitive dimensions of the coach as
the object of reference in the world, of past experiences and already in existence. The degree to
which a teacher as actor / agent can engage with the coach as object as a significant other
determines the level of access a teacher has to the transitive / intransitive dimension of the
coaching intervention. This may have varying effects such as a low level feeling or recognition
(Immediate Interpretant), or it may strengthen a teachers planning practice (Logical
Interpretant), or the relationship that the sign has to the object may even lead to a bodily action,
that is, it becomes inculcated in practice only if the sign reshapes the object (Energetic
Interpretant). In the same way Peirce’s semiotic triad suggests the degree to which a coach as
actor / agent can engage with the teacher as object determines the level of access the coach has
and the transitive / intransitive dimension of teaching practice in the school.
Sign / Representamen
Iconic. Where the sign relates to its object, e.g., a picture.
Index. Where a sign relates to its object in terms of causation
Symbolic. Where the sign relates to its object by means of convention alone, e.g., a word.
Interpretant / Effect
Mediates between the OBJECT and SIGN so that what the agent is constructing is what the sign is changing. The effect is “Immediate”, “Logical”, or “Energetic”.
Dynamic Object
Dialogic and or dialectical nature of an individual’s mental access to knowledge, i.e., the intransitive or external dimension
Immediate Object
The transitive or internal dimension of knowledge
A relationship exists between the two
OBJECT
Figure 8. Semiotic triad after Peirce
40
Figure 8 shows that signing is a process where the representamen has a specific relationship to
an object, for it is “… something which stands to somebody for something in some respect or
capacity…” (Hartshorne et al., 1931–1958, Vol 2, p. 228). For example, the coaches lesson
strategy of a “warm-up” activity at the commencement of a maths lesson can be seen as an
object that signs or affords a teacher a tool for controlling an unruly class, or perhaps a tool to
engage students with their learning, or even act as a formative assessment tool. The above
demonstrates the way in which a material object such as the “warm-up” activity (mediating
tool) is pre-disposed to multiple narrative representations affording the social actor a way of
perceiving and of doing in a specific spatio-temporal context (Gibson 1979). A sign is
meditative as it connects two things, the object to its interpretant; it may also mediate between
two objects, one as a mental image, and the other as being relatively independent of the present
thought (Nellhaus, 1998). The interpretant more often than not leads to subsequent semiosis
thereby forming a fabric of interconnected triads by which humans come to know, produce and
reproduce their social world (Cobley & Jansz, 1997). Signs therefore don’t have one but rather
multiple meanings, used in context to illuminate what an individual considers important at a
particular time and place in order to realise a project of significance all of which illuminates the
“enabling condition” of human experience. As outlined above, a useful model for the
interpersonal flow of skilled action is conversation where conversation is taken to be a kind of
ultimate reality for it demonstrates that humans construct and reconstruct their social reality
through discourse, through the transaction of signs.
Emotion in the analysis of the teachers’ narrative of the coaching intervention
Narrative plot structures such as comedy, romance, tragedy and satire / irony dramatized the
emotional world that maths teachers’ in this study performed in (Frye, 1971; Kuzmics, 2009).
For example, rhetorical irony was used by some of the maths teachers in this study. Irony
represents the contradictions between purposes and proposed procedures to dismiss the
coaching exercise as absurd. Kuzmics (2009) describes an irony of form
“… where there is a contradiction between message and its medium and the
formal characteristics of its presentation; an irony of events or conduct, where
mutually exclusive frames are juxtaposed, and finally, dialectical irony with its
three variants: unmasking a social event or phenomenon by carving out its
meaninglessness; highlighting a mutual dependency between alleged opposites;
the dialectical dissolution of opposites.” (Kleres, 2010, p. 192).
41
Identifying the plot structure of irony / satire in some teachers’ narratives, assisted me to
describe the emotional experience(s) as conveyed in narrative, where teachers felt their agency
was rendered inactive or active only as a result of other’s action(s). Other types of emotion
narratives configured teacher agency in specific ways. For example, grammatical features may
index helplessness - an illocutionary force of specific local exigencies and contingencies in their
classroom teachings. In a further example, a teacher anger narrative may dramatize the
shameful sense of having to be coached. Both examples show human experience as De Sousa
(1980) puts it, through “paradigm scenarios”, in which agents identified themselves with
emotional universals embedded in narratives that are socially transmitted through storied
experiences. The study of emotion and its relationship to meaning making has attracted little
research attention particularly with respect to the narrative construction of agency in terms, for
instance, of “who is doing what to whom” in a particular social situation. Thought and emotion
are embodied and made comprehensible from a social perspective. A “cry for assistance” made
by a stressed novice teacher of mathematics appointed to an “underperforming” school for
example, evokes a situated emotion, one composed of interdependent cognitive, somatic and
social components.
The coach as myth bearer: The mythopoesis of a new lesson structure in the
improvement of mathematics teaching
Vygotsky (1978) and Dewey (1963) proposed that organizational learning is a culturally
mediated activity where established members of a community pass on practices to aspiring
members who come to accept normative and warrantable forms of activity. Activity is mediated
through artefacts and tools historically ascribed signs and signing, both formal and social and
are all characteristic of the flux in which the teachers’ in this study come to know their teaching
world. Given that resources at hand mediate activity, teachers may not blindly follow what
came before them to reproduce social reality but rather as Sleeper (1986) puts it, thinking and
reflection are “means of conducting transformational transactions with the world, a means of
changing or reconstructing the world” (p. 3). Engagement with the coach may inspire teaches to
aspire to membership of an intellectual community of mathematics teaching and in the process
support their agency in the self-improvement of their material practice. The coach may be a
resource in curricular myth making. The coach may be viewed as the bearer of a myth, which is
a possible reality that does not mean an untruth, of reform or a new teaching praxis. The coach
can be seen in her work in teaching classes to be demonstrating this new possible reality,
however this demonstration can’t be a proof of what good teaching is, at best, it can only be an
42
invitation to a conversation about becoming a good teacher. Phenomenologically as Voegelin
puts it, a myth
“… consists of a description of the existence of consciousness as it transcends
itself to become aware of the body, the external world, the community, history,
and the ground of being.” (cited in Leonard, 1983, p. 18).
Leonard (1983) argues a transformation of curriculum discourse requires an essentially mythic
form that permits the creating of order and meaning as they relate to the mysteries of existence.
By way of example, the title of a Western Metropolitan Regional policy document released
during this research period titled “Every Child, Every Opportunity” (DEECD, n.d.) presents a
myth that every child can learn (mathematics). It provides direction and a place from which
educators and their communities can commence a transcendental journey. However, as Leonard
(1983) argues, the myth cannot solve all the problems associated with it and therefore requires
an apologia to defend it. The message articulated by the DEECD at a western regional
numeracy meeting as reported by Mandy, one of the teachers in this study (refer Chapter 5) was
that “we can no longer justify failing students”. Mandy’s satire connotes “the absurd”. The
coach, as representative of the DEECD challenges teachers of mathematics not to reject the
myth. Rather, endowed with a parable, a magical lesson structure, held in proper perspective
teachers can transcend their everyday problems to chart new directions, develop new
possibilities. The coach it is hoped can mytopoetically evoke and bring forward a reflective and
transformative imagination in teachers (Leonard & Willis (Eds.), 2008)
Mythopoesis, Aadlandsvik (2009) argues is about securing a balance between the inner world
and the outer through story telling; “…to restore balance between the cultural, imaginal, and
emotional (on the one hand) and the rational, pragmatic, and scientific (on the other)” (p.94). In
this sense, the coach’s mythopoesis is about challenging the current standards based reform
agenda as a rationalist paradigm. This dominant technical rationality that positions curriculum
within measurable parameters may prohibit imagination as a reliable mental faculty destroying
teachers’ artistic spirit producing a culture of apathy in response to which is seen as “absurd”.
Mythopoesis encourages a reflective imagination where personal and social myths are
considered forms of knowledge that presents transformative qualities within an individual and
also within a subject department as a community of practice; for minds are forms of cultural
achievement and if denied expression leads to an impoverished spirit that only serves the
purposes of power. Myth, Aadlandsvik argues, can open the mind fostering reflection of a
person’s place in the world. A myth is transcendental in fostering consciousness that life is
43
bigger than what can be presented by scientific data alone which is a contradiction in the terms
of the coaching policy’s testing rationale and its process narrative. Myths, Leonard argues are
fabrications of a narrator that can offer relationships to dominant patterns of beliefs, ideals and
ideology, of inherent biases that assist in the reconstruction of a social reality that denies
teachers and others their honour and status. Dewey argues that the mythopoetic imagination is a
vehicle of learning, of bringing new understandings to existence for “[a]rt…renders men aware
of their union with one another in origin and destiny.” (1934/1980, p. 271).
The discursive psychological positioning of the coach and her message, in teachers’
storylines of their practice
The mutually determinate triad as outlined in Figure 9 of storyline, illocutionary force and
position (Harré and Van Langenhove, 1999) is applied to determine the social psychological
meaning of discursive acts and actions that illuminate a teacher’s life as narrative, one that
negotiates multiple narratives. The storyline shows how human beings come to some sort of
order; the order as expressed in a narrative as “... the ordering principle that gives meaning to an
otherwise meaningless life” (Bamberg et al., as cited in Slocum-Bradley, 2009, p. 5). For
example, the storyline of the school administrator may be that of meeting the needs of the day-
to-day functioning of the school, student enrolment, the hiring of teachers, of making sure that
the school in which they administer has an academic standing in the community…. This
storyline is negotiated through roles and responsibilities and is ever present as tacit knowledge,
Figure 9: Mutually determining triad in a conversational episode
Discursive psychological position(s) of speaker(s)
Storyline(s) The illocutionary force - The social significance of what is said and done
44
as schemata and policy and as such, frames how individuals behave as presented in the
normatively constrained speech act types they may draw from.
The illocutionary force, on the other hand, represents how language / words that are inscribed
with meaning, and other tools are used to accomplish certain tasks in a given situation. Austin
(1961) distinguishes between illocutionary / performative force, the locutionary force and the
perlocutionary force. For example, the speech act is the actual act of saying something
(locutionary force) where I request (illocutionary force) that you follow a particular “warm-up”
activity to begin your math’s lesson with, in which case you would nod your head and comply
by saying “okay” (perlocutionary force). Such a speech act is dependent upon the identity of
the actors involved and interpretations of contextual factors such as the social and cultural
context. Finally, the
“[p]osition is relational, expressing the rights, duties and obligations with
respect to the social acts that people engaged in a small scale interaction have or
are ascribed from moment to moment” (Harré, 1997, pp. 180-181).
Therefore, position, act and story line form a mutually adjusting triad, that is, as positions are
interpreted so too are acts and storylines all of which are evident through conversation.
In addition, the mutually determining triad interprets teacher accounts of their multiple small-
scaled intentions through normatively constrained conversations and as such permits an
explanation of the moral order the teacher inhabits. Each element of the positioning triangle is
contestable and it is done so through the myriad of experiences that is brought to and lived out
by actors. Conversations are therefore a window and disclose aspects of human life that may be
relevant in the unfolding patterns of what it means to teach mathematics. A conversation is
inscribed with multiple meanings that expose the myriad of narratological contexts all of which
illuminate an actor’s ability to act, to reach out, and to achieve a desired effect on a stage at a
particular time and place. This mass of normatively constrained human intentions whilst
appearing messy comes together through narrative structure, that is, people are pulled together
to come to some sort of order by means of a storyline. In living a narrative, individuals draw
from a set of normative rules expressed as rights and obligations with a corresponding set of
speech acts. Therefore, analyzing a teacher’s “account” involves extrapolating the social force
and explanatory content that provides an understanding of why they behave in the way that they
do for it provides a lens to the genesis of intelligible and warrantable social action (Harré,
1977).
45
Locating the person of the teacher in their storyline
Harré (1999) describes how discursive symbolic devices realise the phenomena of our mental
lives. This represents a move away from scientific realism and recognises the significance of
symbolic systems such as normatively constrained pronoun grammar usage to illuminate the
private realm, the private self and the personal uniqueness of the agency of teachers in social
episodes. The private realm of the teacher is primarily acquired in the public domain and later
re-expressed through the skilful use of words and symbols in public. It forms a continuous loop
of never ending learning and re-learning of rules and responsibilities that are normatively
constrained and expressed in warrantable and intelligible ways. Humans learn and relearn
culturally specific skills and norms, about language and context from others through
conversation that is mediated by tools and symbols within a community of practice. Humans
are therefore embedded beings, produced by others through rules, norms and conventions of
symbolic practices as expressed in conversation.
Further, intrapersonal conventions inherent in conversation, symbolically mediates interaction
where the private use of learnt symbols and cognitive skills becomes public and comes to
represent the joint enterprise of human meaning creation (Mühlhäusler & Harré, 1990; Harré,
1999). It is in conversation that social actors express psychological phenomena such as
attitudes and feelings, which is evidence of their intentionality and their position within the local
moral order. It is here in conversation that agency is expressed particularly through the use of
pronoun grammar. Acceptable pronoun use such as “I”, “you”, “they” are symbols that
temporarily index a teacher’s fluid position and also expresses their identity. As we will see
below, pronoun grammar use or signing indexes the location of embodied actors to each other
with respect to roles and responsibilities in a time and place all within an arrangement of
material and social events.
46
“My kids just don’t get algebra, I’ve tried everything and they just don’t get it”
This utterance made by a teacher upon entering the staff room is a dramaturgical performance.
Goffman (1959) argues that this should be interpreted as a window on a moral career,
performing to role expectation of having the capabilities and capacities of a teacher, that is of
projecting an honorable self to others. In projecting a self to others, the self as performer is
revealed to others. In doing so, the teacher shapes out and is bound by the moral persona that
they have created through their expressive abilities that is accountable to themselves and to
others in the local moral order. Social actors attempt to create and manage an accepted way of
behaving or enacting various personas of being a teacher in the context of the conversation that
govern their normative and warrantable behaviours thereby committing themselves to an image
of themselves that is believable and convincing. Therefore the utterance above expresses a
moral and heroic purpose one that pertains to the guidelines of honor in the local moral order.
A teacher is bound to the rules and dynamically repositions themselves to ensure that they do
not stray too far from the norm for it affords them a social standing in the local moral order, i.e.,
a position and a corresponding sense of identity, agency and self improvement permitted by a
subject department as the community of practice to which they seek ongoing membership.
The above utterance is an expression of identity through the indexicality of having a location in
space, a position in the moral order in relation to other actors and of having a life trajectory in a
sequence of events that comes before and sometimes after an utterance. If we take a speech act
in an episode, it represents just one “atom” that makes up the realm of conversational ontology,
a powerful particular that is interrelated with other conversational “atoms” that provides an
insight into the private; an actor’s intentionality (Mühlhäusler & Harré 1990). The utterance by
a teacher who exclaims “My kids just don’t get algebra, I’ve tried everything and they just don’t
get it” analysed using pronoun grammar after Mühlhäusler & Harré (1990) illuminates the
teacher’s agency and therefore the position of the teacher in their own storyline juxtaposed
against culture and context. For example, the teacher starts off with a possessive pronoun that
indexes the students that she / he is responsible for teaching algebra to as their teacher of
mathematics. The second pronoun “[I]’ve” indicates their moral commitment to not only the
teaching of mathematics but also in ensuring that students understand and are able to apply
algebraic concepts and ideas in order to solve problems to a prescribed standard. This moral
commitment is embedded in the role, duty and responsibility of what it means to be an effective
teacher of mathematics, as expressed by the community of practice, the stakeholders and
guardians of mathematics, and through student data that measures teacher effectiveness and
47
therefore quality. The teacher’s utterance, in this instance, could be a cry for help or simply
seeking support, recognition and acknowledgement from colleagues that teaching algebra is
difficult and that as their teacher “I” have failed. This latter aspect may be the actual position of
the teacher and is perhaps revealed in the third person plural pronoun “they”. “They” may
index a shift away or absolution from moral responsibility thereby shifting the blame of failure
onto students. Finally, the “it” may indicate an invitation to other teachers who are listening, to
respond. Responses to the “it” may index amongst other things that students are not
academically gifted or the “it” may index a pedagogical approach discussed previously at a
meeting. The possible meanings of these doings and sayings can only be explored further in the
conversation in which they occur.
Narrative research for understanding the sense making of teachers
In this study, the utterance “My kids don’t get algebra, I’ve tried everything and they just don’t
get it” explored through a narrative lens illustrates which social sense teachers make, of what
knowledge is shared and or not shared, and of judgments made based on that knowledge. The
utterance also shows that a fundamental premise of narrative analysis is the assumption that
teachers know more about their experience than they can present in abstracted terms for
teachers have narrative knowledge, within which the epistemological authority of their
experience is grounded. The knowledge of how things come about is only accessible in its
narrative form and as such, meaning making requires a shared sense of social reality and social
rules, which guide interpretation of experience and purpose in the teaching of mathematics.
Rawls’s (2011) argues that meaning making in modern society is based less on shared beliefs
than on the requirements of social action. That is, collaborative sense making needs to replace
more artificial and “mechanical” social orders of the past, that were often served by off-site
professional development or perhaps the constraints imposed by a contrived relationship
between coach and coachee. Constitutive practices presented by example in the Lesson Study
(APEC, 2009) Rawls (2011) argues are generally grounded in constitutive rules, which are
prospective and are influenced by, but distinguishable from, traditional institutional rules that
are maintained by retrospective accounting to “head office” on the assumption of common
beliefs or ritual behaviours in teaching. As Harré (1983) has pointed out the problems with the
idea that a social order, in this instance teaching mathematics, can be maintained or transformed
by “following rules” is vague and rarely actualized in any particular school. The narrative
grammars that define a social order in the subject department as simply an administrative unit in
48
the schools studied, loosely govern action for the teacher’s who are isolated in their classroom.
The quote “My kids just don’t get algebra, I’ve tried everything and they just don’t get it” is a
snapshot of the actual “rules” for the teacher’s social actor in the hiatus between the practical
(for maintenance of position in the local moral order) and expressive order (for honour and
status). This is a response to the contingent and exigent realities of the classroom and is directly
related to the shared purpose, actual moves of play, and directly constitutive of shared meanings
with colleagues that have been promulgated from past transactions.
It is argued that mutual intelligibility in self-improvement or professional development between
the coach and teacher and amongst teachers is a constitutive practice. It is not only a matter of
connection between a word or perception and a new institutional way of doing and saying.
Rather mutual intelligibility involves the prospective relationship between constitutive moves as
teachers of junior mathematics in their discursive circle who work with a coach in moving
forward to social solutions (Garfinkel, 1948/2006). Each move forward through a dialectical
interplay has the ability to change the meaning and relevance of historical grammars, of what
went before. A move, together with the ensuing interpretations and confirmations constitutes
meaning. Garfinkel (1948/2006) argues that responding in this way with the orienting
constitutive background expectations is a moral imperative that assists movement from one
paradigm to another and from one identity to another. Without mutual intelligibility there is no
way for an individual to know anything more about one-self. Research analysis of discursive
practice in on-site professional development projects can make the site-based constitutive rules
evident in the back and forth collaboration of the moment. This notion of constitutive order can
allow more clarity in the end because the collaborators, in principle, can be counted on to see
the process through. The interpretation of each act in relation to a constitutive order will be
concerned primarily with a consideration of whether or not the action of the teacher is
adequately orienting the teacher to respect the rights and responsibilities that are the underlying
condition behind any transformation of rules.
Summary
The personhood of the mathematics teacher is recursively and dynamically interrelated to their
agency and the local social structure in which they work. Neither structure nor agency can
alone account for teacher behaviour but rather emerges in the interaction between the two in
time and space. That is, humans develop through social organisations collective agreements as
expressed through symbolic processes that have been left behind in the wake of human activity.
49
It is this Vygotskian social interaction that humans use rules to support the myriad of life
projects that are activated through symbol systems dialectically forming higher processes.
Language constitutes one of these systems and it is here where humans develop their identity
through discursive episodes; conversations that position and reposition thereby forming and
reforming their fluid social selves in the material world that in turn promulgates the private self,
the self of the subjective singularity. The subjective singularity, the private world represents a
historical repository of umwelten experiences that constitutes a person’s biography and it is
through the exploration of discursive episodes that allows for an understanding of how social
actors negotiate and interpret meaning in different situations. For as Dewey, Vygotsky and
Harré put it, humans act towards something on the basis of meaning, the meaning of which
arises from social transaction and is modified and reinterpreted through this social point. To
explore human agency is to explore discursive acts, for it is here where agency is located and it
here where the utterance of the teacher shows their professional identity within a community of
practice as expressed through discursive signing acts. It not only illuminates for the outside
observer the umwelten of the teacher with all that it affords but also shows the actor’s modes of
adaptation given their position within a community of practice. Through utterance, discourse,
conversation and the like, fluid identities are realised and come to highlight practice, identity
and storylines all of which come from a dominant discourse inherent in the setting where tacit
cultural and social influences are explored.
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3
Language and self-monitoring, the basic particulars of personhood
“… a person is not a natural object, but a cultural artefact. A person is a being who
has learned a theory, in terms of which his or her experience is ordered. I believe that
persons are characterized neither by their having a characteristic kind of experience
nor by some specific genetic endowment. They can be identified neither
phenomenologically not biologically, but only by the character of their beliefs.”
(Harré, 1983, p. 20)
Introduction
This qualitative study explores the discursive relations between secondary school teachers of
mathematics and their coach in enacting Department of Education and Early Childhood
Development (DEECD) (2010a) policy. This research is different from program evaluation
studies, which would focus on the rhetorical production of bodies, and see the body of the
mathematics teacher as a surface for textual transcription (Foucault, 1977). Instead of the
metaphor of educational policy inscription which sees the person of the mathematics teacher
positioned as disciplined, regulated and turned into the subject of power and their practice
theorized as resistance, this research considers the ways in which the agency of the mathematics
teacher is made active in social action. The study is interested in the social conditions in which
recommended practice in policy presented by DEECD may become or fails to become a
committed grammar. This is a study of how teacher agency is brought into being and mobilized
by positioning and signing in the interweaving networks of interdependence not only between
student learning outcome measures, sanctioned teaching practices and a teacher’s professional
identity formation but also between the more proximal social orders.
The social orders of the school does not form one interconnected whole but may be fragmentary
and disparate to teachers themselves. The dispositions and capacities of teachers will not be
51
uniform within schools, because within any group of mathematics teachers are different
characters, skills, beliefs and or abilities, due largely to the varied influence of social relations
upon them. The textual metaphor for understanding the person of the mathematics teacher is
therefore too one-dimensional for teachers are active in a multi-dimensional world. This can be
understood as a complex materiality composed of relations between human beings, relations
between humans and pedagogical objects and through the joint production of symbolic forms of
understanding. To explore the world of the social actor is to uncover the “rules of production”
inherent in a specific culture that actors inhabit and draw from that render their world
meaningful (Willig & Stainton-Rogers (Eds.), 2008).
The chapter presents a description of the research approach and overview of this study including
subject selection, research sites, data sources, sequence of activities, the methods of data
collection and the analytical tools used. Extracts from a conversational interview in a pilot
study is analysed to introduce the approach developed.
Discursive accounts
Positioning theory and semiotic analysis were used to explore teachers’ discursive practices in
their norm referenced “accounts” of their professional identity and its putative transformation
associated with working with a coach who was positioned as an agent of change in their
“underperforming” school. The study adopts an ethogenic approach in that it explores the moral
and normative context of teachers’ intentional agential action. The ethogenic approach to the
study of norms of teacher behaviour can be summarised according to three principles all of
which explore the relationship of rules and roles. Firstly, a sociological principle where society
involves two social orders, the organisation of work (practical maintenance function) and the
organisation of honour and status (the expressive function) in actor accounts. The organisation
of honour usually has priority over the organisation of work in these accounts. Secondly, a
psychological principle, which describes all social action as, structured and realised from prior
structures and therefore located in the intentions and belief system of both individuals and in
collectives. The final principle is social psychological describing the many features of mental
life that are either a permanent part of our cognitive resources or improvised as part of a shared
cognitive resource, one derived from social forms that encourage humans to act in warrantable
and intelligible ways (Harré, 1977, 2007). In this approach an individual tends to be the kind of
person his language, his traditions, his tacit and explicit knowledge allow him / her to be
(Cohen, Manion & Morrison, 2007). The “accounts” teachers gave of their experience in
52
conversation with the researcher about the coaching program, involved extrapolating the social
force and explanatory content. This approach affords an understanding of why teachers behave
in the way that they do, for it provides a lens to the genesis of intelligible and warrantable social
action (Harré, 1977).
The discursive psychological approach adopted here after Harré (1999), Shotter (1992),
Vygotsky (1978), Wittgenstein (1953/2001) take everyday conversation to be the basic social
entity. Conversation affords both participants and readers an understanding of human
behaviour, here in the field of mathematics for teaching is best understood from the perspective
of the intentions of the individual actor. Further the perspective presented is not presented as a
monologue but as a conversational dialogue between the researcher and teacher in which the
context and the person are both held in focus and observed as co-constructed and emergent.
Harré and Van Langenhove (2010) argue the discursive ethogenic approach allows for the
exploration of the human umwelt or life space; here the human aspect of the social realm that
surrounds but also affords access to the private inner world of the teacher of junior mathematics,
as they go about their everyday tasks of teaching at the intersection of their intentions and
necessities. The use of conversation to explore the social episode of mathematics coaching and
the way social actors present themselves and are seen to present themselves in their ongoing
discursive acts and actions that structure meaning, is central to the descriptive “accounts”
offered in this research. The research conversations are not concerned simply with
interpersonal relations between teacher and coach, but rather the semiotic interactions generally
include gestures and strategies that cast a light on how best to understand how the teachers as
actors use social-psychological spaces available to them in the micro-culture of mathematics
teaching to index, negotiate, construct and reconstruct their social world and their professional
identity.
To analyse the teachers’ “accounts” is to explore the inherent use of symbols through which the
actors attribute meaning to in this constant state of flux, that is forever changing, and guides
them in their everyday practices. Taking a symbolic interactionist perspective Woods (1994)
rejects the notion that it is in conversation, broadly defined, that individuals’ position
themselves and others in pursuing their individual projects on shared horizons as presented in
their “accounts” as a personal record of events experienced that express an actor’s past, present
and future directed action.
53
Conversational perspective taking
Martin (2005) defines perspective as the “… perceptual or conceptual orientation to a situation
with a view to acting in that situation” (p. 231). Perspective taking, Martin (2005) argues,
allows an individual to develop and maintain good interpersonal and community relations
extending their own personal qualities for entering into dialogic relations with others.
Perspective taking exists in an interrelationship with others and with the environment and as
such is a collective achievement, realized through the communication of gestures that transform
into a conversation of significant signs. Signs are mediative as they enter between and connect
an object to a significant effect and it is in this way that individuals orientate themselves to
themselves, with each other and to their environment. Perspective taking is conceived through
conversation for reality does not exist independent of the mind but rather resides in both the
individual and socio-cultural world.
Conversation as a universal characteristic of human behaviour allows for the positioning of
material objects, humans included and allows for the monitoring of our own self-monitoring of
performance, of the possibility of continuity, conscious self-awareness and identity. A person is
a logical unity that shows an awareness of and monitors his / her performance and intentional
agential actions upon material objects in time and space through their linguistic / symbol using
powers. People form ideas about themselves through the myriad of interactions both with their
environment and with other persons. It is through transacting with others that people form ideas
about themselves thereby demonstrating their conscious ability. This conscious ability becomes
evident through pronoun use for pronoun use demonstrates the existence of a teacher’s identity,
its shifting nature and the way it is shaped by social forces demonstrated by the “accounts” they
provide (Mühlhäusler & Harré, 1990). In order to study the shifting nature of the reciprocity
between personal identity formation and organizational transformation, it is important to
understand the life space a person occupies within an ethogenic landscape (Redman and Fawns,
2009). For as Harré and Secord argue,
“[i]t is [within] the existence of this (plans) while they are going on
(commentaries), and in retrospect [the] derivative capacity to comment upon our
actions, in anticipation (accounts), that is our most characteristic feature and
around which the science of psychology must turn.” (Harré & Van Langenhove,
2010, p. 19).
54
“Accounts” of each of the teachers of junior mathematics (eight in total) who volunteered to be
part of this research were constituted in conversation with the researcher. Three conversational
interviews with each respective teacher were conducted with the purpose of building rapport as
well as follow emergent themes. All transcripts of interviews were provided to each respective
teacher to check for accuracy and with the purpose of extending the conversation. All
interviews were audio recorded. Questions posed in interviews, and information collected in the
form of training manuals, timelines, memos… explored how the coaching program framed and
performed its function, the degree to which change was achieved and sustained, the way in
which the coach contributed to the process of school reform, to outcomes that were valued by
school participants, and the degree to which participants re-cast their teaching and learning
practice.
Overview of the study
This study adopts an ethogenic approach to explore the “accounts” offered by eight teachers of
junior mathematics, four of which belong to one school (Lambertia College1) and four to
another (Grallina College) and all of whom had been encouraged to work with a coach. The
study began in 2009 in the last term of the academic year where a coach was positioned by the
DEECD on a weekly rotational basis in both schools. A narrative approach was adopted in
which teachers gave accounts of their experience of the coach and of the coaching interaction.
Their interpretation of their rights / responsibilities and obligations / duties in the episodes was
sought in their accounts. This is a realist symbolic interactionist framework after Blumer,
(1969) and Shotter, (1992) who describe that human’s act towards things, including self, based
on meaning ascribed through social interaction and modified through an interpretive process. It
is in this process that the self or identity comes to be realised and expressed as determined by
the narrative in which they occupy. The social positioning and signing employed by the
teachers presents an exploration of both the influence of the local moral order and identity
formation of these teachers in everyday discourse.
1 All names of schools, school locations, teachers, principals, deputy principals and the coach in this study are pseudonyms
55
1. Subject selection
In 2007 there were eleven coaches of numeracy appointed to work with a select number of
primary and secondary schools across the Western Metropolitan Region of Melbourne. The
researcher selected school(s) based on a random selection from the coaching pool appointed by
the Western Metropolitan Regional office of the DEECD. The coach selected was positioned to
work with teachers of mathematics in two secondary schools on alternating weeks. The
researcher first sought permission from the respective principals to conduct this study in their
schools before seeking permission from the coach and teachers selected by the School’s
Administration to work with the coach. All interviews took place in the last term of the 2009
academic year in which all teachers were separately interviewed three times each and
transcribed interviews were subsequently verified by each respective teacher. In addition to the
teacher interviews, the researcher collected background data of whole school perceptions of
professional development in the form of a survey2 and conducted interviews with the coach3 and
with each principal4. Further, the researcher also collected observational data, artefact data
(information released by the DEECD) and training manuals, timelines… all of which allowed
for “data triangulation” (Creswell, 1998).
The purpose of this multi-theoretical study of the umwelten of eight secondary school teachers
of junior mathematics in two “underperforming” secondary schools was to explore professional
development they associated with being coached; whether new practice habits were formed
specifically in line with lesson restructuring as modelled by the coach or more generally
whether teachers felt their teaching was improved as a consequence of working with a coach.
The study explores accounts of teachers of junior mathematics who worked with a centrally
appointed coach.
Given the focus was primarily on the eight teachers of junior mathematics in two
“underperforming” schools and how they responded to the coaching program, the dominant
emphasis was placed on a social phenomenological approach that attended to teachers’ social
ontologies. The dominant data component of the research was the descriptive accounts of the
teachers. Conversational interviews with each teacher of mathematics explored how the
coaching program was experienced, their perspective on changes achieved and or not achieved
2 Appendix 2: Whole school survey. Appendix 3: Survey structure. Appendix 4: Survey results for Grallina College. Appendix 5:
Survey results for Lambertia College. 3 Appendix 6: Interview schedule - Coach. 4 Appendix 7: Interview schedule - Principal
56
towards structural reform and in their own practice. The collection of both the survey and
interview data occurred at the same time.
2. The school research sites
The City of Behriana is located to the west of Melbourne. Both schools in this study are located
in the City of Behriana. According to the Australian Bureau of Statistics (ABS, 2010) the City
of Behriana is a rapidly developing area represented by the growing western suburban spread of
Melbourne. The township of Behriana was established in 1830 and the land (area of 527 km²)
was mainly used for grazing and farming. The construction of infrastructure was encouraged by
the gold rush that took place from the 1890s to the early 1900s. From the 1970s onward rapid
growth took place particularly around the township although smaller towns grew in the outlying
district. The population doubled between 1991 and 2006 from 35,000 to over 78,000.
Approximately 40% of the population is under 25 years of age, 19% are between 25 to 34 and
23% between the ages of 35 and 49 years of age making the City of Behriana a very young area.
Approximately 80% of working families’ travel to work outside the town and as a consequence
young people spend a significant amount of time without adult supervision and or supervise
younger siblings. Approximately 69% of the residents were born in Australia, 24% were born
in non-English speaking countries and 6% were born in English speaking countries. The City of
Behriana is the 10th most disadvantaged local government authority in Victoria according to an
ABS index that measures the welfare of Australians in local communities. The Socio-Economic
Indexes For Areas (SEIFA) ranks an area by providing a method of determining the level of
socio-economic well-being. The SEIFA rank for the City of Behriana is quite high and is
therefore reflected within each of the schools studied. The two schools in this study are
approximately 2 km apart. Grallina College is situated in the south and Lambertia College to
the north of the town centre.
3. Data sources
The collection of three types of data on teacher’s dual praxis as social product and producer of
the social allowed for data triangulation (Creswell, 1998). The three primary data sources were:
observational data, interview data and artefact data, i.e., information released by DEECD,
57
training manuals, timelines, memos… (Yin, 2003). In addition, a survey5 was used to capture
background data. Data collected from all sources including the researcher’s familiarity with
government secondary schools and the coaching program assisted in the construction of eight
teacher “accounts”.
4. Steps in the research (2008 to 2010)
The following summarises the sequence of activities undertaken in this research. Whilst
presented in a linear fashion steps undertaken in some instances occurred concurrently.
• Review of literature undertaken.
• University approval acquired to conduct research.
• Pilot study undertaken with respect to an unstructured / conversational interview
with a teacher of mathematics who worked at Skipper College6.
• Questionnaire piloted and amendments made.
• Approval sought from respective principals of Lambertia and Grallina College.
• Semi-structured interviews took place with the coach and respective principals.
• Three unstructured interviews took place with each of the teachers of junior
mathematics.
• Staff from each school surveyed with respect to professional development.
• Artefact data collected from the coach.
• Classroom observations undertaken.
• Transcript of each interview was given back to each participant to cross check for
accuracy and or make any further statement originally omitted.
• Interview with the Regional Coach.
• Regional Coach invited to provide a comment for each teacher’s respective
transcript of interview.
5 Appendix 3 – Whole school survey. Appendix 4 – Survey structure. Appendix 5 – Survey results for Grallina College. Appendix
6 – Survey results for Lambertia College. 6 Skipper College is a P-12 College situated in the western metropolitan region of Melbourne. Skipper College identified as an
“underperforming” school by the DEECD. A Regional Coach was positioned at Skipper by the DEECD to work with teachers of mathematics.
58
5. Data-collection methods
This qualitative approach builds a holistic picture through a multi method process that includes
interviews, observation and document reviews as well as survey results from the staff of both
schools to capture background data on professional development. The study was conducted in
the natural setting where the researcher’s intention was to make sense and interpret phenomena
based on the behaviours presented in context.
5.1 Surveys
The survey instrument consisted of 50 questions that dealt with nine themes7. These
themes were randomly placed into the survey organized using a five point Likert
scale. The survey was piloted with the staff at Skipper Secondary College and
contradictions and omissions were adjusted accordingly.
The majority of schoolteachers from both Grallina and Lambertia College were
surveyed as a means of collecting background data on professional development.8 The
survey was conducted during a staff meeting at Grallina College where at Lambertia
College the researcher approached teachers inviting them to complete the survey.
The advantage of a survey was that it produced a quick way to gather data, in an
unobtrusive easily managed fashion. Whilst the survey data presented in Appendix 4
and 5 had limited value for examining complex patterns of social interaction, personal
habits, interpretation or belief, it sought to explore group experiences and perceptions of
current professional development practices. This assisted with the fine-grained analysis
afforded by the qualitative approach used. The questionnaire was a purposeful adjunct
to other methods of data collection used to triangulate discursive meaning of the duties
and responsibilities of mathematics teachers under consideration (Bloomberg & Volpe,
2008).
7 Refer Appendix 3 – Survey structure. 8 Refer Appendix 4 and 5 – Survey results for both Lambertia and Grallina College respectively.
59
5.2 Interviewees
The coach and respective principals of both colleges were interviewed. Interviews
conducted were structured9 and assisted to capture the social milieu and position of each
respondent as it pertained to current education policy. Interview data was purposeful as
a means of triangulation. Data from the structured interviews were transcribed and
offered to principals and to the coach, to check for accuracy.
Conversational interviews were also conducted with eight teachers of junior
mathematics, 4 from Grallina, and 4 from Lambertia College. The conversational
interviews focused on coaching as a professional development approach to the
improvement of practice. Each teacher of mathematics was interviewed a total of three
times. The purpose of conducting three separate interviews with each participant was to
develop a relationship with teachers making them feel at ease, in sharing their
experience working with a coach. Subsequent interviews provided the researcher with
the opportunity to follow emerging themes. Finally, information provided was
transcribed and provided to each teacher to cross check for accuracy before the next
conversational interview took place.
5.3 Observations
In addition to the structured and unstructured interviews the researcher observed
classroom interaction of how the coach went about coaching. Observations recorded in
notes were also used to triangulate understanding of conversational meanings.
5.4 Artefacts
Artefacts obtained in classroom observations together with DEECD policy and the
coaching program developed for the Regional Coach and school-based coaches was
also gathered and used as a source of triangulation.
9 Refer Appendices 6 & 7 respectively
60
5.5 Presentation of narrative functions of discursive episodes
Vladimir Propp’s (1928/1968) work on narrative as articulated in his seminal work the
Morphology of the Folktale proposes that the form of narratives may appear different
but are really the same, and that narratives may be divided into component parts /
events. The folktale Propp argues has the same “deep structure” of meaningful actions
(“functions”) performed by characters in a narrative (Refer Appendix 8). The
Morphology of the Folktale Silverman contends
“… establishes a narrative form that is central to all story telling across
many cultures. The [folk]tale is structured not by the nature of the
characters that appear in it, but by the functions they play in the plot.”
(1993, p. 165).
The dramaturgical narrative of story telling is therefore a form of social life, not simply
an ontological claim but rather a moral proposal that “[h]uman beings can be held to
account for that of which they are the authors [while] other beings cannot” (MacIntyre,
1981, p 209). The teacher’s story telling “accounts” here are also taken to be a
recreation of their identity, situating themselves in a narrative that defines their purpose
in life in a particular place and time through the choices they make as they narrate their
ever evolving storyline. Their stories illuminate the protagonist process of being and
becoming in their everyday life (Harré & Van Langhoven, (1999); Bruner (2004);
Schafer & Polkinghorne, as cited in Schiffrin, Tannen and Hamilton (Eds.), 2001). As
Schiffrin, Tannen and Hamilton (2001) describe, conversational stories are a way of
understanding the teacher’s habits of interpretation and habits of belief about their
world for the socially constructed personal narrative is how they make sense of
themselves individually and as members of groups. As Linde observes
“[i]n order to exist in the social world with a comfortable sense of being a
good, socially proper, and stable person, an individual needs to have a
coherent, acceptable, and constantly revised life story” (1993, p. 3)
Propp’s work on narrative forms the basis of extrapolating information from the
voluminous amount of conversational data gathered provided by each of the eight
teachers of junior mathematics in this study, affording an analysis of conversation based
61
on a relationship to semiology. The data reported in Chapters 4 and 5 are extracts from
the teacher accounts. They are presented using Propp’s narrative functions (1-7) and
characters as summarized in Table 2. In doing so, the self-as-process identity of each
teacher in this study emerged as both a social product and producer of the social (after
Bhaskar (1993) & Harvey (2002)). For example, once a teacher and their initial
situation is introduced, that is, of the temporal, physical setting and situation, an
interdiction may be addressed to the hero / heroine in the form of an edict of keeping to
the syllabus, that is, the “path” or the “script” of teaching maths. The villains appear in
the form of difficult students / teaching conditions and in the confusion of battle, the
hero / heroine violates the interdiction; data makes the lack known. A coach appears as
donor and brings magical agentry to heal the lack… The magical agentry in the form of
a “warm-up” activities that Harré (2002) would see as “[a]n object … transformed from
a piece of stuff definable independently of any story-line into a social object by its
embedment in a narrative.” (p. 25). The narrative is that of “underperformance” for
“[m]aterial things have magic powers only in the contexts of the narratives in which
they are embedded.” (Harré, 2002, p.25). This quest type narrative continues until its
optimistic finale. That is, whilst the narrative commences with prosperity, of
personhood entering a mythical platform of “making a difference”, the result is a new
prosperity via crisis.
Propp’s narrative functions, as presented in Table 2 assisted to tease out the generalised
process of self improvement for the utterances provide a relationship between
temporality and narrative as the most typical form of social life. For example, it is
impossible to understand a teacher’s existence without considering their intentions and
the setting in which their behaviour occurred. The setting of a subject department is
made up of practices, of individual histories that have evolved and make a social setting
intelligible. The identity of a teacher of mathematics is in the unfolding of a story that
is meaningful and purposeful. It is through an account of actions that a teacher
interprets him / herself in an unfolding narrative that gives meaning to their existence.
Ricoeur (1981) argues that it is through language that the moral agent is revealed. It is
in this revealing that the agent is positioned within a social and political moral order, in
a lived narrative based on their history and it is in this environment that they become
enculturated to the legitimate narratives that abound in a community of practice. To
continue on, as Bruner (1991) suggests, is to accept narrative as a part of our existence.
62
Presentation of function in narrative
1. Initial
situation
Introduction of the teacher hero: temporal, physical setting, and situation.
2. Preparation A rule in the form of an edict from “head office” to improve student outcomes in
mathematics is imposed on the teacher hero, in the form of a coach.
3. Complication The lack such as the numeracy results is made known and the teacher hero is given a
request to rectify the situation by working with the coach / donor.
4. Transference The hero uses the magical agentry provided by the donor. Represented as
pedagogical tools such as the “warm-up” activity or in the form of resources such as
the electronic whiteboard….
5. Struggle The initial misfortune or lack is put into proper perspective.
6. Return A difficult task such as the implementation of the Mathematics Lesson Structure is
set for the hero and the task is accomplished.
7. Recognition The hero is recognised by the subject department and or by the school’s
administration.
Characters in the narrative
• The teacher as hero.
• The coach as the donor.
• The pedagogical approaches presented by the coach as the magic agent.
• A helper supports the teacher hero, such as a teacher colleague, mentor, or a family member.
• The need to improve student outcomes represents the lack.
• The barriers to the improvement of student outcomes considered as the villain(s), which may
include the coach.
Table 2. Application of Vladimir Propp’s (1928/1968) theory of the “folk tale” to the teacher narratives offered in this study
63
Recapitulating, the teachers in this study were each storytellers recounting their
individual as well as group identity, situating themselves in a local moral order through
choices they made as they narrated. Episodes in the teacher accounts, framed within
their function in the plot line, (see Sally’s Initial situation, Complication and Struggle
p.70-77) assisted to keep them and their context in focus together, at all times, in each
episode, biographically bound in a conjoint dialectic of self-cultivation and cultural
appropriation. In this way the utterance makes a person who she / he is, for it hints to
the essence of their universal humanness providing a lens to their teacher self in how
they understand the world and of themselves within it. Episodes in the narrative
accounts provided by teachers in this study cast light on identity formation as emergent,
as a recursive process of transformation by way of a dialectic of agency and structure,
illuminating the dispositional power of self-as-process, one that is multifaceted and
uncertain. Agency, whilst limited by the capacity of their biography, temporality…
unfolds within an irreversible rhythmic context inherent within the narrative of the
practical and expressive orders.
5.6 Data analysis
The conversational interviews explore particular social episodes. The two approaches
taken to explore and illuminate further the ontological practice of teaching are semiotic
(Refer Figure 8, p. 40) and positioning theory (Refer Figure 9, p. 44). Practice let alone
teaching practice cannot occur without semiotic interaction, i.e., imagining what
improvement to teaching might look like and ways of going about this improvement.
The sign is dialogic, in that, it exists in the mind, and it also exists socially. The sign in
its many manifestations is therefore a window on how the mind interacts with the world
thereby representing something for somebody for it is through the sign that maintains a
connection to history and to society. Peirce argued that given that semiosis is mostly
social as action, semiosis points to the pragmatics of discourse and to its inherent
connection to an agent’s practice in a time and space all of which occur in a community
of practice (Hartshorne, Weiss, & Burks, (Eds.), 1931–1958). The teachers and coach
in this research are not only sign users but are also signs themselves both as constituted
in and through signs. It is with this in mind that the semiotic analysis brings to the fore
the myriad of signs that come into play in the everyday practice of a teacher of
mathematics. The signs, tools, artefacts and the like are internalised and become part of
the social actor’s worldview or umwelt. It is through signs / signing that an actor /
64
agent comes to identify themselves as teachers of mathematics casting light on their
identity.
Positioning theory also assists to illuminate the ontological practice of teachers.
Positioning theory locates the agency of an actor within their storyline in the context of
the broader narrative, that is, the culture and the time in which the episode took place.
Data collected was coded according to pronoun use thereby assisting to track the many
fluid positions an actor presupposes in day to day encounters assumed in relation to the
coaching / coached rule-role moral order or ethogenesis (Redman & Fawns, 2009). The
fine-grained pronoun grammar analysis (Mühlhäusler & Harré, 1990) was used to
analyse conversational interviews with teachers of mathematics in order to locate the
agency in their own story line.
The scope of this research
Table 3 schematically presents the ontological and phenomenological dimensions of social
activity after Nellhaus (1998, p. 19). The vertical column to the left outlines the general
ontological levels of society as Structures (Possibility), Agency (Actuality) and Discourses
(Semiosis). These ontological levels appear to the actor / agent through the material,
sociological and meaningful experience of practice and provide a way in which social behaviour
may be explored. For example, the Technical dimension describes how technical / material
reality predisposes an agent to behave in a certain way. What emerges from the Technical
dimension is a response by the agent to the disposition attributable to structures that either
facilitate or resist their operation in order to achieve their intended goals. This response is
achieved through reflexive monitoring on the part of the agent or agents since social practice
involves transformational interactions (transactions) between agents who hold different
positions and therefore different reflexive motivations; motivations based on social position,
biography, gender, interests, intentions…. Agents in a subject department as a community of
practice, whilst differentiated and holding various reflexive motivations act predominately
through meanings acquired through social interaction. It is through this socially created
meaning ascribed to action that influences an agent’s intention to act. Therefore, socially
created structures of meanings disclose how a teacher of mathematics acts in accordance with
their position within the school’s hierarchy and the given material resources at hand (Nellhaus,
1998). Given that “… the most characteristic form of human behaviour is the conscious
following of rules and the, intentional carrying out of plans.” (Harré & Langenhove, 2010, p.
65
19) it follows that semiotic and positioning analysis illuminates the way in which social actors
in a community of practice ascribe symbolic meaning to structural readjustment imposed by the
DEECD to their practice.
Phenomenological Dimensions of Practice
(Exploratory modes)
Material
(Technical)
Sociological
(Reflexive-
motivational /
Functional)
Meaningful
(Hermeneutic)
Ontological
Levels of
Society
(General
ontological
domains)
Discourses
(Semiosis)
Policies, Texts,
utterances, locutionary
acts of coach (material,
signs / representamens)
Illocutionary forces,
intended meanings in
coaching
Psychological
processes (inner
speech)
Power as ability to
choose, interpret, and
express
Discursive
articulations or
formations; reasons /
reasoning / ideology
of coach
Symbols
Agency
(Actuality)
Habits/habitus
Institutions,
organisations
Communities of teacher
interviewee
Intentions / Teacher
interview
Social interaction
Power as ability to act
Identities as self-
images, other images;
identifications of
teacher interviewee
Discursive and
performance strategies
Indexes
Structures
(Possibility)
Forces of production
(e.g., economic,
communicational)
Bodies
Social positions
Social relations of
production
Power as domination,
exploitation
The discipline of
mathematics.
Image schemata,
basic-level concepts;
pedagogical structures
Icons
Table 3. The Scope of the Research - Ontological and Phenomenological Dimensions of Social Activity after Nellhaus (1998, p. 19)
66
Pilot interview with Sally
The following “account” was selected based on three themes that emerged from a
conversational interview with Sally, a senior maths teacher and Key Learning Area (KLA)
coordinator of Mathematics at Skipper College with a purpose of providing an overview of data
analysis and presentation of findings. As at Lambertia and Grallina College a coach was
deployed by the DEECD to work with the Mathematics department at Skipper College to
improve its academic standing on nationwide tests. The interview took place on the 10th of
August 2009. Excerpts from her interview “account” are presented in sequential order with
conversational data omitted because of repetition. The sequence follows that of the plotline
functions presented in Table 2 after Propp (1928/1969). Here Sally interprets herself in an
unfolding narrative that gave meaning to her teaching existence and illuminates how identity
formation (self as process) may be used to analyse organisational reproduction and
transformation. The analysis commences with Gee’s (2000-2001) “four ways to view identity”
as it applies to Sally.
Nature
perspective
Institutional
perspective
Discourse
perspective
Affinity
perspective
A senior female. Teacher of mathematics
who shares a leadership
role with a colleague.
Role, duties and
obligations embedded
in leadership role are
more administrative
than constitutive.
Sally lacks agency,
overwhelmed with the
degree of change
perhaps fearful of
failure as a teacher /
leader and a loss of self
worth.
A teacher of
mathematics aligned
closely with colleagues.
Sally occupies a
position composed of
rights, duties and
obligations as a teacher
rather than that of a
leader of the maths
KLA. One based on
collegiality rather than
prescribed by an
institutional order.
Table 4: Sally’s discursive identity formation, after Gee (2000-2001) and Bullough (2005)
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Initial situation
Sally10 is a senior teacher and shares a position of leadership at Skipper P-12 College as the Key Learning
Area (KLA) coordinator of mathematics. Laura11 the Regional Coach brings a new set of resources.
Theme
“… Laura take us out of our
comfort zone.”
Semiotic analysis Positioning analysis
There has been a lot of positives
about having Laura here, she’s
had time to resource if we
wanted a particular lesson on
something she’s had time to
resource that lesson because of
the in-servicing she’s had from
the region12 she’s much more
skilled up on a lot of the
department things that are very
useful for us to use and know,
she sort of brings a different,
probably a wider perspective
than we have within the school
cos we have a certain view of the
way we’ve done things and the
way… we’d like to do things,
Laura takes us out of our
comfort zone and shows us new
things and heads us in different
directions.
Laura the Regional Coach
represents the social object,
indexed by to the instructional
improvement in mathematics.
The sign comes with qualities
such as time, resources,
knowledge afforded by the
DEECD.
This functions as a logical
proposition, a rule that joins /
establishes a relationship
between the sign (effective maths
teaching) to the coach as the
social object.
The surface effect is that Sally
feels obliged to perhaps adopt the
wider knowledge that the coach
brings however the underlying
effect is that Sally together with
her colleagues are being
redirected away from their
“comfort zone”.
Herein lies the first moment of
crisis and of resistance.
Laura is viewed as a positive
resource and rule bearer for Sally
and her maths department.
Laura is positioned by the
DEECD as the one that brings a
new teaching directive, skills,
knowledge and resources to
change current teaching and
learning practice that is different
from the current local practice.
Perlocutionary effect - Sally not
quite convinced that Laura brings
an approach that teachers are
willing to accept.
Sally uses “we” and “us” (first-
person, plural pronoun)
indicating a bond with teachers /
colleagues in her maths
department. Teachers of
mathematics are brought into the
conversation and share the same
10 Both Sally and Jess share the role of managing the Maths department at Skipper P-12 College. 11 Laura is the DEECD appointed Regional Coach. 12 The Western Metropolitan Regional office of the DEECD
68
moral obligation as Sally. In this
way, Sally positions herself as a
representative of the Maths
department rather than as its
leader.
[Laura would ask Sally] “Have
you used any Digilearn13
resources Sally? Have you
thought about doing the online
testing before you start and the
online testing afterwards…”
showing us new things we could
do, showing us new resources
and she also brings a regional
perspective. The region [is]…
now big on getting kids to write
about their maths. So Laura
[has] sort of given us indications
of ways we can go to stimulate
kids, to actually do that writing
so it’s a little more interesting for
them. The region wants to have
lots of literacy stuff in
classrooms so Laura [has] been
able to have time to [help]
develop some of that material
that we’re doing in classrooms.
We want to get glossaries in
books so Laura [has] started
doing [a] glossary wall… in one
of the 5 to 9 (middle school
classrooms) complex so she’s
been able to have time to do
those sorts of things... we were
keen to do “smart testing” which
is a Melbourne University project
Coach indexed to improvement
to the teaching of mathematics.
The coach is indexed to the
region, as having moral authority
to work with and change practice
for teachers at Skipper College.
The effect is immediate for Sally
sees the coach as the one that
comes with a message from the
“region” and is the one that has
the epistemic authority to do so
from the resources she brings.
Symbols presented in the form of
Digilearn resources, literacy
strategies, glossary wall… all of
which establish logical
propositions that further establish
an immediate effect of
improvement to teaching indexed
back to the contingent reality of
the classroom, i.e., of not having
enough time.
Coach positioned as having
authority to direct from “head
office”. The coach uses second
person plural to emotionally
engage Sally with departmental
policy indexing resources such as
Digilearn.
Sally not engaged. Lack of
agency as presented by use of
“we” and “us” reducing Sally’s
responsibility to the “it’s”, i.e.,
the method of stimulating
students with the use of resources
to enhance learning performance.
The coaching relationship
confirms Sally’s existential
world, one that is sandwiched
between the contingent and
exigent realities of the classroom.
The coach from the “region”
comes from a different reality
bearing resources that Sally
realises she does not have the
“time” that Laura has at her
disposal.
13 DEECD on-line teaching and learning maths resources
69
to do with testing kids online and
getting instant feedback Laura
[has] had time to resource that
for us.
Summary:
Sally recognises that Laura the Regional Coach has been given time and authority by the “department” to
institute a new pedagogical direction. Sally whilst recognising the value in what Laura brings positions
herself away from the coach and in line with her colleagues, perhaps as an indication of the ensuing threat
to her “comfort zone”, i.e., the traditional practice of teaching mathematics.
70
Complication
Sally feels overwhelmed with the “push” to change her practice of teaching mathematics.
Theme
“…you do feel push from the
outside to move you in different
directions that you’re not
comfortable with.”
Semiotic analysis Positioning analysis
We see that there are a number of
positives from having the
coaches on board and we’ve have
been very grateful for a lot of
things that Laura can do. There
are times when Laura is pushing
in regional directions and we are
not ready to go in those
directions… you do feel push
from the outside to move you in
different directions that you’re
not comfortable with.
Sally indexing coaching to the
improvement to mathematics
teaching.
The coach is a symbolic
representation of the “region”
(DEECD). The “region” is a
sign of authority. The authority
to articulate what is important to
teach students and how to teach
as to effect improvement in
student learning.
The effect of which is to change
the practice of teaching
mathematics (a new social
order). This of course places the
local moral order in conflict with
the “region”.
Storyline of change as directed
from the “region” is an imposing
force and Sally feels
disempowered for she doesn’t
have ownership of the change
process.
Sally uses “we” (first-person,
plural pronoun) indicating a bond
with her colleagues. Teachers of
mathematics are brought into the
conversation thereby reducing
Sally’s responsibility to the
change espoused by the coach.
In doing so, Sally speaks as a
representative of the Maths
department rather than as a self.
Sally’s use of second person
pronoun “you” to engage the
researcher as teacher to index her
emotional engagement creating a
dramatic effect of resistance to
the push from the DEECD.
We’ve always been a fairly
traditional maths area and while
we may do problem-solving and
while we may do, you know, use
Two sign systems in conflict.
The first is the traditional
approach, one that indexes good
teaching practice and its
Sally’s sees her position
(epistemic and moral authority),
as KLA coordinator undermined
through the edict from “head
71
other resources we’ve relied a lot
on our textbook and Laura [is]
trying to move us away from
relying so much on the textbook
so that’s one of the conflicts that
has been brought in and that’s a
regional push.
relationship to a textbook.
The coach indexes the second.
The effect of which is
problematic for the coach brings
a linguistic turn to problem
solving as the preferred practice /
sign as opposed to the meaning
ascribed by Sally to the textbook.
office” that the traditional form
of teaching is no longer valid.
The story line of a challenge to
the existing teaching practice; a
tradition that is important as
emphasized by the use of the
collective first person personal
and possessive pronoun use.
There [have] been a whole lot of
materials developed scaffolding
numeracy resources, which are
department based, and there’s a
lot of problem-solving material
that comes with that and we’ve
been directed, pushed in the
direction of using that material. I
guess there’s a conflict between
changing from what you’ve done
to change into new things, so
that’s where the difficulty comes
at times.
Sally speaks reflexively about the
signed meanings in the proposed
change to instructional practice.
On the one hand she indexes the
material objects offered by the
“department” (DEECD) to good
teaching practice affording the
opportunity for change to occur.
Whilst on the other hand Sally
acknowledges the traditional
approach to teaching as good
practice. The contradiction
places difficulty upon teachers
shifting their practice particularly
if the change is imposed by the
DEECD.
Story line of conflict as a
consequence of difficulty
experienced by being
repositioned into a new paradigm
of teaching mathematics, one that
is directed by the “department”.
The second person pronoun
“you’ve” addressed by an
outsider, presents a corrupting
view of what has traditionally
occurred at Skipper. The
personal attainment /
commitment is ignored as a
consequence of the imposition
that the new paradigm brings.
There’s a lot of inertia… no I’m
not confused about what I want
to do but there’s a lot of inertia
there. This is the way we’ve
done it and we’re comfortable
with this and we don’t want to
change so and it’s more the
inertia of because of what people
have been doing and what their
perception of maths are rather
than…
Traditional approach to teaching
maths indexed to good teaching.
The logical effect is one of
inertia, i.e., a consequence of
having to view traditional
approach as not indexed to good
teaching.
Sally remains clear about what
she feels is important with
respect to the “good lesson”.
Sally holds an ambivalent
position as belonging to the
maths department in the way
maths has traditionally been
taught and then away from her
colleagues for they are
comfortable with their style of
teaching and consequently
72
resistant to the efforts currently
being made to change their
practice by the DEECD / coach.
I think Maths of itself is a very
structured subject and people like
to have it tied down and know
exactly where they’re going and
what they’re doing and the
textbook is an easy way to do
that.
Mathematics is a structured like
discipline indexes the textbook
that is also offers a structure that
makes teaching it
comprehensible and warranted.
The effect is energetic for to
teach mathematics requires a
structured program, one offered
by the textbook, in order to teach
it well so that students may learn.
Sally positions herself as not
belonging to her colleagues for
they have their own way of
teaching mathematics. Teachers
of mathematics need to control
the domain. Using the textbook
allows them this control.
Summary:
Sally feels overwhelmed with the change imposed by the DEECD and positions herself away from the
coach and the coaching program. Teaching mathematics using a traditional structured approach services
the need to get through the curriculum pointing to the local specific exigencies of the classroom.
73
Struggle
Sally struggles against the existing on-site approach to professional development
Theme
“…up until this year that’s not
been done before and so KLA
meetings are really about
teaching that good lesson.”
Semiotic analysis Positioning analysis
We would just share things
informally with each other so I
would say to my colleagues’
“I’ve got this great new lesson
and I’ve done this with my kids
and this worked” and then we
would pass it around informally
from person to person, there was
no structured way in which we
were sharing things that we were
doing and lots of people do
innovative different things but
the structure for sharing it wasn’t
[there]…
The “… good lesson…” (sign)
indexes learning, the effect of
which is a sense of achievement
which provides the necessary
evidence that the sign is morally
justified, which leads to a moral
act of sharing this sense of
achievement with others.
Locally initiated “lesson study”
sign indexed to good teaching
practice is introduced as a
comprehensive alternative. The
energetic effect of which is
evident in the way that teachers
participate in sharing a “… great
new lesson…”. The weakness is
an absence of structural support /
time to meet.
First person pronoun use
indicates Sally practice in
enacting what it means to teach
well.
Positioned as both a KLA
coordinator and as a maths
teacher she describes the
storyline of the “good lesson” as
one that is tried and tested and
passed on to colleagues to
perform.
Sally’s practice emanates from
the exigent realities of the
classroom.
There were KLA meetings, but
rarely, you get so much passed
on from [the] school
administration that you have to
do, that rarely does a KLA
meeting get down to the level of
the lesson and the good lesson.
KLA meetings in the past
indexed to a focus away from
teaching and learning. That is,
the KLA meetings have
encouraged a shift away from the
modelling of the “… good
The KLA meetings in the past
did not value the “… good
lesson….” Use of first person
plural indicates the informal
approach of passing the “… good
lesson….” Sally as the KLA
manager and the KLA that she
74
We’ve started this year
modelling what we think are
good lessons or good activities
for classes and doing that in KLA
meetings but up until this year
that’s not been done before and
so KLA meetings are really
about teaching that good lesson.
lesson…”. manages are not afford moral
authority in the improvement of
practice.
Summary:
Improving the practice of teaching involved passing the “… good lesson…” around to colleagues to try in
their class. The school did not sanction the regular KLA meeting as the place where improvement to
practice could take effect, for time was taken up with administrative items. Sally positions herself as a
frustrated leader and teacher of mathematics with respect to the specific local exigencies of the classroom.
75
The above analysis outlines the difficulty Sally found in constituting with her colleagues social
objects (tasks, tactics, plans that had shared meaning to which they had commitment) and by
which they could negotiate their teaching world in the face of the “absurd” expectations of state
norms incorporated in the P-10 continuum and testing required. Themes that emerged provide a
narrative of teacher practice that is balanced between her purposes and necessities in the form of
specific local exigencies and contingencies of the classroom. She had a narrow “comfort zone”;
where any move away from what she knew and understood was met with anxiety. Formal KLA
meeting agendas stultified reflection on practice. Self-improvement in practice rather relied on
a chance meeting with a colleague in a corridor. The positioning analysis further illuminated
the position of power held by the coach installed from “head office” as the one that was
responsible for effecting change. The coaching program was positioned outside the everyday
reality of the classroom.
Issues of trustworthiness and other limitations in this study
This approach rejects the conventional positivist notion that a reality exists external to our
perception of it and that validity therefore should be concerned with the “truth” or “falsity” of
an observation as it relates to this reality. This study has limits as they relate to the common
critiques of qualitative research inherent in this study’s overall research design based on
collaboration with 8 teachers in 2 schools. Careful thought has been given to accounting for
these limitations, as too in minimising their impact on the applicability or validity of this work.
No eligible teachers were excluded from the research and every teacher approached agreed to
participate. Whilst there are a number of limitations to do with the limited time frame of the
data collection and the small scale of the study, the issue of researcher subjectivity is perhaps
the most important given the researcher’s own perspective as a former coach across primary and
secondary schools although never in the study schools. The overriding concern in this instance
may be that of researcher “bias” as it pertains to actions assumptions, perceptions, and views of
the teachers’ in this study, the Regional Coach and respective school administrators. This
concern may be focused on the conversational interviews; questions posed prompted by prior
perception or issues raised by subjects that were left unquestioned based on unqualified
assumptions. Participants could have been providing less than candid responses to questions
raised.
76
With these limitations in mind, the researcher took several measures to validate and authenticate
the teacher’s accounts and their analyses. The research agenda was stated at the outset to all
participants, where the transcripts of all interviews were checked against the original recordings
and then provided to all participants to verify accuracy and to make any further comments. The
positioning and semiotic analyses were scrutinized by advisors and also by peer group review.
In addition, multiple data sources were used as indicated in an effort to better understand and
represent discursive circles in each school. Finally, given that formal objectivity is impossible
to achieve in such research, the researcher’s extended experience in schools was important in
responding to and sustaining the research conversations and interpreting colleagues intended
meanings.
Thesis structure
This thesis is organised into seven chapters and explores teacher professional learning through a
centrally initiated policy to improve the instructional practice of teachers of mathematics. A
social-psychological approach is used to frame human behaviour as the interplay of agency and
structure played out in a time and space continuum. It is in the psychosocial world of the
teacher of mathematics that the local moral order was explored bound by a history that preceded
them and from which they ordered their social world constructed meaning and negotiated
external expectations.
Extracts from a pilot study demonstrate the approach developed to explore moral contexts in the
intentional action of mathematics teachers from both government secondary schools as
presented in Chapters 4 and 5. The research to this end explores the ways in which a teacher of
mathematics is made active by positioning and signing in the myriad of networks that exist in a
secondary school context. Chapter 6 reviews the discursive analyses and presents a
transformative model of the dual praxis of teachers’ social action in a subject department as a
discourse community.
The dual praxis is their socialization and their reproduction of transformation of society.
Collaborative mentorship is offered as a generative mechanism / enabling condition, one where
agency is conceived and collectively realized in the community of practice of the subject
department, one where teacher practice may improve through a process of inquiry. Finally,
Chapter 7 presents the conclusion. This chapter reflects on the guiding research questions
presented in Chapter 1 and the significance of the research.
77
4
Lambertia College
“… we need to improve our numeracy more than anything else… that’s probably really
really low…. They’re coming in very low, but their [teachers are] not working to,
we’re not working to improve that as much as we should… ”
Maria Oslava principal of Lambertia College
Lambertia College is a Year 7 to 12 state government secondary college located to the north of
the Behriana township and situated in a developing residential area that was, until the 1970s,
largely rural. The college was founded in 1986 and had at the time of this research an
enrolment of approximately 800 students. Students were predominantly from English-speaking
backgrounds and approximately 40% come into the college with lower than expected levels of
literacy and numeracy. In 2009 the student enrolment in Year 7 was 116 a steady decrease from
a high of 209 in 2001. The decrease was not due to a change in the number of the grade six
cohort in feeder primary schools but rather reflective of local community perceptions about the
school. Lambertia College offers a broad curriculum but unlike Grallina College does not have
a Select Entry Accelerated Learning program (SEAL1). The college is designed along separate
faculty buildings, structured along senior and junior schools and a newly built flexible open-
plan learning space that encouraged inquiry-based and differentiated approaches to learning.
Lambertia offered a traditional curriculum structure and domain specific meetings were held on
a regular basis after school. Science and maths meeting were scheduled on at the same time
where teachers would attend one over the other based on their teaching time fraction or interest.
Whilst there was no maths staff room / department, maths teachers at the time this research was
undertaken were relocating into one room, in line with the implementation of the Mathematics
Lesson Structure. Finally, Lambertia promotes a student culture of continual improvement as 1 The Select Entry Accelerated Learning (SEAL) Program is currently offered in 36 Victorian secondary schools. The SEAL
program addresses the learning needs of academically gifted students offering an accelerated in depth study of core subjects. Students usually complete Years 7-10 in three years.
78
demonstrated with the reintroduction of the House system that supports student participation in
extra curricula activities. This was evident in the school newsletters and data2 collected at the
time of this research, demonstrating a commitment to the fostering of strong relationships
between teachers, students and the community.
The quantitative data (Appendix 4) shows how teachers in this sample subscribed notionally to
the idea that professional development was best provided in their community of practice for it
was here that they could share their experiences and feel supported and validated in the process.
For example, teachers did not value nor did they source professional development provided by
school administrators, attend off-site workshops, research teaching and learning approaches on
the Internet, and or appreciate coaching. Rather, teachers valued working collaboratively with
their peers, viewing this approach above all else as important to the improvement of practice.
Samantha, the Regional Coach
The Western Metropolitan Regional office (WMR) of the DEECD recruited both literacy and
numeracy coaches in 2007 as part of its reform program known as the WMR Blueprint for
School Improvement (DEECD, n.d.). The development of the program involved extensive
consultation with stakeholder groups and was in part a response to the region’s poor
performance in student outcomes and staff morale (Pettigrew, 2010). Coaches were recruited
from the teaching pool in the middle of 2007 and inducted into the role of coach. By the end of
the 2007 academic year, coaches were deployed to schools. Samantha was deployed to
Lambertia College in 2008 as her first coaching assignment. In 2009 she continued her
coaching work at Lambertia but was also assigned to Grallina College, working at both colleges
on alternating weeks. Samantha’s coaching repertoire was developed and supported by ongoing
professional development provided by the WMR of the DEECD. Although chemistry trained,
Samantha drew from her 21 years of teaching mathematics3, on-line Mathematics Continuum
teaching resources, and supportive coaching network to assist in her work as a Regional Coach.
Like all coaches she was expected to report “informally” at Principal meetings in the schools
she coached in.
The Principal of Lambertia in 2008 was Jim Perrycoat who would retire at the end of the 2008
academic year replaced by Maria Oslava who was appointed Acting Principal and later as
2 Attitudes to School Survey, Staff Opinion Survey, and Parent Opinion Survey. 3 From the time of this research in 2009
79
Principal. Samantha worked closely with the maths coordinator and commenced the coaching
program by administering the Scaffolding Numeracy in the Middle Years program4 as a method
of engaging maths teachers with the coaching program. It was envisioned that the student data
generated from administering the Scaffolding Numeracy in the Middle Years program would
engage teachers in the coaching program in order to improve student performance. This
approach formed the initial stage of the coaching program, the aim of which was to strengthen
the organisational capacity of the Maths department through the use of data. Whilst the
coaching program was met with resistance in 2008, the introduction of the Mathematics Lesson
Structure, PLT meetings and school-based coaches in 2009 appeared to have established some
traction for change in recasting the practice of teaching mathematics.
The coaching program didn’t “take off” as anticipated for the private tradition of maths teaching
at Lambertia, together with the teaching culture were perhaps the obvious inhibitors.
Samantha’s difficulty at Lambertia in engaging and encouraging a cooperative coaching
program in the maths department may also be attributable to the inherent ambiguity in her social
position as a quasi-inspector for the DEECD weakening her moral authority and capacity to
coach for school improvement. In addition, Samantha alludes to the contingent realities of the
class as another reason for her difficulty in engaging teachers with the coaching program. For
as Samantha said,
“… I’m finding the resistance, I’ll be brutally honest, it’s to do with laziness… in
that… the job isn’t a high priority, it’s a job and they have to be there and fair
enough, you know, I understand that… and so if I ask them to document their
lessons, I’m giving them extra work to do because it’s something that they don’t do
they go in with a textbook they teach out of the textbook on the spot without any
planning. So if I’m asking them to plan, I’m giving them extra work to do and they
don’t want to do extra work and so I can understand the resistance in that they’re
walking into work at 8:30 walking out of 3:30 not doing any work at home and…
feel that they’re working hard because they have a hard time with the kids and they
probably don’t want to think about school when they’re at home. So I do I
understand their resistance… the teachers feel totally unsupported and they feel
with the changes in leadership and the leadership that’s been there for the last few
years… the morale is low as it can go. Teachers feel like the clientele, they don’t
have a belief that the kids can learn that’s a big problem is that id doesn’t matter
4 The Scaffolding Numeracy in the Middle Years program was an Australian Research Council initiative between the Victorian
Department of Education and Training and the Tasmanian Education Department from July 2003 to June 2006.
80
what I do these kids can’t learn and so I may as well give up, why should I work
hard for these kids…”
This up-hill battle was the reality that Samantha faced in her first coaching assignment at
Lambertia College.
Maria Oslava, Principal of Lambertia College
Maria Oslava was a newly appointed Principal of Lambertia College in 2009. Maria did not
rise up from the ranks of Lambertia, but rather appointed from outside, having worked as an
Assistant Principal in another secondary college in the Western Metropolitan Region of
Melbourne. Maria’s tenure commenced after the previous principal had set the school structure
for the 2009 academic year, leaving Maria with a set curriculum and timetable structure with
“little room to move”. In her first year, Maria faced
“… a bit of a challenge with staff… trying very hard to change… the capacity of
the teaching cohort… trying to build it to become more [of a] 21st century learning
environment… having a lot of teachers that are very traditional in their way of
presenting to kids and… some of the kids just don’t connect really well with that
and…. [2009] is the first year of the new Strategic Plan , we’ve introduced several
coaches as part of the Leading Teacher5 role…”
In doing so, Maria set her sights on changing the teaching culture of Lambertia. For example,
Maria, herself a science trained teacher of mathematics realized the merits of teaching to a
differentiated approach, and encouraged the Regional Coach to plan a program for
implementation with teachers of junior mathematics. The differentiated approach was a move
away from the traditional reliance on using the prescribed textbook to engage teachers to trial
another approach of delivering mathematics to students. In preparing for the differentiated
approach, the teachers of junior mathematics were released from scheduled classes to plan with
the Regional Coach who worked at Lambertia on a weekly rotational basis. Teachers were at
first encouraged by the differentiated program; however, it required a commitment that they
were not familiar with, one that strayed from their traditional private world of teaching.
Despite the set back, Maria was adamant that something had to be done for as Maria explains,
5 The Leading Teacher classification is a stage in the career structure for aspiring classroom teachers. The classification encourages
teachers to consider positions of leadership and management commensurate with a salary range.
81
“… we have a lot of our kids that come from the primary schools with very very
low numeracy skills, so there’s no point getting the Year seven [mathematics text]
book and an you know starting Algebra when the kids don’t have… the skills to
multiply and divide, they [teacher’s] don’t understand that they [students] have no
concept of that, you need to start where the kids are at and that is now become a
real focus with the teachers and the program….”
As a result, Maria restructured the timetable for the 2010 academic year to encompass the sixty-
minute period as proposed by the authors of the Mathematics Lesson Structure6. In addition,
Maria envisioned that
“… the Year 7 program… [is] going to be on a volunteer basis and the
expectation’s going to be very clear, and certainly for the teachers that were in the
program this year… we gonna be talking to them about the fact that they have to
prepare, and they have to, and it’s just as important, and you can’t just rely on the
textbook because it’s not engaging enough for the kids and most times you’re not
connecting with the kids learning.…”
Maria’s vision for reform had a moral basis in attending to students who arrived at Lambertia
College without the necessary skills as confirmed by data. Her goal was appreciably to reverse
the trend, changing the structure for the 2010 academic year. The Regional Coach together with
the school-based coach and the Mathematics Lesson Structure were thus positioned as change
agents for implementing a new institutional order.
Tony Roma, Lambertia College7
Tony Roma, a fourth year maths science teacher held the role of Student Manager at the time of
this research. Tony was encouraged by the previous administration at Lambertia College to be
trained as a coach and to administer a coaching program that was terminated soon after. The
experience left him disillusioned, perhaps resentful, given the appointment of a Regional Coach
to Lambertia College in 2008. Tony did not participate when the Regional Coach and the maths
coordinator administered the Scaffolding Numeracy in the Middle Years program to his junior
maths class. When later provided with the results Tony was dismissive for he felt comfortable
with his own repertoire appreciating that his teaching was varied and “pitched” to his students 6 Refer Appendix 1 7 Interview 1 – 17th Nov 2009. Interview 2 – 24th Nov 2009. Interview 3 – 11th Dec 2009.
82
and that data did not indicate anything other than what he already knew. Tony felt that the
coaching program did not allow for dealing with the everyday contingencies of the classroom
denying Tony of his epistemic authority as a teacher of mathematics and also perhaps even
denigrating his position in the local moral order particularly given that he was once trained as a
coach.
By the end of the 2009 academic year, Joel Hindrict, a maths consultant was invited to deliver
an on-site professional development (PD) session in preparation for the implementation of the
Mathematics Lesson Structure in 2010. This session engaged Tony and his colleagues. Whilst
it may be viewed that Tony’s engagement with Joel, rather than the Regional Coach, was
perhaps brought about by gender differences, it stands that Joel’s PD to the maths department as
a community of practice had an effect on Tony’s practice. The effect perhaps as a consequence
of a discourse community led by a significant other, inviting teachers of mathematics to a
conversation related to “warm-up” activities. Tony indicated that he was excited by the
presentation; he was excited by the experience of seeing his colleagues engaged in the
presentation, and as a result applied a strategy to his own Year 7 maths class. According to
Tony, the Regional Coach together with the coaching program were not constituted by
discursive practices within the local moral order, but rather imposed and as such did not assist
him to recast his teaching practice. It was only by way of discursive practice with colleagues
where teaching experiences were traded based on artefacts presented by Joel. It was in this
place, space and time that Tony felt the “energy” that contributed to a transformation of his
practice.
The junior teachers of Mathematics involved in this study are Tony Roma, Josh Ryan, Sarah
Farqua and Peter Milios. Tony’s experience follows, whilst Josh, Sarah and Peter’s accounts
and corresponding analyses are located in Appendix 9, 10 and 11 respectively.
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Tony’s self / identity analysis
Martin argues that an individual’s subjectivity has its source in objective reality (2005). This is
made evident from Tony’s “accounts”, one that reveals a perspectival self that is constituted
through social encounters emergent from two temporal psychological perspectives. Martin
defines a perspective as “… an orientation to an environment that is associated with acting
within that environment” (2005, p. 234). Perspectives emerge from an individual’s interaction
with the world. As we see with Tony, his self is emergent on the one hand as an active agent
represented by the Meadian “I” and on the other, as a repository of perspectival understandings
as represented by the “Me”. The self thus emerges from both temporal perspectives, from “…
both the achieved wisdom of the past and the agentive cultivation of the future” (Martin, 2005,
p. 238). It is in the “immediate moment of action” where the “Me” and the “I” are
simultaneously present in dealing with a current concern, one that brings past recollections of
activities to the fore in dealing with an anticipated future (as cited in Martin, 2005, p.238). This
is brought into focus using Gee’s (2000-2001) self / identity analysis as represented in Table 3
to show how Tony’s identity functioned in the context of the coaching paradigm.
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Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
Natural identity of controlling / competitive athletic young male.
Tony viewed by institutional order as competent, one that can follow rules, and get the job done. Appointed first to “role” of coach and then to that of a Student Manager.
Viewed as competent in dealing with student concerns / conflict. Strict in performing to “role” expectations based on role of Student Manager.
Approachable by staff with respect to dealing with student issues. Viewed as nurturer by intern he supervised in 2009, for Tony is very friendly and helpful as mentor.
Conversely as coach perhaps not viewed as a sensitive counselor, given his limited tenure.
A helpful individual by the administrative staff, parents.
Perhaps viewed as misogynistic / indifferent by the coach and maths coordinator.
Competent member of the teaching staff who teaches maths and science.
Member of leadership team with respect to student management.
Administrators and teachers alike view Tony as one that has the ability to control and manage students.
Tony sees himself as a manager of students for he decided this himself.
Table 5: Tony’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
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Orientation
Tony is a fourth year teacher who majored in science and education. He holds a position of leadership at Lambertia and was trained in his second year as a coach.
Theme
“… being a science teacher it comes hand in hand that you need to know a little bit about maths…”
Semiotic analysis Positioning analysis
1/28 ... I didn’t want to be a teacher… I never really liked my teachers back at school.... [I] wanted to be a stunt actor, believe it or not… I was always into fitness and always liked, you know, [to] put my body on the line… and be active and all that sort of stuff and… when it came to the crunch and I had to pick… subjects... the subjects with the human body… were the ones that interested me, so biology and… PE (Physical Education)… and so all those sorts of subjects interested me…. I had to do the respectable... European thing and… work hard to get into a… university and make my family proud.… I applied for the Human Movement courses to get into… PE not to be a PE teacher but just to get into PE. I didn't have the marks to get into Human Movement… and so I had to go for the next best thing, still to do with biology…. A... biology... degree rather than a Human Movements degree... and I said… why not do a... double degree and do education at the same time. So it was... science and education…. I… became a
A tertiary course indexed to emerging personhood becomes the object of a further semiosis such as family honour, relegating human movement to the realm of the personal, and possibly missing out on a Human Movement course all of which may have had the effect of encouraging Tony to enter teaching as a vocation.
8 The number preceding the forward slash represents either interview 1, 2 or 3. The number after the slash represents the turn taking
account number in the conversational interview with the researcher.
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science teacher… it wasn’t a stunt actor, it wasn’t a PE teacher, which would have been the next best… thing, it was a science teacher.... During my [teaching] rounds... I started to enjoy science a lot more.... I knew that it was probably easy for me to do science and teach science and enjoy it… with the kids a lot more and… get involved in all those experiments than to do something like... PE where I have to have the whistle in my mouth all the time; I’d... you know… have to have the kids running wild out there in the open.... I… saved all that sort of stuff for myself in... that… I like to keep fit… but in my line of work I prefer to be a… teacher in the classroom. Being a science teacher, it comes hand in hand that you need to know a little bit about maths. So coming into… my first job as a secondary school teacher, it was science and you’re gonna… take on junior… maths whether it was Year seven or eight. First year it was Year sevens, the second year was both Year sevens and eights and then the following year it was... just Year eights and now this Year it’s back to Year sevens...
A further semiosis of science teaching indexed to teaching mathematics. The effect of which is energetic for we find Tony as a science and maths teacher.
Tony has taught at Lambertia College for the last four years. He holds a middle management position and is mentoring Josh through the VIT9 registration process.
Throughout this account, Tony’s use of first person personal pronoun indicates that he speaks from the authority of self periodically positioning the researcher (“you know”) in agreement with his “teacher talk”.
Summary:
The account outlines Tony’s reasons for deciding to teach as a vocation.
9 VIT – Victorian Institute of Teaching is a statutory authority to regulate the teaching profession established by an Act of the Victorian Parliament in 2001. Graduate teachers are required to undertake a structured induction program.
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Preparation
A sense of ambivalence surrounds Tony’s predisposition to the coach.
Theme
“… that’s the first thing that came to my mind, oh yeah, a teacher who’s done some training in coaching, big deal…”
Semiotic analysis Positioning analysis
1/66 ... when… I first… met Samantha [she] was… another teacher, another person here at the school, who is… here to help, never really thought [of] her… as a… coach, never thought of her as anything bigger or stronger or anything that can change a maths program, just sort of as another person. It’s probably not until… early this year where there was a big push [from the administration] for the Year seven program and let’s get this Year seven [maths] program up and running and… Samantha’s really stepped up to the plate and she’s been more… a coach then… I would’ve had her last year. Last year… her role was with another teacher [the maths coordinator], they would come into your classroom once a fortnight and assist with… the class…. They would do not games but… they would come into the classroom and they would get the kids involved with activities. They would collect... certain books that they had for the kids and there was a different activity that they would do with the kids every... fortnight or what ever it was… because they had to get around to all the… same level maths teachers…. At that point it
The coach indexed to a person who has little moral authority in the local moral order. The immediate interpretant is that of recognition that a coach exists.
The sporting reference of “stepping up to the plate” (iconic representamen) positions the coach as an immediate social object who has performed to a perceived perception of what coaching meant to Tony, demonstrating Samantha’s credentials and accepted as a coach by Tony; a logical interpretant.
When the coach worked
Tony positions himself in the local moral order as a leader / hero / protector of his students. He faces a challenge from the coach realising the “magical” agentry that she bears. The “magical” agent reveals the “lack” when students become engaged with the practice that the coach brings to teaching mathematics.
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was like… this is just an extra… part of the curriculum, it wasn’t anything which… would’ve help[ed] my kids... but there… wasn’t the… direct link with what I was doing with my kids, topic wise.... It was just every now and then we’d have an extra person in the room and we’re doing a different activity and… let’s get together and… let’s try to make maths a little bit more engaging and that’s what it was, engaging.
with the maths coordinator in Tony’s class, the coach brought with her an approach that engaged students with their mathematics. This hinted to an intransitive dimension; a window that perhaps referenced an ontological dimension of mathematics teaching that Tony indexed as engaging student with their learning.
This perhaps had the reverse effect on Tony for it strengthened his already existing teaching habit given that the coach was working outside of the current curriculum paradigm.
This may have had the reverse effect for Tony indexed Samantha as not working to the rules ascribed to what it meant to be a coach (immediate interpretant). It was only when Samantha led change by bringing the teachers of junior mathematics together that demonstrated that she was able to “step up to the plate”.
Pronoun grammar use indicates a distancing away from the coach through use of third person singular feminine and neutral. Despite this, Tony has a paternalistic approach to his students positioning himself as belonging to them (“my kids”).
1/74 ... it means absolutely nothing… I did a coaching course, it would have been about three years ago.... The school sent me to do a coaching PD and it fell flat on its arse and when I say [it] fell flat on its arse... they send three teachers... I was probably the most experienced out of the other two and this was going back
Tony selected and trained to be a school-based coach. The position of responsibility was short lived for there was no corresponding structure to support coaching at Lambertia. As a consequence his coaching role came to a premature end leading to scepticism and resistance to the new
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three years ago so I’ve only had one year experience at the school and I was sent as a coach and the idea was that we come back to the school and we [would]… get into people’s classrooms and we’d go through all these... formats of, you know the post... interview, the… prior interview and… we were... helping the person [teacher] in the classroom, they would open up to us and let us know what their problem was, all that sort of coaching…. I… didn’t enjoy it… and then when I came back to the school and it’s like well now… that you’re a coach... good on ya... what… are we going to do from here, absolutely nothing! I… felt like it was a real waste of time. So when… I hear here’s another coach... once again… that’s the first thing that came[s] to my mind, oh yeah, a teacher who’s done some training in coaching, big deal, honestly…
The coach is iconically related to a conceptual program of pre-coaching, observation and post-coaching. The immediate object hints to the transitive dimension at improvement to teaching. The effect is an immediate recognition of coaching as an on-site PD approach.
Tony’s personal experience of training to be a coach and then of coaching iconically acts as the sign in its relationship to Samantha as social object of coach.
The effect is energetic for Tony behaves accordingly in rejecting outright the coach and the coaching approach brought to his practice.
coaching model. As a result, Tony talks from the authority of the self and positions the regional coach and the coaching program at a distance as something that has little value.
Tony positioned as teacher “hero”, particularly so given that it was in his second year that the School’s administration selected him to be trained as a coach. This is confirmed for he positions himself closely to the senior members of staff who are also selected by the School’s Administration to be trained as coaches.
Tony return prematurely back to the classroom, perhaps losing his status as a heroic figure amongst his contemporaries. He bears ill feeling as a result and thus positions the new coaching initiative as a failure.
Summary:
Tony’s initial attempt at coaching failed to materialise thereby weakening his hero status within the local moral order. He feels resentful of this and relates his sense of loss to resisting the advances of the Regional Coach who is really a “trained teacher” and also to the coaching program that will also not amount to much. Tony’s cynicism positions him away from the coach and the coaching program, all the while positioning himself closer with the students in his care.
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Complication
Ambivalence of the role of the coach and of coaching.
Theme
“I… like to think that… a coach can also be a person…”
Semiotic analysis Positioning analysis
Context: Tony is referring to the previous year’s initiative when the Regional Coach worked with the Maths Coordinator to implement a problem-solving program that tested the mathematical ability of students. Student performance data collected was provided to teachers in an attempt to assist them to focus their teaching on where their students were at with respect to their learning.
1/170 …. If I… have my… Year seven maths class and I’m gonna be putting board notes up every Monday… for 15 minutes… maybe jumping to some times table work for another 10 minutes… and then maybe exercises out of a book, finish up with some reflection, that’s fine. I’m not because Lucy (Maths Coordinator) and Samantha are doing activities, I wouldn’t then turn around and say, you know what, from now on every Mondays and Tuesdays we’re gonna do activities just like Samantha and Lucy are doing because that would take the focus off what they’re doing, that’ll make what they’re… trying to present to the class probably a little bit dryer because the kids are doing it every single maths lesson and they need variety and I was happy for them to come into the class and provide that variety but I wasn’t gonna take that variety away from them by doing the same with my class every single lesson…
In this “account”, the immediate objects the Regional Coach and the Maths Coordinator are indexed to an institutionalised approach to teaching mathematics.
Tony distances himself from this approach indexing it to a lack of “variety”. Tony is resistant to the advances made by Samantha and Lucy to change thereby strengthening his teaching resolve (energetic interpretant).
Tony’s justificatory / contradictory description of his approach to teaching mathematics is presented as meeting the needs of his students. He feels that his practice engages his students and to follow the program as demonstrated by the Regional Coach and the Maths Coordinator would deny him of his moral authority in the local moral order.
Pronoun grammar use indicates a distancing from the maths teaching program as demonstrated by the Regional Coach and Maths Coordinator whilst positioning himself as belonging to his “kids”.
1/292 … that’s where my other Tony indexes coaching to
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problem lies with coaching. I know that a coach should be basically another pair of eyes [in the] back of the room… helping you reflect on your self… where they can obviously help students who need assistance, I think… that’ll be the minimum… but… you know, I… like to think that… a coach can also be a person and when I say it can be a person… if you… as a teacher [are] having problems… the coach is there to help you self-reflect, sometimes you don’t have time to self-reflect right there and then if… there’s another person in the room, another adult, another person… who can take some sort of control over… a situation… then yeah step up… to the plate and… that’s what’s missing from a… lot of coaching roles and I’ve seen a lot of coaching roles out of the maths department.… I’ve seen coaching roles take place throughout the school because we’ve got, you know, coaching spread… not only through numeracy but other coaches and the feedback that I’m getting from teachers is “oh… they didn’t really do anything, they just… like they were assessing me” and… that… shouldn’t be the coach’s role, it’s not assessing you it’s helping you reflect on yourself and a little bit of assistance, a little bit of standing by someone’s side… can also… help… ease any sort of tension.
supporting and improving teaching practice through a process of reflection and in-class support. The immediate object hints to the dynamical, that is, of a real object of reference in the world of teaching, of classroom support and collegiality in the improvement of teaching practice. The effect of which is immediate for Tony whilst recognising the coach and the coaching program has merit he is relatively sceptical of the current institutionalised approach and therefore remains resistant to the idea of being coached and of the coaching program.
To support his stance Tony indexes coaching to teacher appraisal. The effect of which is energetic for it weakens his view of the coach and of coaching even further.
In this “account” Tony views the coach as a social object analogous to a therapist, personal trainer, even as an inspector / assessor of teacher performance. Whilst Tony abhors the latter he senses that teachers would benefit from a coach.
Tony presents a narrative of teacher improvement and support by a caring individual as coach. For example, a coach would assist teachers to reflect on their practice as well as lend a helping hand in times of need. Tony refers to this aspect of coaching as the “that”
Tony positions the coach as “villainous”. He sides with his colleagues in a master narrative that coaches do little and serve an institutional function of assessing teacher performance.
Tony’s pronoun grammar distances him from the institutionalised form of coaching experienced and positions the researcher as agreeing with his “teacher talk”. That a coach provides classroom support at the same time assists teachers to improve their practice by way of reflection.
Summary:
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Tony resists the advances of the coach to improve his practice perhaps feeling that to do so may compromise his teacher status within the local moral order. Despite this, he feels that a coach must be a “person”, one who works along side classroom teachers, one who displays a supportive role in the class what ever the need and one that assists teachers to reflect on their practice. This is the type of coach Tony prefers, one that has a constitutive “role” over one that has an institutional mandate.
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Transference
A maths consultant captures Tony’s imagination.
Theme
“… he [Joel Hindrict10] did not speak ... from… [the state] departmental point of view…”
Semiotic analysis Positioning analysis
1/274 He… has got a way of presenting that… you know... makes you feel, nice and warm and fuzzy... he’s not a dictator, he’s not standing out the… front saying I’ve done teaching for you know, 20 odd years and now I’m into, you know all this PD…. Nothing like that, down-to-earth, gives you simple models which you turn around and say oh yeah that makes sense and if you as a teacher saying oh yeah, that makes sense giving the same sort of information to students you would expect a very similar reaction.... So it’s not… his units of work, it’s his presentation skills and his… ability to apply different... techniques... that’s what he’s just given... a lot of the teachers, a lot of maths teachers here just a little bit of a buzz, the fact that this… is so simple, some of the models that he’s using is so simple and… why aren’t we doing it?
The consultant (Joel Hindrict) indexed to professional learning as demonstrated by the “warm-up” activities presented. The effect of which is logical, strengthens Tony’s practice for he considers an improvement strategy to his teaching practice.
Joel Hindrict as an immediate social object related to sign iconically for the consultant mobilises Tony and his maths-teaching colleagues into action, just as personal trainer would.
That is, a personal trainer / coach who is inspirational and who provides specific skills to the “players” to make the team feel good about themselves. The message is that they can achieve if they commit themselves to the game plan, the “it”.
Tony positioned, as a teacher of mathematics in a local moral order that is encouraged by the motivation provided by Joel Hindrict, a maths consultant.
A consultant is positioned as the one that bears “gifts”, as a past teacher who has lived through the experience of teaching and engaging students with mathematics.
Joel presents a way of doing and saying that engages teachers’ to improve practice.
Tony’s use of first person pronoun “we” positions himself with his teacher colleagues of mathematics.
Tony’s use of grammar indicates a distancing away from an institutional order to someone that can inspire confidence.
Tony positions the researcher into agreeing with his “teacher talk”.
3/118 Yes... specific examples not general examples, not you
10 Joel Hindrict is a mathematics consultant encouraged by the DEECD to implement the Mathematics Lesson Structure. The
Mathematics Lesson Structure encourages teachers to start with a warm-up activity to engage students with their learning, followed by a brief period of teacher led instruction where the bulk of the lesson is made up of one-on-one instruction based on a set of exercises. The lesson end by students completing a reflection type activity outlining what they had learnt. A minimum of sixty minutes is recommended for the Mathematics Lesson Structure.
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might be able to do this if you do that, specific examples, “this is, what I do with my Year sevens for algebra, exactly that, this is what I do with my Year eights for… angles, this is one exercise that you can do, please write it down don’t… be shy this is what I do” and… we’d be writing them down, we’d be like school students… we gotta write this one down, we would want to write it down, not some general pitch that it works in so many schools around the state and this is what works generally and now you guys need to form little teams and sit down during a lunchtime and come together and you know get… it running, that… to me is not the way it should be done. The way Joel… Hindrict… did it, is the way it should be done giving us specific examples and then energizing us into wanting to learn more.
Consultant indexed to successful teaching (a prescription for healing the “lack”). The effect is energetic for Tony appreciates what Joel has to offer.
Improvement to practice is indexed to professional development, one PD that offers a practical guide that recognises the contingent realities of the classroom and not contrived as represented by the coaching program.
The interpretant appears energetic for Tony appears inspired by Joel’s presentation.
Pronoun grammar positions Tony as belonging to his maths department and to the “it”. The “it” refers to a collective engagement to the improvement of teaching practice one that is pragmatically presented by a consultant and analogous perhaps to that of a personal trainer as represented in Tony’s biography.
3/120 See… it’s a shame I… didn’t have a chance; only… did… one exercise because it was so late in the year it was… three and a half, four weeks back and I only did one exercise that he showed us on the board and I couldn’t wait to do it. I… really could not wait to show my kids what I had learnt… I would have really loved to have that program at the start where we didn’t have so much of the other stuff going on and so many mixed programs.
Pedagogical approach provided by Joel as dynamical object is indexed to effective learning. The interpretant is energetic for Tony trialled one of the “warm-up” activities provided by Joel.
Tony indexes the programs offered by the Regional coach as a “mixed program”, i.e., to a low level recognition of its effect.
Tony positions himself as a teacher of mathematics. The perlocutionary effect of attending the Joel Hindrict PD was that he presented one of the activities to his students.
Tony’s use of “I” and “we” pronoun grammar use indexes his moral capacity as a teacher of mathematics aligning himself closely with his colleagues.
Summary:
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The coach is positioned at Lambertia as a consequence of poor results on nation-wide mandated tests. Tony is resistant to the efforts the coach has made so far. Joel, a maths consultant offers pedagogical approaches at a maths department meeting. Tony notices first hand how his colleagues are engaged with Joel’s presentation preferring this traditional approach to the improvement of practice over the one that is offered by the Regional Coach as representative of the institutional order.
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Struggle
Agency and structure: How can teaching practice be improved?
Theme
“… it wasn’t a reflection on how we teach…”
Semiotic analysis Positioning analysis
Context: Tony reflects on the outcome of the previous year’s initiative when the Regional Coach worked with the Maths Coordinator to implement a problem-solving program that tested the mathematical ability of students. The data generated from the program confirmed to Tony where students were at with their learning in maths.
1/222 … our students across-the-board are almost at the same level except for one class that we have which is considered the advanced class or the LEAP (Learning Acceleration Program) class, the rest of the classes… the students are all medium or below par… so there were no surprises, we wouldn’t look at our data and say, wait a minute… you know… Tony’s class is really… struggling in fractions… Pete Milios’s class surprisingly enough, all his kids know so much on angles it wasn’t a reflection on the way we teach… and students basically fared out the same as far as we were concerned because there was no major point made on it in terms of specific teachers and specific students within the classroom, there was no major point made on that.
Data as a social object indexed to measuring student ability. The institutional effect of which was to engage teachers to improve their teaching practice in order to improve student performance. This had little effect for data, as an institutionalised mechanism did not indicate to Tony anything other than what he already knew about student ability. No further use was made of the data, i.e., no analysis was made of the data to indicate how certain students performed for certain teachers and or the way they taught. As a result the interpretant was immediate, i.e., of a low level recognition of the importance of data to the improvement of teacher practice.
The storyline is of the authority placed on data by the institutional order to the improvement of practice. Tony positioned to respond to the data however it did not indicate anything he didn’t already know.
Tony positions the researcher in agreeing with his “teacher talk” and positions himself closely to his colleagues in taking a stance in the way in which data was used to inform their practice.
2/204 I… would think that it would run successfully if… a meeting was taken off the meeting board and it was replaced with a coaching… session where all the coaches can get together with the staff so it might
Coaching (improvement to teaching practice) indexed to time, time to meet with respective coaches. The immediate object points to the dynamical for this is what the sign cannot express
Tony speaks from the self to indicate that he feels overwhelmed as a teacher to improve his practice with the support of a coach. It follows that if coaching were to work, it would have to take place
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be… five, six, seven coaches around the school and they have their three or four, five people that… they coach and they can get themselves into a group to reflect on the week’s activities… and have that one-hour… conversation to reflect and you can set up the week from there…. If… it was to run successfully it would need to happen on that level, that you dedicate one session one meeting time a night for everyone to get together.
but inferred from collateral experience, i.e., of teachers not having quality time to reflect with each other and to plan ahead all of which impinges on improvement to practice.
The effect of which is logical for it is a strengthening of Tony’s recognition the importance of time has to the improvement of practice.
instead of another school meeting.
Tony, positions the listener in agreeing to his proposal. Despite all of the above, Tony’s use of second person pronoun “you” perhaps indicates a distancing away from his own proposal, rejecting and therefore resisting the concept of coaching as a means of improving practice.
Summary:
Data does not show Tony anything he doesn’t already know about his students and that he feels that he is adequately attending to the needs of his students. Tony feels that improvement may come from a readjustment of the school structure one that allows for a coaching program to meet with teachers on a regular basis for the local specific exigencies impede improvement to practice.
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Transformation
Tony adjusts his teaching practice.
Theme
“I… feed off other people[’s] energy…”
Semiotic analysis Positioning analysis
3/62 ... with... regards to how… do I get there I… feel like I improve and I… have more of a passion when I see the people around me being influenced, honestly, if I… have a really… good lesson with my Year tens and they come out of there smiling or they turn around and give [a] comment of “oh, that’s the best science class I’ve ever had” that to me helps me get better, that to me give[s] me drive to further investigate something else… you know… if… they liked it the first time maybe I can evolve, expand on that… idea if I deal with a parent and the… parent says, “oh look, this is the most support my child has received from secondary school or from a primary school ever and I’m glad the way you did this or you did that.” I take note of them and say wait a minute that was… a positive… it’s almost like… I… feed off other people[’s] energy and if I see… people around me happy satisfied and… content with… what I had to offer I… take… a step forward and I… go up a notch and I … improve from there but in saying that… it can also work in the reverse where if people say… you could have done that better or you could
Teaching indexed to student engagement and learning. The effect is energetic for Tony enjoys and feeds off the effect a “good” lesson has on students thereby improving his practice.
Tony’s umwelt / social being comes from positive “energy” resulting from his offering(s). The interpretant of improvement is energetic for it mobilises him into action, perhaps strengthening his resolve as a teacher and affirming his status and social being within the local moral order.
Tony positions himself as teacher “hero” in the local moral order both with students and parents.
Use of first person
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have done this a little bit different I… think about it… [it] doesn’t mean I would hate myself or go backwards because that hasn’t happened but… so far so good, everything that’s been given to me has been positive… all the feedback that I’ve been getting is positive so I continue to take steps forward when I do get… the odd one or two negative comments that… really hurts me…
personal pronoun indicates that Tony is talking from the authority of self. In addition he positions himself closely to his students and engages the listener / researcher in agreeing to his “teacher talk”.
Tony distances himself away from constructive criticism perhaps provided by a coach through use of second person singular “you”.
Context: Tony demonstrates one of the activities provided by Joel to his students.
3/126 Oh mixed… reaction… they hadn’t seen that before so a lot of them were like “oh, why are we doing this now?” some of them were like “oh yeah, I see how that works” and they… say, “that’s interesting”… If I had started that from the start of the year or even if they had done something like that in grade five or six it would’ve been a little bit more beneficial because then it would’ve just been linking stuff that they’ve already done and they would’ve …“oh yeah, I remember doing this, this is fun, this is the tables stuff”. I… [will] have a chance to expand on that… next year, first thing... when I have my Year sevens hopefully… that’s the first thing I’m gonna be doing with them… just doing, showing them different ways of… actually doing some basic calculations whether it’s dividing or multiplication or addition but just showing that
A pedagogical approach (demonstrated by Joel Hindrict) indexed to the improvement of practice one that professes to engage students with their maths learning. The effect is energetic for Tony presented it to his class.
This becomes the object of a further semiosis for the pedagogical approach did not have the desired effect. The logical interpretant that resulted was a strengthening of his understanding that primary school teachers do not prepare students well enough.
Tony positions himself as teacher who applied the “magical agent” (the pedagogical approach) to his students.
First person singular pronoun indicates that Tony is talking from the authority of self in the way he positions primary school teachers and his students away from him through use of “they”. The storyline as embedded in the “that” has its basis in mathematical understanding and the importance for students to be numerate.
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different way and if they haven't done it before by the end of that year they will have known three or four different strategies of actually doing the same sort of equation.
Summary:
The coach and the coaching program does not appear to provide Tony with the magical agentry to adjust his practice but rather he is motivated to engage from the “energy” that he receives from his colleagues, students and parents in the local moral order. These elements alone appear to contribute to Tony’s material transformation.
Samantha’s response
Samantha was afforded an opportunity to make a comment on Tony’s transcript of interview to
which she responded.
“I was surprised by the negativity about coaching in general. There didn’t seem to
be any positives about the impact of the coaching except the provision of
professional learning.
It surprised me that the Scaffolding Numeracy Program was seen as a set of
activities to engage students rather than an approach addressing the various needs
of students from the evidence collected.
Some good ideas about providing time with coaches emerged.”
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5
Grallina College
“Behriana struggles with achievement… that’s why we’ve got coaches…”
Sonya Peterson, Principal of Grallina College
Grallina College is located to the south in the City of Behriana and situated in an urban and
rural area located near the town’s railway station and a campus of Queens University. Grallina
a government secondary college is a Year 7 to 12 government secondary college. It had
experienced rapid growth at the time of this research in 2009 with an average Year seven
enrolment of over 160 students per year. This increase was not due to an increase in the number
of the grade six cohorts in feeder primary schools but rather reflective of local community
support. Grallina College had an expected enrollment of 900 students for 2010. The growth
resulted in the employment of new teachers the staffing profile of which was predominately
young, presenting the college with challenges in student management, curriculum development
and in leadership. Students were predominantly from English-speaking backgrounds
approximately two-thirds had come into the college with lower than expected levels of literacy
and numeracy.
Grallina College offers a broad range of programs. For example, it has a 60-seat restaurant,
which forms part of its Vocational Educational and Training (VET) hospitality program, a 300-
seat auditorium and four open-design learning spaces that is used for inquiry learning. In
addition, Grallina College is one of 36 Victorian secondary schools accredited to deliver the
Select Entry Accelerated Learning (SEAL) program1. All students in years seven and eight
study a common curriculum where in year nine students study a core curriculum complemented
by a subject from a pathway of their choice. At year 10, students may either decide to study the
1 The Select Entry Accelerated Learning (SEAL) Program is currently offered in 36 Victorian secondary schools. The SEAL
program addresses the learning needs of academically gifted students offering an accelerated in depth study of core subjects. Students usually complete Years 7-10 in three years.
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Victorian Certificate of Applied Learning (VCAL2) or a selection from a range of Victorian
Certificate of Education (VCE3) subjects including Vocational Education and Training (VET4)
leading to entry into tertiary education.
The quantitative data collected by the author from Grallina College5 suggests a cover story
(Clandinin & Connelly, 1996) narrative from the perspective of the schools teaching staff; of
their perceptions of their own practice of professional improvement and that of the emerging
culture of “building teacher capacity”. The cover story articulates a teacher professional
development culture based on collegiality, one where teachers discussed with one another
student improvement motivation and engagement that best catered for the situations of their
classroom. Whilst there was a maths staffroom, the increase in teacher numbers at Grallina
meant that maths teachers were located throughout the college. This perhaps frustrated the ease
at which teachers were able to share pedagogical knowhow with their colleagues. Opportunity
to share professional domain specific knowledge was further constrained given the curriculum
was horizontally structured. That is, there were no domain specific coordinators / managers and
no corresponding regular KLA meetings were held. Instead, there was a Program Manager for
each year level who ran regular meetings that consisted of teacher representatives from all of the
8 KLAs. The curriculum was horizontally structured. The responsibility for coordinating the
scope and sequence of the curriculum for Years 7-12 fell on the Curriculum Coordinator.
The qualitative data also indicated that teachers sourced teaching resources from textbooks, the
school’s computer database or more commonly from researching what was on offer on the
Internet. Whilst the mathematics teachers were aware of the on-line DEECD Mathematics
Continuum6 material as a professional learning tool, they did not make full use of it perhaps
given the lack of organisational support to explore and implement it. Off-site professional
development workshops or professional association services did little to attend to teacher
interests or concerns. Knowledge and understanding reflexively afforded through
conversational transactions with colleagues who taught the same cohort of students was
preferred.
2 VCAL is a recognised senior secondary qualification that focuses on “hands-on” type learning. Students who study VCAL are
interested in further study within a field of vocational education, an apprenticeship, or in getting a job. 3 VCE is a recognised senior secondary qualification. The majority of students in Victoria receive a VCE on satisfactory completion
of their secondary education. The VCE provides pathways to further study or training and to employment. 4 VET provides accredited training in job related skills. VET may be undertaken as part of the VCE or VCAL program. 5 Refer Appendix 7 6 The Mathematics Developmental Continuum P – 10 is a DEECD developed Internet based resource that provides indicators and
descriptive tests for classroom teachers of student progress on a learning continuum. The continuum highlights understandings required by students in order to progress through the Victorian Essential Learning Standards for the mathematics.
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Samantha, the Regional Coach
As mentioned in the previous chapter, Samantha was appointed to Lambertia College working
there throughout 2008. In 2009 she continued her coaching work at Lambertia but was also
appointed to Grallina College, working at each college on alternating weeks. Samantha’s
experience at Grallina was much different to that of Lambertia. For one, Samantha arrived at
Grallina with more experience as a coach and a confidence that was supported by the
Mathematics Lesson Structure. The Mathematics Lesson Structure was the platform from
which Samantha would frame her coaching program providing teachers with pedagogical
approaches (“gifts”) and a focus for the ensuing coaching relationships. The School’s
Administration, in addition, welcomed the coaching program, all of which afforded Samantha
the opportunity to quickly develop a Professional Learning Team (PLT) with the Year 7
teachers of junior mathematics early on in her placement. These PLT meetings would plan and
discuss aspects of teaching mathematics using the Mathematics Lesson Structure as a platform.
The teachers of junior maths were also periodically positioned as leaders in sharing their
understanding and experience of the Mathematics Lesson Structure, in particular, the “warm-
up” activities with the broader membership of the maths department. The Mathematics Lesson
Structure thus had a secure platform. This together with the emergent constitutive nature of
shared meaning making in the PLT engaged teachers where no maths department had done so
before, one that discussed practical approaches to improving student engagement and
improvement. Another motivating factor for this team of maths teachers was that they were all
relatively young. This was of benefit for as Samantha said,
“… [it had] a lot to do with the positive attitudes of the teachers they’re fresh,
they’re young, they’re… still really enthusiastic [and] passionate about what they
do.... [They] were wonderful to work with because they had the confidence to take
risks and the passion as well, so it was just that perfect timing for them I think…”
The coaching program established for the teachers of junior mathematics had a flow on effect to
other members of the maths department. As Samantha described
“… we ran a lesson study, professional learning last night after school and there’s
some really experienced teachers in there that are much better teachers than I ever
was. But at the end of it, I asked them if there was one thing that you can take
away from tonight’s meeting and for them to say “yeah, this is great because I've
learned something about differentiation that I didn’t know before”. It’s fantastic,
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you know, that is positive, as long as you can give them something they can take
away and use…”
Samantha’s moral authority and moral capacity as a coach were more pronounced at Grallina
than Lambertia.
Sonya Peterson, Principal of Grallina College
Sonya publicly supported the policy push for evidence-based accountability on statewide
student testing, of coaching teachers to expand professional development to challenge and
improve teacher “capacity”. Sonya’s recollection of Grallina College before her appointment as
Principal was that of
“… a sad place, of… isolated teachers with lots of curtains on windows and no…
openness and no identified policies of support for teachers, so teachers worked in
isolation… luckily when I arrived the school was so low in numbers that all… I
guess all poor performing teachers had been declared in excess and… they were on
their way out or declared, so… at least the people who, that were here could teach,
but they were all really just operating in isolation.”
Data made apparent the prevalence of low achieving students, made more evident when they
arrived from primary school not having an adequate understanding of mathematics. As Sonya
explained
“the challenge… for Samantha, as the coach and as the wider regional helper in the
school is to say to the maths staff in those meetings, “hang on… some of you have
children whose skills are baseline; forget about [times] tables, they don’t know
what equals means….”
Sonya aligned herself with the prevailing policy shift and coaching as a device to assist in the
cultural transformation of improving teacher and student “capacity”. Sonya saw herself as a
“… pusher, a bit of a velvet steam roller, never to go back, but sometimes…
stand… a little bit still and re-gather ourselves… just gently move forward…
giving people a little bit of time to get on board.”
Sonya welcomed and embraced the coaching support provided as a means of effecting change
to teacher practices. This corresponded to a shift in her own perception of her “role” one from
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bureaucratic manager to a front-line leader of instructional practice. This change in Principal
role definition towards improved classroom outcomes was popularized at the time in political
and academic writing (Mulford, 2003; Hallinger & Heck, 1998). Sonya’s “account” highlights
an ever necessary public optimism for change, as demonstrated in an example where she
encouraged teacher visits to primary schools, where they could see firsthand how students were
settled and engaged enabling a “move towards group work… and [an] increase [in] capacity for
teachers to be able to deliver [to] a differentiated curriculum.” Her account also casts light on
the struggle of teachers who are sandwiched between the specific local exigencies and
contingencies of the classroom at Grallina. Sonya, either way, appreciated the state funded
coach and coaching support provided through the Western Metropolitan Office of the DEECD.
Mandy Fitzpatrick, Grallina College7
Teachers who taught junior mathematics at Grallina College were novice (“graduate”) teachers;
Mandy was the only exception. A third year out in 2009, she was selected by the School’s
administration to be the school-based coach to replace Samantha the Regional Coach, in 2010.
Mandy entered teaching after a career as a chemist in industry, and as a science technician at a
local secondary college were she was encouraged through her quasi teaching role to become a
teacher. The young staff at Grallina College appreciated the wealth of knowledge that she
brought to her position as a teacher of mathematics and science and adopted her as their leader,
particularly given the absence of a subject department head and also because the staff at
Grallina were mostly young. Mandy appreciated her status, position of responsibility, and the
extra-curricular science and mathematics activities that she enthusiastically implemented, one of
which was the development of the Environmental Club. The principal encouraged Mandy to be
the school-based coach and sent her together with Samantha to the regular professional
development sessions run by the Western Metropolitan office of the DEECD. As a result,
Mandy was to relinquish the Environmental Program to another teacher so that she could focus
on coaching.
Mandy initially did not respond well, deeply concerned with her lack of experience and feeling
apprehensive about her appointment. She said in an interview with the author in 2009 that she
felt overwhelmed with her new position and the expectations placed upon her by the Principal
and as a result, prepared herself to be isolated and ineffectual. She said she could not see how 7 Interview 1 – 7th Oct 2009. Interview 2 – 22nd Oct 2009. Interview 3 – 7th Dec 2009.
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other teachers would respond to her as a coach knowing that she experienced difficulty
particularly in “controlling” her own classes. She also felt that she would inevitably lose her
identity among colleagues who thought her “role” would be to judge their performance
reporting this back to the school’s administration. Whilst Mandy felt positioned by the
Principal and Regional Coach, by 2010 she had repositioned herself more closely to the
coaching program and the narrative of improvement as it sustained her new identity as a school-
based coach in the school and region.
The teachers of junior Mathematics involved in this study were Mandy Fitzpatrick, Ray Bush,
Liz Tayhlor and Jon Adams. Mandy’s experience follows whilst Ray, Liz and Jon’s “accounts”
and corresponding analyses are located in Appendix 12, 13 and 14 respectively.
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Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
Natural identity of leader, tireless, enthusiastic and selfless. A strong and enthusiastic mother figure.
Mandy viewed by institutional order as a hard worker and one who expresses a moral capacity to get the job done. Mandy is relatively new to teaching and does not as yet possess the necessary self-assurance of her ability as a leader.
Mandy viewed by colleagues and the school administration as a competent manager of a domain, although not as a teacher of teachers.
This is evident to her in how colleagues traditionally viewed others who are unable to “control” their classes. As such, Mandy felt her contemporaries viewed her as an ineffective role model of a good teacher.
Colleagues view Mandy as a helpful and competent colleague dedicated to student welfare and with common problems and difficulties to their own.
Students encouraged by her personal dedication to their extra-curricular program.
Promotion viewed by the School’s administrative team to be based on a dedication to teaching and allegiance to an institutional order.
Affinity identity closely linked to maths and science colleagues rather than one of management of colleagues.
Table 6: Mandy’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
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Initial situation
Mandy is in her third year of teaching. She graduated with a degree majoring in chemistry and initially worked as an industrial chemist. Marriage and family life followed before family circumstances transform Mandy’s perspective and as a result completes a qualification in teaching.
Theme
“I’ve got a job I like, it’s really, really varied and hectic …”
Semiotic analysis Positioning analysis
1/28 … I went through High school, country Victoria in…. Did HSC (High School Certificate)… and did a chemistry degree, majoring in Applied Chemistry. [I] worked as an industrial chemist... chemistry wasn’t really what I really wanted to do after school but I sort of got directed that way by my parents…. I love chemistry but it wasn’t what I thought I wanted to do right then... finished it in a shorter time.... In that time, I also met my partner and so I was married very soon after finishing my third year of uni and graduating and we went and lived in the city and I worked in the city and then… we [went] back to Gippsland and did a few different jobs; travelled, had children, moved several times… and we’ve been where we are about 10 years now so it’s the longest we’ve ever lived anywhere. So we did a bit of overseas travel…. I suppose the way I got into teaching really was I was working as a lab technician part-time at Acacias College and a lot of
Personhood as sign indexed to science degree (immediate object) that bears a reference to the dynamical object, i.e., personhood goes hand in hand with having a vocation in one’s life. The interpretant of which was energetic for Mandy who briefly worked as an industrial chemist. Mandy’s degree in science indexed to working in the field of science, first in industry and then supporting her family in part-time work as a laboratory technician at Acacias College. The immediate object hints to a dynamical object of schooling, the logical interpretant creating a
The storyline is of emerging personhood where the protagonist leaves the security of the family home to complete a university degree in science. Mandy’s identity is demonstrated here by the way she quickly completes her science degree as an industrial chemist working in a number of industries. Mandy defined herself as an actor driven by conviction that leaves the security of the family home and starts a family and successfully career of her own. This is evident in use of first person singular and first person plural pronouns indicating her agency in establishing and defining her personhood.
8 Interview number followed by the account number during each respective interview
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teachers… that I was helping out either weren’t science trained or… they didn’t really want to be on maybe the junior campus or a bit of both or they were graduates… and I could sort of see that… I had this degree and I was earning like the maximum... $12 an hour and I thought I’m so stupid you know I could be earning so much more money and you know my kids were getting a bit older and getting more settled in school and everything and then my husband was actually hit by a car and… very badly broken leg and you know, intensive care and lots of rehabilitation and all sorts of things and of course he was our breadwinner and you know I… couldn't pay… the groceries with what I was earning and I thought I'm so stupid… I ended up doing teaching because I felt that would fit in best with our family life… I did a Bachelor of Teaching, so I’m P (Preparatory) to [year] 12. [I] trained, did a lot of my teaching rounds here in Behriana… and just found I got on really well with all my mentors… and basically had this job before I finished my degree. I applied and got it as a graduate and it was ongoing and… I’m getting more and more responsibility…. I’ve got a job I like, it’s really, really varied and hectic but... you know, they’ve given me some extra responsibilities and things like that and I got a round “A” position this year... and I had a
change in habit. The interpretant becomes the object for a further semiosis as the sign mediates between numbers of objects and finally comes to rest with an energetic interpretant that sees Mandy apply for a university teaching program. University program indexed to teaching and leads to an energetic interpretant for Mandy is now a teacher.
In the next part of this “account” Mandy expresses her agency as a heroic cry from within when she realises that teachers at Acacias College don’t fulfil their moral duties. The storyline turns to Mandy’s changing circumstances in life where she heroically pursues a teaching degree to enter a system of rights and duties that not only supports her family, but also her identity as upholder of a moral responsibility. Mandy’s moral characteristics are exemplified as a figure fulfilling duties to her family, colleagues including the school administrators and to her students attributed by virtue of being defined as a strong mother figure.
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round “B” position last year...
Summary: Mandy’s biographical summary shows emerging professional personhood as represented through a vocational transformation.
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Preparation
Mandy is an enthusiastic member of Grallina College and quickly demonstrates her epistemic and ontological authority as a teacher in the local moral order.
Theme
“I’m on that curriculum team …”
Semiotic analysis Positioning analysis
1/4 So what they call them here round “B” position is like it’s a little job, I’m on the curriculum team, the teaching and learning team and round “B”, usually you get some time allowance but you don't get any money. With a round “A” position you get both, a bit of both, so this year I’ve been the Year 10 Programs Manager so that means you work with the Year 10 Coordinator and I’m on that curriculum team so you’re responsible for checking up on things like reports and exams and you know, things that we could do to enrich the year ten student’s time in year 10.... I also sort of took on my own back to try and get recycling going here at the school, paper recycling, I got to go on a free PD (professional development) last year for this area… to do with becoming Aussie Vic Resource Smart Schools and I went to that cos it was free and they let me go.... Anyway to cut a long story short, we got on a free module of that… there’s four modules in becoming a sustainable school and it’s quite complicated, but anyway we got to sign up on one of the freebies that they were
Mandy indexes her position as teacher to role expectation hinting at the dynamical object, that is, how the role of teacher enriches the lives of students. The effect is energetic and made evident in a further semiosis where she attends a professional development (PD) activity on sustainability also indexed to student enrichment. The effect of which is energetic for she implements a whole school environmental program on sustainability at Grallina.
Mandy positions herself as teacher with a responsibility in the local moral order. The position of responsibility reflects her identity in fulfilling duties as those that are normatively expected of teachers. The duties range from teaching to the management of teachers, students and programs. Mandy’s interpretation and expression of her many roles shows administrators that she has a moral capacity and predisposition to lead the school in line with regional expectations. The administrators’ of the school position Mandy to be the school-based coach for the following year.
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offering for people. So Sonya (principal of Grallina College), I approached Sonya and… we talked about it... we signed up and so there’s certain things you have to do to meet those criteria.... We felt that waste was one of the first ways we could start so really it was just really me… I got a Land Care grant a $1000 and started doing… paper and cardboard recycling and…. [The] Environmental Education Officer from Behriana Shire has been very helpful… and helped me out with that... and… I’ve got a little Enviro club going, which is a few kids... so that's been something I’ve done this year. So I’m so really pleased that we got recycling off the ground but that thousand dollar grant doesn't go very far and… what we really have to do is develop up a school environmental management plan, which is not my area… of expertise and... management have been really busy and haven’t… had time to look at that, although we all know it’s something that schools should be doing.... Then I got involved in this coaching at the start of this year after taking on the Programs Manager job and sort of being dead, dead keen to get going with recycling, then they put me on this PD, I got sent to this numeracy PD not knowing at all that it was gonna turn into this regional, all these PDs.
Mandy and her enthusiastic approach indexed by administrators as one who is able to deliver, ascribing her to the role of school-based coach (energetic interpretant). Coaching (immediate object) indexed to improvement to teaching. The effect on Mandy who is instructed to attend ongoing regional numeracy PD programs is immediate, i.e., a sense of uncertainty for it conflicts with her moral role and responsibility as a teacher.
Mandy positions herself away from administrators, (bearers of the system of rights and responsibilities) as expressed through use of third person pronoun “they” and clearly positions herself in line with wanting to care for the environment and to educate students in the merits of doing so. This is evident through use of first person pronoun “I” where Mandy speaks from the authority of self. She also speaks with authority when describing her positioning as a coach; however, at this stage she is unclear about her ability to take on the responsibility of school-based coach.
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Summary:
Mandy’s teacher role / world is readjusted by administrators of Grallina. Transformation is morally accepted by Mandy although there is a sense of disquiet as a consequence of being displaced in the local moral order and positioned in an unfamiliar and unrecognisable space.
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Complication
School structure, Government policy directive, student needs and a traditional teaching paradigm are the challenges Mandy is presented with as an emerging school-based coach.
Theme
“… when I came… maths and science was… in the doldrums… we can no longer accept that we have underperforming students… it’s not just their literacy that’s low it’s a lot of just any general knowledge even… you just don’t have enough eyes and ears and hands…”
Semiotic analysis Positioning analysis
1/10 No, well see… that’s the other thing, people always say that we got a new lab tech (laboratory technician) and he (a new member of the teaching staff) wanted to know was there a science coordinator and at that stage I was kind of like the unofficial maths science person that people would come and ask about stuff and…. See I’ve been a lab technician and we only had a part-time lab technician, so I could sort of help out if people need anything and I was, you know, passionate about getting, cos when I came in here maths and science was… in the doldrums a bit, science particularly and I just started, you know… National Maths Day or World Maths Day, Literacy and Numeracy, Science week. I started just running a quiz in the Student Bulletin in the first year I was here for Science Week. Just little things, but I don't know, somehow it’s sort of… people kind of, and you know someone’s away
Laboratory technician indexed to understanding of pedagogical know-how teacher support in the science classroom. The effect on teachers in the science department is energetic for they source support from Mandy because of her past position as a laboratory technician.
The “he” refers to a new member of staff. Mandy as heroine in the local moral order for saving two key learning areas from the “doldrums”. This demonstrates her moral authority and capacity. Mandy has a following of teachers whom she supports and also from administrators who turn to her for support when a teacher is absent. Mandy positions herself as a
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and they need work they’d sort of come to me, not that I know what other people are doing but you know you can usually find something and... it just sort of became that way. I’m not a coordinator of anything and there isn’t a maths science coordinator cos we don’t have that KLA (Key Learning Area) structure you see, we have that horizontal teams across, across the curriculum areas so... no I’m not a maths coordinator.... I did a lot of maths and I did quite a lot at uni, I did the maths up to the VCE (Victorian Certificate of Education) and everything but… HSC (Higher School Certificate), but… I wouldn’t want to teach senior maths really, I think it’s a very big responsibility. I’m sure I could do it but I’ve got... enough on my plate with chemistry… there’s other people who are better at maths so... no, I’m not a coordinator of anything.
Faculty members index Mandy to providing support and leadership. The effect is energetic. Maths / science coordinator (object) indexed to leadership (sign) where the immediate object hints at the dynamical for a coordinator of maths / science brings a reference to history of knowledge of past experience. This leads to a further semiosis in that Mandy acknowledges that she is able to coordinate and teach maths / science. The effect is energetic for Mandy behaves as a leader of both domains assisting teachers and administrators alike.
domain leader in response to biography. Whilst not ceremonially recognised for her hard work and commitment she comes to be viewed by her colleagues as a leader in the domains of maths and science. Whilst Mandy does not position herself as a senior teacher of mathematics because of her lack of qualification, she still believes she has the capacity to do so. This account articulates Mandy’s identity as a teacher leader indicated by her use of first person pronoun “I” in a master narrative of teaching and learning. At times in this “account” Mandy positions the researcher in agreement to her “teacher talk”.
1/14 …That’s the Western Metropolitan region, you know, they’ve looked at the data and everything and they’ve said look we can no longer accept that we have underperforming students, we have to do something, we’re not getting good results, what are we going to do about it? So they’ve made this big push for literacy days and numeracy days, but I don’t think even my boss knew that there would be so many over the course of the year and they go into next year as well. So the long and short of it, is that I was asked last term
Mandy indexes the data (immediate object) as presented by the Western Metropolitan Regional office of the DEECD to improvement in student performance (sign). The effect of which is an immediate interpretant, both recognition and an uncertainty of her role as a school-based coach.
The local moral order has its base in improvement as articulated by the regional office of the DEECD. Administrators position Mandy to lead a coaching initiative based on her performance. However the perlocutionary effect is one of confusion and of frustration in having to give up her environmental program. That is, her true heroic endeavour is not recognised or validated as important. The administrators are putting her identity / heroic position to the test.
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to, sort of, give up the environmental stuff, and that I would probably be a coach next year. I’ll have to apply for it and everything… and I didn’t know that I would have to apply at that stage they said “look we want you [to] hand over this environmental stuff to someone else, cos we want you to concentrate on maths”.... Part way through the year I’m thinking but who said I was the maths expert and they said “we don’t want a maths expert we want someone whose passionate and... enthusiastic”, and in the end I thought yeah I think what they want is someone who will do the work, basically, because they know I’ll work, so for a while there I was feeling a bit...
Mandy acknowledges a numeracy coach as having an indexical relationship to the improvement of the teaching of maths, the effect of which is uncertainty. This leads to a subsequent semiosis, one where Mandy acknowledges that the school administrators recognise the object of an enthusiastic teacher indexed to “getting the job done”. The effect of which is logical for Mandy strengthens her understanding of what is occurring and realises a possible lack in her identity as a leader.
Mandy, feels that her identity as an emerging teacher will be compromised. Pronoun grammar indexes a separation between Mandy and the administrators as perhaps not to be trusted.
2/62 It’s not necessarily about learning, it’s about meeting time deadlines with some people; I am… miles behind the year eight teachers with maths and science because I’ve got a low literacy group… a literacy supported group, but I just teach differently. I mean, I very rarely use the maths textbook, it depends on what we’re doing… but those kids don’t cope well with lots of text or looking up, looking down, looking, trying to… they can’t do many things at once, it’s… and the textbook sort of requires them to be able to read and be able to work things out and be able to look up and listen and look at explanations on the board and it’s not just their
Students in Mandy’s class indexed to having learning difficulties. This has the effect of Mandy presenting modified work to her students and abandoning the prescribed traditional approach to teaching (energetic interpretant), i.e., based on meeting a timeline and of summative assessment of the prescribed text.
Mandy acknowledges that the traditional expectations placed on her students are unachievable and morally objects by approaching her teaching differently. Mandy positions herself as defying normative convention espoused by the DEECD in order to best support the learning of her students thereby illuminating and strengthening her identity (heroic endeavour) in the local moral order.
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literacy that’s low it’s a lot of just any general knowledge even, they don’t have. You see, you spend a lot of time talking with them about things… and going over things, so I guess a lot of my stuff I’ve made myself, not so much this year because I’ve been so busy, but I’ve taught year eight, two years in a row now. So and I… know what they don’t get now… and I’m not prepared to just give them a test because we’ve done all the exercises in the book.
Summary:
Mandy provides a narrative account of the position Grallina College finds itself in with respect to low student performance data. In response, Mandy is positioned as the school-base coach for the following year and in preparation she attends a number of DEECD sponsored professional development sessions. Mandy feels overwhelmed perhaps as a consequence of her limited teaching experience that her heroic position built up to this point will be compromised by the newfound role expected from her by administrators of Grallina College. Whilst a little resentful, she shares a moment of truth about the children she teaches as requiring more support than the traditional teaching approach places upon them by an institutional order that encourages failure.
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Transference
Samantha the Regional Coach is positioned by the DEECD to work with a group of teachers at Grallina. Mandy together with Liz, Ray and Jon comprise the team of teachers who teach year seven mathematics that have been selected to work with Samantha, the aim of which is to improve student performance on state mandated tests.
Theme
“… she’s directing me at this stage …”
Semiotic analysis Positioning analysis
1/82 So… I was introduced to Samantha in the staff room very briefly, they were at briefing (a meeting at the start of the day before classes commence)… and then later on she popped up to my desk and said “Mandy have you got any… someone told me you’d be the person to ask about… unit outlines and things like that for maths”, and I’m going, oh my God, oh my God, oh my God, I’m panicking, and I’m thinking, we have not got much documented, but I said “look I can really help you with year eight because I know what’s been documented for year eight because I did quite a bit of it with one other teacher last year and I’ve also put it on Moodle9”, which was the other thing we’ve had to do in my time here and we’ve gone from just having like normal old “staff share” or whatever you call it, to Moodle and in the meantime the bloke that sort of pushed all that left as well, so that’s been interesting. So I was able to give her what I had for
The coach (object) indexed to improvement to teaching. That is, we know that when we see Samantha that the sign represents her. The immediate object hints to a dynamical object, that is, the real object of reference in the world. In this case, it is an improvement to teaching as represented by a coaching program indexed to data, one that encourages change to teacher practice. The immediate interpretant is one of acceptance and recognition that a coach will be working with the teachers of year 7 mathematics. At a later stage when Samantha asks Mandy for curriculum documents the significant effect is energetic, that is, Mandy panics (interpretant) showing that she had constructed what the sign (coach) represents, i.e., improvement to teaching. In this instance, the immediate object points
The master narrative in this passage is that of improvement to the teaching of mathematics. Mandy’s heroic endeavours are demonstrated in her agentive approach to the improvement of teaching through use of first person pronoun “I”. Mandy positions herself in the local moral order as belonging to a group of teachers who are all working at improving their practice. This is represented when teachers place completed curriculum (“it”) on the school’s curriculum site (Moodle). The above demonstrates Mandy’s identity in a number of ways. Firstly, in the way Mandy fulfils duties attributable to one that is teaching mathematics and secondly in how she is responding
9 Software program for producing internet-based courses for students
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year eight maths, which was, you know, what we had to teach… so if you have to teach… indices for example, what do the students have to know? So I had all that and I was able to give her that and then we were told… that instead of going to the Tuesday night meeting one night that myself, Jon, Ray and Liz had to go to a different meeting and meet with Samantha, cos we’d obviously been chosen to be coached
to a dynamical object (intransitive/ontological dimension), represented in the form of curriculum documents. The interpretant leads to a further semiosis in that Mandy indexes objects such as the year eight mathematics curriculum stored on Moodle to the improvement of teaching. The interpretant is energetic. It is presented as evidence of Mandy’s ability as a teacher and not of as failure. In the final semiosis Mandy and her colleagues become the new social objects, i.e., of teachers who need to be coached. The effect of which is an immediate interpretant.
to and trying to overcome the tragic circumstances of teaching mathematics (her heroic efforts are thwarted by the prevailing contingent and exigent realities of teaching at Grallina). The coach positioned by the DEECD and supported by the administrators as possessing authority endorsed by “head office” to improve maths results and therefore practice. Perlocutionary effect of encounter indicates that Samantha positions Mandy as requiring assistance (a new power relationship, perhaps one of surveillance and forced inscription on the bodies of the junior maths team). This is further reinforced when Mandy acknowledges that she together with her colleagues have been selected to work with the coach. Finally, Mandy refers to Samantha throughout this passage in the third person, that is, as a person to whom she does not belong, positioning her at a distance.
2/18 Well, they’ve got this bloke called Joel Hindrict whose pushing for numeracy, cos there’s sort of a numeracy push and a literacy push but then different people doing it, so... we get split up, so we go on separate days, the numeracy people go separately to the literacy people and he’s been an
Regional consultant as the immediate object indexed to and mediates between signs. Signs include change in numeracy and literacy policy and a change to the way mathematics is taught; the “structured lesson” approach to teaching mathematics. The effect
Mandy positions herself as teacher directed by a consultant who presents a magical agent in the form of a “structured lesson” approach for the improvement of teaching mathematics in schools. Mandy positions the consultant as maintaining a position of power, as the
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educator he’s worked overseas, he’s now [a] consultant, he was a principal for a while at Suncity Grammar… and now he basically just works [as a consultant]… he did Lambertia last Monday night... with her (Samantha’s) group over there and his thing is, you have to have at least an hour for a numeracy lesson, “warm-up”, introduction, activity where you do some target teaching if they’re not getting it and a reflection.
of which is immediate for Mandy recognises and accepts the consultant’s approach. The immediate object perhaps hints to the intransitive, to a reality of improvement to the teaching of mathematics, of a world of possibility.
one with epistemic authority in the teaching of mathematics. Pronoun grammar analysis demonstrates that whilst Mandy positions herself as belonging to the leadership team at Grallina College with the reference to “we”, she distances herself from the regional office and to the students in her class referring to both in the third person plural. Perhaps apprehensive and unsure of the ensuing changes that are occurring.
3/221 Yeah a few things, a lot of it she (Samantha) got from PD’s as well which I got as well so some of the things she did at PD’s the same day as me we were there together some things she did it at a PD and came back and talked about cos she got more PD than me with people like Joel Hindrict (regional consultant) and stuff but you know some of it was just straight out of his books, here’s a set of activities from Joel Hindrict’s book so it wasn’t... you know, in a lot of the things… you’ve done before or you’ve seen someone else do... but yeah we shared what we’d done both of us what she’d got from PD and me.
Pedagogical approaches indexed to improvement to practice, the effect of which is immediate for Mandy realises that activities come from the consultant. Mandy grows in confidence (identity) as she acknowledges the sources of the pedagogical practices, the objects that Samantha uses that affords her epistemic authority in the local moral order; is but a thin veil.
The “it” refers to pedagogical approaches to engage students with their learning. Mandy grows aware of the coaching program and her confidence and identity strengthen, when she realises where the source material comes from and an acknowledgement that the coach perhaps isn’t as absolute in her mathematical understanding as she first thought. Mandy positions the listener / researcher in agreement with her awareness, of the political game being played out. That Samantha’s isn’t as omnipotent as once felt for her understanding comes from a book peddled by a consultant. Once this is uncovered both Mandy and Samantha assume and identical role.
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Summary:
Mandy an enthusiastic teacher of three years drew from her experience as a laboratory technician working in secondary schools to become the defacto leader for both the maths and science departments at Grallina College. She was recognised by her peers for her knowledge and engaged the school community in extra-curricular programs that she implemented.
As a teacher of year 7 mathematics Mandy and her team were selected by the school administration to be coached. Later it was revealed to Mandy that she would be the school-based coach for the following year. Having to relinquish her extra-curricular activities she attended regional professional development provided to schools that were selected to be a part of the coaching program. Intimidated at first by Samantha the Regional Coach and perhaps of the fact that she was going to be coached, Mandy grew more confident when she realised what the coaching program entailed and feeling more at ease with Samantha’s position.
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Struggle
In the following episodes Mandy, selected as the school-based coach, feels overwhelmed by the task that lies ahead.
Theme
“I don’t know if I make… any difference to these kids, you know, how am I ever gonna help anybody else if I can’t even control my own class?”
Semiotic analysis Positioning analysis
1/100 Oh if I say to Samantha... look, “oh god, it’s awful... they never shut up or you know I can’t even control my own kids”, I said to her sometimes, “how am I ever gonna help someone else if they’re wanting me to be a coach [be]cause that’s the kind of person I am”, and she says to me “but, Mandy your kids are good, you do the right things with them, you have structure, you have routines, you won’t let them speak, you know, over me or over yourself or over another student, you know, you expect certain things and you follow through and you give them homework and all these sorts of things... it’s… what’s your doing is okay” and you kinda go oooh!... you know cos it’s a pretty lonely thing I think for a lot of teachers.
Mandy indexes the coaching to the improvement of practice. Mandy indexes the coach to a preconceived idea of an effective teacher and of teaching. Mandy does not view herself in the same way as Samantha, for she does not recognize nor accept her ability to coach others. Samantha affirms and validates Mandy as an effective teacher (object). Samantha’s response indexes Mandy’s teaching to that of an effective teacher. This perhaps has a logical effect for it strengthens and supports Mandy’s ability to be coached and or to coach others. Finally, Mandy indexes the private world of teaching suggesting that teacher’s need to have their experiences affirmed by a significant other, perhaps by a coach.
Mandy positioned in the local moral order as a school-based coach by the administrators of Grallina College. Mandy positions herself as feeling alone and a failure as a school-based coach for she doesn’t believe she has the ability to coach her colleagues. She views herself as ineffectual in the eyes of her peers. The coach validates Mandy as an effective teacher confirming her heroic efforts given the persistence of privacy that teachers experience never knowing whether they are making a difference.
2/52 We generally discuss that when we meet on the Monday again and say well yeah, what do you reckon we need to, what worked, what didn’t work and
The coach indexed to improvement, although the immediate interpretant is suggesting that support is perhaps inadequate. Mandy indexes students
Mandy positions herself as belonging to the coaching program and to Samantha but feels that the program is not effective in meeting the
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Samantha will say, cos she’s only here every second week, she’ll say “where are you up [to] now”, and then we’ll talk about that in relation to what was already done. So, “like terms”, I’ve done that sort of teaching stuff, this was just practice, practice, practice, cos they need, they, they go “I don’t know, I don’t know what a like term is”. And they come back in, half of them might or half of them might not all admit to it. A lot of them, you know, you just don’t know if you’re doing the right thing whether they’re, they just don’t listen, they’re not engaged whether they’re just tired, you know, all those reasons.
as displaying learning difficulties. The interpretant is energetic for the only way to improve student understanding is by way of repetition.
needs of her students. Pronoun use indicates that whilst Mandy positions herself as requiring help, she distances herself from her students and from teaching possibly as a consequence of uncertainty experienced based on students inability to understand or their learning disposition. Mandy positions herself away from her students perhaps putting the blame back onto students as the source of the problem, for they are unwilling to learn, or don’t have the skills and not responding to the coaching treatment.
3/197 Yeah, I mean, [I] think sometimes I felt like Samantha was saying nice things to me... just to raise my confidence because they’re a tough group those year eights that we’ve worked with, they’re hard work and... you know and I’d say to her sometimes you know “I don't know if I make… any difference to these kids, you know, how am I ever gonna help anybody else if I can’t even control my own class?”, you know, those sort of comments that you make... and she would say “no, no, no, you’re fine, you’re a good teacher, you do this, you do that, you do something else”, you know.... So on the bad days I suppose having someone around who says that, is… good and also someone who sees the way the kids
Year eight class indexed to a difficult teaching experience, the effect of which is immediate for it is recognition and acceptance that Mandy’s students make her job difficult. The effect becomes the object of a further semiosis in that a school-based coach as an object is indexed to good teaching, one who is able to teach and control their class. The effect of which is logical for Mandy acknowledges a lack perhaps weakening her perception of herself as a teacher or possibly “testing the water” to come to an understanding of whether she has what it takes to be a school-based coach. This perception is indexed to a lack of confidence, the effect of which is energetic for
Mandy positions the listener / researcher in agreement with her plight in teaching a group of difficult students. Mandy positions herself throughout this episode as someone distant as someone that is not confident in the role that she is expected to fulfil (that of school-based coach). Mandy positions herself as ineffectual in carrying out her duty to improve practice. Consequently, positions the coach (helper) as the one who can perform to task in this master narrative of improvement and can also provide Mandy with the guidance that she requires
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behave because you’re on your own often in the classroom with these really difficult kids who don’t give a shit about maths and science, you know what I’m talking about, you’ve met all those sorts of kids, you’ve been teaching longer than me and you can feel extremely sort of alone and... I suppose having someone else experience what they can be like when... you know, you’re both in it together. So if you discuss that child later they know exactly what you’re talking about, it’s not like talking with someone who’s never taught the kid.
Mandy responds to Samantha’s support. The coach as social object indexed to that of a significant other, one who affirms and validates Mandy positive qualities.
to perform according to the expectation placed upon her by the school’s administration.
Summary:
Mandy is ambivalent about her capacity to work as a school-based coach for the coming year. Mandy feels overwhelmed perhaps as a result of her level of experience as a teacher and because of the expectations placed upon her by the school’s administration. She also feels overwhelmed with the thought of being the school-based coach because she believes that she feels ineffectual as a teacher. This was brought into sharp relief when Samantha as part of her role of coach witnessed first hand Mandy teach her difficult class of students. The result are feelings of apprehension that a lack of experience and realisation of ones capacity given a lack of guidance in an environment relatively free of support. Mandy feels that because she cannot teach her difficult class of students she therefore feels ineffectual as a teacher and consequently as a school-based coach. Samantha’s affirmation is a welcomed sign from a significant other and highlights both a lack and a corresponding need for emerging teacher leaders.
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Return
Mandy returns from a regional professional development program for school-based coaches with further understanding of what is expected from her only to find that the task set for her has been made difficult for it is met with obstacles.
Theme
“… oh my God, is that what people think coaches are for…”
Semiotic analysis Positioning analysis
2/34 Lots of ideas, but generally make your own resources. So a lot of it just... there’s professional readings there’s activities we do, you know, hands on things that we do but we would have to go away and make ourselves which is the sort of thing I do.... Talking about just the coaching relationship a lot of that happened to start with so what does it mean to be a coach or be a coachee, what are the expectations of both parties. One… session was a morning… spent on hard and soft coaching which is, it’s an American term, a lot of this has been done in America and some of the videos were American as well, so, you know, that was a bit hard to sort of “Oh yeah, that will really work in Australia, won’t it!”, sort of; different contexts to us, they teach differently anyway. But, you know, they try to illustrate the kind of conversations that you have… which you’d (referring to the researcher) be interested in, I guess… I think hard and soft coaching is like, okay… soft coaching’s where you support the coachee, your there, you help them, you run things together, but you
Resources provided at the regional PD session index student improvement, whether it was professional reading or hands-on type activities, all of which represented an immediate interpretant. The interpretant became the object for a subsequent semiosis. Coaching in this instance was indexed to the provision of feedback to the coachee. The idea that Mandy was to provide feedback that either confirmed or confronted a teacher’s practice had a logical effect of weakening her appreciation for coaching. The interpretant becomes the object of a further semiosis in that data presented by the regional office is indexed to school improvement the effect of which is logical for Mandy sees it “…as a big responsibility.” “Hard” coaching” implies appraisal of a teacher’s aligned to student performance data. “Soft” coaching indexes supporting teacher effort.
Mandy positions herself as a competent teacher; she is able to make resources for the effective teaching of maths. Mandy positioned by the administrators of Grallina College as the school-based coach for the 2010 academic year. The story line is of a teacher who is able to get the job done. Teachers and schools invited to attend the regional PD session positioned as ones that must improve their practice and are provided with guidance in the form of an American coaching model….
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never actually get to the nitty-gritty of going well okay this is, this is something the kids are still not getting or we’re not, what are we gonna do about it? Or the results are not happening what are we gonna do about it? Or, let’s talk about that last lesson, this didn’t go well so it’s getting to that really hard stuff where you may actually have to do that kind of cool feedback and try to get results, cos the whole idea of this is to lift data. They, they judge schools, and you know this; NAPLAN (National Assessment Program – Literacy and Numeracy) data, VCE results and the parent, teacher, staff, student surveys, that’s basically what they’re looking at. So if those things are not moving on they’re going to be saying, “well, you know, what the hell’s going on?” So, I mean, I would take it as a big responsibility. I also don’t feel like I’m in any position to judge anybody else and… yeah, like I said, I mean some of those classes are pretty tough as far as just behaviour, keeping them in their seats even.
Mandy aligns herself to “soft” coaching as an energetic interpretant. Mandy indexes the expectations placed on schools by the DEECD (“they”) as unrealistic for difficult classes challenge teaching and learning at Grallina, all of which leads to an energetic interpretant a response of the mind to the realities of the situation.
Mandy positions herself as having a commitment to her “role” as a teacher from Grallina. The coaching story line of having to give “hard” feedback discourages Mandy and she positions herself away from the coaching program, i.e., of having to give “hard” feedback to teachers particularly given the contingent realities of the classroom.
2/66 … the head of our curriculum team the teaching and learning team actually said it at one of the meetings, but that’s what coaches are for, cos we were talking about bringing in whole school reading at a meeting, and then we had to bring up two proposals for the student management team to work at how we
The coach as social object indexed by an utterance made by the head of curriculum as monitoring the “rule” following behaviour of teachers. This has a logical effect on Mandy, one that weakens her belief in her role as school-based coach for her fears are confirmed by the head of
The “that” that Mandy indexes at the beginning of this account is a negative perception of coaching. Mandy is positioned in a storyline of school improvement, sitting in on a curriculum team meeting that she feels that she belongs to (“we”).
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might do this in the whole school.… One was… started off term four… Teachers introduce [a] session of maths after lunch every day…. The other proposal was, and quite a few people were keen… to take five minutes off every 50-minute session. That would give you half an hour a day and then we’d allocate [that time] straight after lunch, half an hour, whole school reading and everyone would down tools and read, silently. And a lot of people agreed to that and liked that idea which meant a complete revamp of the timetable and everything and bell times and everything.… They said… how would you monitor it, and I’m going, “does everything have to be monitored?” and they kind of went well yeah it does and our head of curriculum actually said, “well that’s what coaches are for” and when she said that, I thought, oh my God, is that what people think coaches are for, I don’t wanna be a coach, I don’t want to be in a classroom with people thinking that I’m there to monitor what they’re doing because, you know, that can be a perception.
curriculum. The meeting agenda is to discuss the introduction of a literacy program that encourages all students to read across the college. It is at this meeting that the curriculum leader (the false hero), attempts to position coaches to monitor whether or not teachers are following curriculum policy. This positioning of coaches by the curriculum leader makes clear to Mandy what she feared; that teachers would view her role as a person who would monitor their practice referred to as the “it” and the “that” in this account. Mandy positions the listener / researcher as agreeing to and understanding her “teacher talk”.
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Summary:
Coaching is brought into sharp relief for Mandy when she attends a regional professional development program. Mandy learns that coaching is about improving student performance data using an approach that is both supportive and confrontational. Mandy does not appreciate the American coaching model presented because it does not appear relevant to the local culture. She is also anxious of coaching in the way in which classroom teachers may respond to her as a school-based coach. Her suspicion is confirmed when the Curriculum Leader articulates how coaches may be used to check up on whether classroom teachers are implementing a program in accordance with school policy. Mandy who is acutely aware of the contingent realities of the classroom, demonstrated an aversion to this perceived aspect of her “role” as a school-based coach.
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Transformation
Mandy aligns herself with the coaching program and demonstrates confidence in what coaching affords.
Theme
“… I think yeah the conversation had been missing, I felt more... I suppose I felt more like... she listened to what I said…”
Semiotic analysis Positioning analysis
2/118 We can get them from the region, usually you photocopy them off someone else, I’ve got lots of games that I’ve made for, I showed them at our meeting the other night just from things I had from years ago… that I’ve got off other people, you sort of share them around, something that’s good, you know… you try and copy or make your own, see it somewhere and make your own, obviously make my own so and the old… Curriculum Corporation (Government funded educational organisation) and Maths 300 (comprehensive on-line resources for maths teachers) they’re good, Maths 300’s good for games.
Curriculum resources, as object indexed to classroom practice one that hints to the teaching of mathematics. The interpretant is energetic for Mandy makes her own resources and shares these resources with others in her faculty.
First person plural “we” demonstrates that Mandy aligns herself to other teachers of mathematics particularly in the way teachers make and share resources. In doing so, Mandy reveals her capacity as an effective teacher of mathematics. Her use of first person singular “I” demonstrates this. Mandy describes making and sharing resources in the second person singular “you”, including the researcher as teacher and perhaps also references how other teachers engage in the practice of preparing resources. Mandy uses “you know” to position the researcher in agreeing with her “teacher talk” in the sharing of best practice.
3/75 Well where they should be making some improvement that you know there… should be certain things that when kids do a topic, you know, the guts of its gotta be this, this and this, you know, you don’t have to use a textbook you don’t have to rely; I don’t use a
A constitutive approach to meaning making where Mandy is having her teaching approach validated by the coach. The textbook as object is indexed to poor teaching practice. Students as social object
Mandy and the coach share the same identity and are shown in this account as working together. Working as a team, as indicated by the use of “we” (first person plural) to make improvement to teaching practice.
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textbook much you know, we would talk about… how we felt they were, you know the high end of my class the low-end the needy kids, you know, talking about their abilities and what they really need[ed] to help reinforce the important bits and pieces for that topic.
indexed to pedagogical approaches to improve student performance. The effect of which is energetic for Mandy articulates that she applies a differentiated approach that does not include the use of the textbook.
Mandy includes the researcher in agreement to her approach.
3/83 … because we could… have conversations, it wasn't like when you have a meeting with other members of your area and it always tends to go into some other… grey patch where you end up talking about whether we should use textbooks or not, or someone saying “well I can't teach senior maths unless I’ve got the big expensive calculator… ” you know, how you always get off [track], people tend to get off track onto other things. Whereas, Samantha and I were really focused about that and also often had conversations about how we could use what we were doing to show other people in the maths group, well things I already [had] been doing that she’d up seeing. She would say to the maths group “look, this is one of Mandy’s activities, we did it together”, same as I would say “Samantha and I tried this”, or we’d seen [this] at [a] PD…. I suppose we lent to each other, we lent some credibility what we said to other teachers as well but I think yeah the conversation had been missing, I felt more... I suppose I felt more like... she listened to what I said probably
Relationship between the coach and Mandy indexed to collegiality that hints to the dynamical object of improvement to the teaching of mathematics by means of a constitutive order. The effect of which is energetic for both Samantha and Mandy work together to professionally develop teachers at a faculty meeting. The interpretant is energetic for Mandy is working with Samantha to effect change to the practice of teaching. This account demonstrates how Mandy and Samantha agree to the importance of conversational interaction for developing mutually intelligible meaning / orientation towards the improvement of practices. Faculty meeting indexed to improvement in teaching by way of a constitutive approach. This leads to a further semiosis, which indexes teachers lack with respect to organisational learning.
Mandy the protagonist aligns herself with Samantha, the coach who in this episode is helping Mandy become a credible school-based coach. Mandy includes “you know” to position the researcher in agreement her “teacher talk”. Whilst Mandy uses first person singular / plural pronoun to position herself with the coach, there is an instance in this episode that indicates that Mandy guards herself against losing credibility. Mandy refers to the coach as “she”, as someone distant, there is a sense of ambivalence possibly in an attempt to secure her position within the local moral order as a coach with credibility.
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whereas you can have conversations with lots of people and think that you get on all right with them and all of that but you know at the end of the day everyone’s really busy...
Despite all of the above Mandy hints to an aspect that is lurking in the shadows (something villainous) that may ultimately expose her as a false heroine and that is, a lack of time for at the “… end of the day everyone’s really busy…”
Summary:
Mandy continues to transform her identity having it validated by Samantha who positions Mandy along side her, no longer as a novice but rather as school-based coach. Despite this, Mandy still has some reservations about her “role” as a coach.
Samantha’s response
Samantha was afforded an opportunity to make a comment on Mandy’s transcript of interview
to which she responded
“It was surprising, once again, to be seen as an ally who understood and supported
this teacher.
I was also glad to be seen as a “listener” as this is an important part of coaching.
The importance of professional trust and collaboration in the coaching role was a
key to some of the success with this teacher.”
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6
The causal power of discourses of reproduction and transformation
“… self cultivation does not tolerate mere mechanical accretions of cultural
paraphernalia to be worn and conspicuously displayed for the sake of a purely
momentary effect. Rather, self-cultivation demands a genuine transformation of one’s
personal identity, one in which the appropriated cultural form is fused to express the
singularity of the self.”
(Harvey, 2002, p. 181)
Systems of transformation and reproduction of “underperformance” in the schools studied were
not seen to reside in the conversation itself that the teachers had with the coach. These systems
were seen to be operating through two distinct discourse circles in which the teacher acted
(Simmel, 1968). One in which the teacher spoke as a product of a social (institutional) order
and the other in which the teacher spoke as a producer of a social (constitutive) order. It is
groups of people with the collective commitment to enforce those discursive norms that are the
source of the causal influence of discourse. But the discursive norms expressed in the teachers’
accounts, which cause the teachers to reject or work with the coach, are methodologically
neither purely a product of individual thinking nor collectivist or objectivist acts in which social
structures directly control discourse without human involvement. The constraints on rejection
and involvement with the coach operate through the thought of individuals but they do so as a
consequence of the causal process of wider social groups in the school. The constraints are thus
a product of normative policies, not determinations, which transcribe themselves by force since
their effect is mediated through the actions of the coach, which are also affected by the
responses of others and many other factors alluded to in the teachers’ accounts and indeed by
individual choices.
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Discursive effects have elements of exteriority while still depending on an interiority to make
them effective. The discourse circles in which individual teachers move can be seen to
influence, sometimes very strongly, what they regard as acceptable discursive behavior and
generate discursive regularities but these circles depend on interactions with others, sometimes
conflicting dispositions, as well as upon reflexive repositioning, so there are no impossibilities
imposed by discursive norms. Discursive norms are compatible with discursive change. As
noted in the accounts of several teachers the moments of interiority in the process of rejection /
resistance and engagement / commitment allow for incremental innovation and change.
This analysis has entailed and drawn on Bhaskar’s Transformational Model of Social Action.
Figure 10 developed from Harvey’s social representation of Bhaskar’s TMSA (Refer Chapter 2)
is framed upon a dialectic between the discursive circles of the institutional order of social
expectations (duties) and the constitutive order of self-improvement (responsibilities). At the
hiatus between these normative discourses, of structure and agency is the mathematics
department, that is, the community of practice. It is here where agency and structure are co-
constructed. Commencing with the top left at T1 the arrows suggest influence of institutional
rules of the local moral order through a process of socialization and social control over teachers
of mathematics through social interaction. Teachers’ own biographies, “espoused theories” and
“theories in use” shape and maintain what they see as shared identity and social operation of the
subject department. The discursive behaviours acquired by graduates and or new teachers in a
subject department in a school are implicitly and explicitly influenced by significant others and
ever present in artefacts, narratives, mythologies, gestures… that have evolved historically in
the positioning, institutional practice and socialized rhetoric in their school. It is in this way that
teachers shape their professional identities through their signing and positioning behaviour in
their discursive practice in the classroom and staffroom. In this scenario, their discursive
identities as mathematics teachers are forged in the hiatus between duty and responsibility are
unlikely to develop in the absence of “collaborative mentorship” (refer Figure 11) concerned
with constitutive reflexive processes of teaching mathematics for teachers will continue to
locate themselves in general narratives constituted in the local moral order by institutionalized
social relationships.
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Research into the discourses of constitutive mentoring, Bullough (2005) argues may be, the key
to greater understanding of processes that connect teachers back to their moral “calling” of
“wanting to make a difference”. A “calling” opposed to one defined by market success,
“… constitutes a practical ideal of activity and character that makes a person’s
work morally inseparable from his or her life. It subsumes the self into a
community of disciplined practice and sound judgement whose activity has
meaning and value in itself, not just in the output or profit that results from it”
(Bellah, 1985, p. 66).
Collaborative mentorship as outlined in Figure 11 reflects the ontological and
phenomenological dimensions of social activity as a generative mechanism, one where agency
is conceived (Refer Table 2, p. 70). All component parts within the schemata collectively
realize and are a generative mechanism of improvement to teacher practice through a process of
constitutive shared meaning through reflexive practice in a subject department as a community
of practice. Commencing at the top of the diagram and working counter clockwise we find the
material structures of society, here represented as discursive forces of production on teachers in
Figure 10. Model of social transformative action in a community of practice
HISTORICALLY ACCESSIBLE CULTURAL
FORMS (SIGN/SIGNING)
COLLABORATIVE MENTORSHIP (Refer Figure 11)
TEACHER BIOGRAPHY FORMED IN THE
DIALECTICS OF CULTURAL REPROCUCTION AND SELF-
CULTIVATION (POSITIONED PRACTICE)
“PERFORMING”
SUBJECT DEPARTMENT
T2
SOCIAL TRANSFORMATION
IN CONSTITUIONAL
ORDER
INDIVIDUAL AGENCY: THE SELF-
CULTIVATED EXPRESSION OF
COMMUNAL POWERS
“UNDERPERFORMING”
SUBJECT DEPARTMENT
T1
SOCIALIZATION
IN INSTITUTIONAL
ORDER
INDIVIDUAL TEACHER AS
PRODUCT OF SOCIAL INTERACTIONS
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the school as found in DEECD policy, the way in which it is communicated, its economic
framework and so on. These material processes surface in new social and political power
structures, in the person of the coach as mentor or a subject department head that acts as a
mentor. The mentor engages teachers shifting the emphasis away from a social arrangement of
power to one that encourages a constitutive order of “use” practices against which meanings can
be measured and specified, involving the creation of social objects.
From the material and sociological dimensions emerge meanings as represented by DEECD
policy; a depiction of this is presented as the “Mathematics Lesson Structure” (Refer Appendix
1). The “Mathematics Lesson Structure” can represent the sequential linear fashion of teaching
mathematics iconically characterized as doors that need to be opened in a sequence, represents
not only a metaphor for success in moving from one dimension of mathematical understanding
Figure 11. Collaborative mentorship as an enabling condition
COLLABORATIVE MENTORSHIP
PROFESSIONAL CONVERSATIONS
Institutional practice Practice development is planned
according to rather than “following” DEECD policy.
PROFESSIONAL CONVERSATIONS
Discursive interpretation of experience Experience of a pedagogical approach
(“warm-up” activity) shared with members of the subject department.
Teaching practice development As a planned process with others
Mentor as significant other A mentor as significant other
engages teachers to maths domain.
Signing: Meaning structure “The Mathematics Lesson Structure” (Appendix 1)
offered as membership to a culture of teaching
mathematics.
Signing: Identity formation/reformation Image schemata provide teachers
with images of “self” and “others”. Images constitute ideas of social
identity / social identification in the subject department.
Environmental conditions A space, place and time to
communicate with others, to reflect on their experiences
linked to practice.
Oral and or written discourse
Material signs and representations made in the subject department.
Expression of teacher identity Biographical qualities, knowledge
of mathematics, perceptions, doings and sayings…
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to another but can also symbolically represent a time allocated syllabic prescription which
entails an institutionalized way of life for teachers of mathematics. The “Mathematics Lesson
Structure” and other type schema formed the basis of socialization and social control of teacher
self for they reconstitute ideas of an institutional social identity and identification aligned to
normative and warrantable discursive and performance behaviours expected of teachers of
mathematics (Mead & Woods as cited in Phillips et al., 2002). Signing in this way, in the
teachers’ accounts, distinguished an agent’s identity and meaningful strategies as they pertained
to a social position within the moral order. And as such, may not have the effect of improving
practices and changing identity unless teachers are afforded an opportunity to constitute
practices that are based on the requirement of social action and collaborative sense making to
replace vague, artificial and mechanical social orders based on institutionalized practices.
The “warm up” activity is another social object or representation used to invite conversation one
that demonstrated an energetic effect on some teachers as evident in the justifications and
rationalizations expressed in their “accounts”. The illocutionary force; the expression of teacher
identity, of biographical qualities, doings and sayings… are socially formed and signed
generating habits that if left unchallenged remain as re-expressions of “past present” practices,
of social positions and an institutionalized way of life denying teachers their epistemic worth
(Phillips et al., 2002). It is in this way, that the coach as mentor was depicted as responsive to
the structural and semiotic effects of teaching, acting as an agent of individual and collective
teacher learning and relearning. A mentor as a significant other acts as a mediating agent in
transforming the material structures and discourses by creating environmental conditions for
teacher practice development, one necessary to engage and encourage embodied individual and
group agency. An emphasis on mentoring in coaching practice may contribute to instituted
teacher learning that further develops teacher collective professional esteem and practice by
improving the normative practices a subject department subscribes to. This was shown to be
achieved in some accounts by means of narrative reasoning around shared resources (ideas and
materials) towards meaning making amongst colleagues as significant others.
In this model of transformation a mentor with epistemic and ontological authority who has
moral authority and capacity afforded by the school and positioned in a subject department may
trigger teacher agency. The mentor as an agent of change comes to be recognised as such by the
membership of the subject department; they don’t appoint themselves. Further, in this model,
teachers do not subscribe whole-heartedly to a new constitutive order unless transactions in their
community of practice represented by new signs / signing position them to challenge their tacit
and explicit understanding. The signs / signing presented by the mentor can bring a new way of
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doing and saying embedded in a narrative of myth making and together with guided leadership
(positioned practice) direct teachers to express their agency to collectively transform their
subject department to one that is performing differently at T2. This collective transformation
through acts of group and individual reflexivity symbolically reformulates knowledge through
guided conversations in a recursive series of dialectical moves. The discursive practices as
broadly defined by Harré (1993) in a community of practice in this way may afford a path to the
transformation of organisational structures concurrent with transformation of teacher
professional identity. Represented diagrammatically, T2 now becomes the new T1 in an ongoing
trajectory of improvement to teacher practice. A community of practice may afford a new
constitutive order if maintained over time and as a recognizable entity of epistemic worth within
the broader school community.
Applying the schemata as represented in Figure 10 to Grallina College, the maths department
located at T1, a department that had Mandy as a default leader and where decision-making was
unclear and commitment of maths teachers low (Siskin, 1994). In the absence of “collaborative
mentorship” as outlined in Figure 11, teachers would be expected to continue to go about their
everyday practices, symbolized by beliefs and values represented historically through restricted
access to mathematical resources (signs and signing) that encapsulate retrospective narratives of
normative and warrantable mathematical thinking indexed to a vaguely defined disciplinary
order and corresponding teacher identity. Knowledge, beliefs and values relatively unchanged
embedded in “underperformance” justified by references to conditions imposed by their socio-
political existence. This scenario presented a challenge for novice teachers’ who were
inadequately prepared for the actualist narrative of having to cover the mandated curriculum in
an impossibly brief time in the face of profound, if not impossible professional obstruction by
their students. They were positioned within the local moral order as “graduates” their discipline
and dispositional knowledge in the normative discourse of student alienation and local
exigencies and contingencies of the classroom.
This situation at Grallina would not have changed had it not been for the personal recognition
and encouragement of the coach who, for the graduates, was a significant other. The coach
brought an offering that assisted the emerging teachers to enquire into their own practice to
imagine an identity different to the one that was represented by their positioned place within the
local moral order. The coach’s narrative of practice as represented by the “warm-up” activities
engaged teachers to jointly construct and reconstruct their storylines of production, signing,
power and self-esteem, which, in turn, repositioned the identity of their maths department. This
social sign / signing represented a committed grammar brought by the coach to the community
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of practice. The coach encouraged the self-expression of communal power expressed in the
PLT meetings that began the transformative process of the maths department to T2. The
graduates appropriated and internalizing new practice through a process of self-cultivated social
transformation. They did this through a process of appropriation, assimilation and
accommodation, moulding their own specific conditions, their biography / identity to the “rules”
constituted at the intersection of their new purposes and social necessities through what they felt
matched the contingent and exigent realities of their classroom. The move towards T2 was a
move to constitutive rules that could enable further social reproduction and transformation if the
conversation that was required could be maintained, a process that requires a sustained approach
to professional development.
Samantha’s two-year placement as the Regional Coach had come to an end at Grallina College
in 2009. Samantha would continue her work as a Regional Coach at another school in the
Western Metropolitan Region of Melbourne in 2010. The Schools’ Administration at Grallina
decided to continue the work commenced by the centrally funded Regional Coach appointing
Mandy to the position of school-based coach for 2010. Before the promotion, Mandy, a maths
science teacher in her fourth year, gave self-cultivated expression to teacher agency at Grallina.
Despite the promotion, Mandy had reservations about her ability to fulfil the coaching role. She
recognised that agential powers was not something that she could claim for herself even if
appointed by the school. Mandy’s reflexive narrative response to the social reality of her own
forced positioning and consequently to others in the subject department signified that instituting
a coach and a coaching program in an “underperforming” domain / subject department needs
careful consideration. For a coach not only needs to be able to exercise moral capacity and
epistemic authority but more importantly be granted moral authority by teachers of a subject
department as their coach.
In a follow up interview with Mandy in 2013, she described how the maths staff at Grallina “…
got on board…” and embraced the “Mathematics Lesson Structure” after the Regional Coach
had left. Mandy also recalled how maths teachers of junior mathematics “… appreciated the
time to talk about maths…” in the PLT instituted by the Regional Coach. Despite this, the
PLTs did not continue for the focus was on “… using data to work on building teacher
capacity…. ” This became the accepted form of improving teacher practice after the Regional
Coach had left where Mandy’s school-based coaching role was primarily used to coach new
teachers of mathematics who did not have a primary qualification in maths. Grallina College
continued to receive support from the Western Metropolitan Regional office of the DEECD and
on occasion, Samantha, the Regional Coach who worked at Grallina in 2009 supported Mandy
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in her role as school-based coach. Despite this, Mandy reported that there was no discernable
difference to the numeracy data for Grallina in the state mandated testing program. Mandy was
appointed the numeracy leader at Lambertia College in 2013.
The experience of coaching at Lambertia College was also problematic. It had been tried as a
strategy and withdrawn as an on-site professional development approach. The Regional Coach
introduced a number of programs searching for a narrative mythopoesis of maths teaching, but
at each turn teachers were unresponsive returning to “tried and tested” ways, of dealing with
specific local exigencies and contingencies of the classroom for there was no self-cultivated
expression of communal power that embodied a prospective view. For Josh, his positioning in
the local moral order as a “graduate” and a teacher on “contract” encouraged him to maintain a
known and safe course. Josh who was in a dependent career relationship with Tony Roma, his
internship mentor appointed by the school, didn’t want to be identified as requiring a coach.
This was Josh’s initial feeling at the commencement of the conversational interviews. By the
end he had come to accommodate and assimilate aspects of the “Mathematics Lesson Structure”
not in response to the coaching program at Lambertia, but rather from a series of off-site
professional development programs he attended during the time of this research. This
professional development program involved teachers from both primary and secondary schools
in the local community who met with a consultant with the intention of encouraging use of the
“Mathematics Lesson Structure”. Whilst the coaching program failed at Lambertia College, the
discourse community, in the off-site program encouraged Josh to explore his own practice in a
more secure context, perhaps highlighting the importance environmental conditions has on
teacher practice development.
In a further example at Lambertia, Pete, an older colleague of Josh experienced at a physical
level the pendulum swings of political change over and over to little effect on the institutional
order of maths teaching at Lambertia. Pete, who did not seriously entertain the value to his
professional identity of being coached, positioned the coach’s program as too “messy”. Pete, as
did Tony, felt the contingencies of the classroom had to be dealt with first and foremost within
the established institutional order; any deviation from this local moral order would only disrupt
the everyday struggle with the reality at Lambertia. Whilst Tony and Pete distinguished clearly
in their narrative “accounts” between public and the private psychological spaces, they had no
intention to account, let alone reform, their practice and identities to serve the purpose of
systems which did not deal with reality on the ground as they saw it and had always been
disinterested in their psychological welfare. Left to their own devices in the absence of any
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personal support they eschewed the pedagogical strategies introduced by the coach to respond to
different student learning needs in favour of familiar whole class strategies.
Sarah, the other member of the team of teachers of junior mathematics at Lambertia found
personal meaning in the coaching program at Lambertia. She had been selected by the
administration to work alongside another school-based coach of mathematics in 2010. The
positioning of Sarah in her new role required her to implement the “Mathematics Lesson
Structure”. The narrative was couched in terms of having the “right people” in the coaching
program at Lambertia and this prospective project represented for Sarah an enabling condition
that supported her commitment to a collaborative implementation of a new junior maths
program as supported by the school-based coaches for 2010. Her narrative reasoning identified
her in the institutive narrative order of improvement through the external accountability of
statewide testing. But, as this current research shows, as Simmel (1968) proposes the influence
of discursive norms on identity formation is not the influence of a monolithic overbearing
“society” but rather the influence of a complex and dynamic patchwork of social circles. Sarah
chose not to share her experience as a school-based coach with the researcher in 2013.
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7
The positioning of the coach and the transformative agency of
teachers: The problem of constituting joint meaning in an
“underperforming” secondary mathematics department
“… it is across the awful, sometimes yawning, gap between teachers’ original ideals
and their present practice that [a narrative approach to] faculty development can
construct a bridge of hope and meaning.”
(Wood, 1992, p. 540)
Two phenomenological questions framed this research. 1. How can shared meaning be
constructed between the coach and teachers? 2. What should pass as research in the
phenomenological sociology of teaching and learning?
How can shared meaning be constructed between the coach and teachers?
Policy directed research on teaching has been charged largely with finding a cure for “under-
performance” assessed using indexes of ever changing public interest. In the discourse of
policy directed research the teaching process is made a “social object” that requires repair by
policy makers and school administrators alike who are the principle audience of research into
school improvement. Teachers are positioned in the institutional order as not capable of
constitutively responding to social necessities as evident to policy workers and need to be taught
the new “best practice” programs to improve the “under-performance” of their students. The
coach armed with a policy warrant is likened to a technological agent and positioned by teachers
in their discursive practice in a grand bureaucratic narrative of school improvement; a clinical
treatment to remedy a medical condition. This was made evident to me when, as a secondary
school teacher, I was appointed for a period to a position as a coach in an educationally
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disadvantaged cluster of schools being amalgamated and reorganized. Ontological questions
about the social warrant of the coaching program and of my “role” in the local moral order
concerned me. I came to see that teacher classroom practices are not simply a product of a
transcendent worldview or values that a teacher believes are shared with the role bearers.
Rather they rationalize their teaching as an expressive response to the specific local exigencies
and contingencies of the classroom using a framework of perceived duties and responsibilities
(Segal, 1998).
This study set out to explore through “accounts” provided by teachers of mathematics how they
worked with a state appointed coach who was sent in to improve their individual teaching
contribution to the school’s standing on national student performance data. An ethogenic
methodological approach was adopted to illuminate the problem of establishing shared meaning
between teachers and coach. The analysis of teacher “accounts” revealed their traditional, tacit
and explicit knowledge, and commonsense understanding of their world (de Waele & Harré,
1979). The semiotic and positioning analyses of teacher “accounts” attended to the content and
agential dynamics respectively. The analysis also informed understanding of teacher identity
formation, for professional identity is shaped in discursive practices within a school setting. A
study of teacher discursive practices thus provides a window on the fluid positions of actors
within the local moral order and of the inherent social practices that pertain to a culture of
“under-performance” in a school. They show tacit or conscious symbolic representations that
amount to a claim “… about the kind(s) of person one (or other) is, how one is (currently being)
related to others and what feelings are to be associated with the social arrangement” (Harré and
van Langenhove, 1999, p. 160). Selfhood studied in these teacher “accounts” show an agentive
transitory accomplishment through discourse that implicates local cultural meaning systems in
an institution, which filter model cultural meanings. This discursive positioning analysis of the
teacher / agent in the moment of their everyday storylines is useful in the fine-grained analysis
of the policy driven attempts at institutional regeneration. The coaching program, the context of
the conversational is only the latest of attempts to reform the expressive order through mandated
changes in the practical order of course descriptions, institutional practices, societal rhetoric and
their discursive relatives.
The teachers “accounts” in this study further illuminate the narrative forms and emotional
universals that exist in the life world of teachers. Teacher ontologies, narrative forms and
emotional meanings have been devalued in the framing of policy-focused research in favor of
an anti-ontological position that produces a positivist ontology of nature. The symbolic
“realities” in teacher stories are politically dismissed and replaced with a categorical truth,
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warranting diagnosis by statewide scientific testing and treatable by a program of pedagogical
reform such as that to be delivered by a Regional Coach. The coaching policy signalled to
teachers, a centralising of authority and control from the state department and for teachers in
these “underperforming” schools the transfer of moral accountability for delivery of
improvement to under resourced local communities. This institutional order positioned a
Regional Coach as a surrogate curriculum leader in difficult to staff state schools, which are
shown on statewide achievement tests to be “underperforming”. This negative public
assessment indexed teachers as “underperforming”, against normative standards of student
performance. The coach as an entity is a discursive sign, iconically linked to that of a sport
coach, as the experienced knower of key team tactics or “moves”, training individuals to
monitor their own development in key play moves devised by the coaching program in order for
the team to win the game. In this way, the policy storyline positioned the Regional Coach as
hero in the western tradition, one who achieves pre-determined social goals against all
contingencies. Reform in teacher behaviour, the policy hero dismisses teacher subjectivities in
favor of a goal-based reality visible only through a lens of rationality (Nussbaum as cited in
Wood, 1992). This heroic narrative of mathematics teaching alienates teachers in this study
who describe themselves more in a tragic hero narrative in which they persist against all the
forces weighted against their best efforts to bridge the gap between their hopes for student
learning and the everyday grind.
The teacher “accounts” importantly cast light on the “technologies of self” by which the
teachers transform themselves within the local moral order; knots of reason as Foucault (1977)
described them, of production, of social power, of signing and of identity. The “accounts”
describe how structure and agency are recursively related in the professional identity formation
of teachers in the school situation. For whilst the coaching policy was a special public
investment that afforded school teachers in this study a degree of recognition of their
difficulties, the coach’s “rules to be followed” largely appeared weak, inauthentic and or
irrelevant against the specific local exigencies and contingencies of the classroom in their
school, where everyday necessities obstructed teachers attempts at maths instruction. Their
praxiological response to the experience of being coached was active resistance and or adaption
to the power, policy and message of the coach. This was made determinate in the storylines,
positioning and the illocutionary force of their “accounts” of the practical and expressive social
orders that apply to the difficulties and neglect they experienced in their school. The “accounts”
of teachers are fine-grained descriptors of the general lack of psychological movement from the
reception of the coach’s “good advice” about teaching to a committed grammar of self-
improvement.
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The psychological spaces afforded teachers working with the coach, brought both possibilities
and uncertainty. Teachers at Grallina College with the institution of a Professional Learning
Team (PLT) sensed the possibility of cultural production where personal meaning and emotion
was encouraged in a discursive space. The constitution of a new order of practice was at least
afforded legitimacy in the work of the PLT, which was to focus on a process of establishing the
epistemological authority of socio-culturally mediated habits of practice, belief and
commitment. The discursive tensions between what strategies and tactics could be usefully
explored and what couldn’t in this local moral order, afforded teachers insight into the
possibilities of shared meaning for comparative improvement associated directly to their
particular classroom concerns. The shared meaning constitutive between teachers and the coach
in each school brought uncertainty about the moral authority and agency associated with this
warrant to improve themselves in an institutional order in which the coaching function was
embedded for the coach and the principals.
What should pass as research in the phenomenological sociology of teaching and
learning?
In asking who is interested in the teacher’s world, the answer can be framed in terms of the need
to shift research attention from the minds hidden in the heads of individuals to the use of mind
in talk between us. Schwab (1969) argues that the strategic knowledge in the narratives that
teachers’ reflexively construct, give meaning to their world. As Lambert (as cited in Page,
2000) further contends, teacher researchers are often best positioned to investigate the practice
of teaching for local meaning perspectives. The meanings outlined in the teacher researcher
narrative accounts captured by this research are largely untapped and or dismissed as a valuable
and rich source of what it means to teach in a particular time, space and social context. Policy,
itself is a storyline put to teachers that often limits if not erases teacher knowing, both on an
individual and at a collective level by reducing teachers’ social capital. Policy and curriculum
workers should be more interest in teachers’ social capital. This social capital “… comprises
social resources that evolve in accessible social networks and social structures characterized by
mutual trust”, pushing the known in policy formulation further into the unknown (Rostila, 2010,
p. 321). Social situations, as Goffman (1964) also argues, constitute a social reality that is sui
generis. Social reality requires analysis of actors’ saying and doings that are inextricably linked
to social situations and as such should not be dismissed but brought forward in
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“… an environment of mutual monitoring possibility, anywhere within which an
individual will find himself accessible to the naked senses of all others who are
‘present’, and similarly find them accessible to him” (Goffman, 1964, p. 63).
It follows that research in a community of practice offers researchers an opportunity to study the
mental life of the teachers as one that is lived in a space of reason, one that is irreducibly moral,
and connected to a historically evolving human practice (Brinkman, 2006). The semantic
necessities espoused in the “accounts” provided by teachers in this research are anchored in
moral necessities of the social reality in which they find themselves. Their meaning making did
not reside independently of their understanding but was constituted by and anchored in the
semantic necessity promulgated through conversational transactions with others including the
teacher / researcher. The practice of teaching as socially framed by the contingencies of student
behaviour in the maths classroom comprises a normative necessity for it is here that the teacher
practitioner individuates, repositions and or redefines his or her practice as a teacher of
mathematics. Researchers and teachers cannot rationally access the worth of different strategies
for the improvement of student learning in isolation since reasoning a moral position rests with
it being comparative and as such an active process between individuals committed to a project
(Brinkman, 2006).
An active emergent process of “mutual intelligibility” is required, one that draws on an active
intentional power at a local level of constituting “social objects” such as strategies, tactics,
meanings and perceptions produced in their use (Rawls, 2011). The pre-existing habits of
experienced staff in both schools were formed in a culture of privacy concerning classroom
practices in the staff rooms and corridors of their schools. Local norms of practice were
constructed in the two schools mainly through private retrospection, on defensive tacit and overt
collegial “accounts” of unengaged or disruptive behaviour and or the limited capacities of
students in their classes. This took place under a historically socialized institutional umbrella of
educational alienation that dominated “accounts” of teacher agency and their life space. This
research positions the teacher at the centre of their own learning and consequent improvement
of teacher practice. As Leonard argues “[c]urriculum is… emergent of the commitments, the
knowledge, the care and communicative competence of teachers.” (1983, p. 21). Leonard calls
on a respect for the developing of teacher consciousness, through conversation about their
practice, for it is in this context of sharing knowledge and commitment that a teacher’s
transcending consciousness may develop for their teaching is seen as a personal expressive and
imaginative public act.
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The state coaching policy seen through teachers eyes, generally functioned to deny maths
teachers their epistemic authority, stultifying their commitment to themselves, to each other and
to their school community. However, Samantha, the Regional Coach did perform a constitutive
role in the PLT meetings at Grallina, where good mathematics teaching was reintroduced as a
mythopoetic construct. The PLT at Grallina encouraged personal talking and demonstration
engaging teachers in a mythopoesis of good mathematics teaching. It wasn’t so much the good
advice and a new institutional order that were presented by the coach, but rather the
demonstration through her place-based affective commitment to the practice of mathematics
teaching that encouraged younger graduate teachers to commit to the reflexive grammar of self
improvement and identity formation (Gee, 2000-2001; Bullough, 2005). The conversations that
were encouraged by the coach as she presented the “warm-up” activities had the effect of
assisting teachers to reflexively imagine their world of teaching; their mythmaking, exploring
the tension between their habits of belief and their habits of interpretation in the way they
connected to the child’s thinking of mathematics and in doing so persuaded teachers’ to share
their world with others as an affective space. In the exchange of myths, teachers shared their
propositions of the social world and in some instances came to a collective agreement. The
enabling condition of the “warm-up” lesson presented by the coach may be viewed as an
embedded affordance, an awakening and opening of transcendental consciousness of
mathematics teaching amongst teachers whose personal identities had been shaped in other
disciplinary communities other than mathematics. It is in the sharing of a teachers’ reflexive
worldviews that the education for an appreciation of the abstract symbolic mathematical life
world come to prominence through shared imagination; it seemed in this conversational
interplay that the young teachers felt the world of mathematics could become more meaningful
and accessible to their disaffected students.
Discussion of the possibilities in the PLT encouraged a constitutive mythopoetic discourse. The
“warm-up” activity as a constitutive practice seemed to advance teacher commitment to self as
process in maths teaching. Mathematics as a universal system for making the “unknown
known” can decipher existence; a place of relative security for students and teachers from the
confusion that mystery can create and in doing so can confirm its inherent limitation as well as
powerful uses. By simply holding up different ways of doing, of social discursive possibility,
the “warm-up” encouraged contemplation as an enabling condition and necessity to future
possibilities. This is the constitutive order that surfaced briefly in 2009 in the coach’s PLT
engagement with the maths faculty at Grallina. The experience in the “warm-up” activities of
sense making, involved teachers teasing out, interpreting and reinterpreting their agency. In
these conversational moments, the “warm-up” activity seemed important as a potential means of
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holding up the received myth of the value of mathematics to students in these schools in proper
perspective. Rather than rejecting the possibility of meaningful understanding they entertained
the possibility of transcending rejection and developing new possibilities for dealing with the
mystery of their own Sisyphian persistence.
What is worthwhile about this research?
Researching teachers acting with ends in mind references their actions to local normative and
warrantable codes of conduct that make teacher “accounts” legitimate in their own context and
in terms of the authority of their experience. This study of the teachers’ phenomenology of
practice in the practical order of maintenance and the expressive order of honour and status
speaks to their lives as teachers of mathematics. Heidegger alludes to a formative value of a
phenomenology that opens up possibilities between who we are and how to act (as cited in van
Manen, 2007). A phenomenology of practice may speak to the professional lives of teachers if
we allow for a pragmatics of possibility of teacher education and institutional learning by
questioning everyday interactions. It is here where the tensions between habits of interpretation
and habits of beliefs can be explored in the study of shifting teacher agency at the intersection of
purposes and social necessities. In social research, the actor may be liberated from “role”
assumptions of a socially determining habitus (Bourdieu, 1980), enacting an unconscious range
of routines, consequences and experiences used to explain how the social order of educational
“underperformance” is produced and reproduced. To this end, teacher agency and identity
formation was studied using positioning theory and pragmatic signing as analytic tools to
explore teachers’ discursive positioning. Miettinen (2006) contends that a community of
practice such as a subject department in a school can function as a collaborative unit of
organisational learning in which new joint activities mediated by significant others may provide
the impetus for understanding the current and prospective conditions of practice.
Conversation was not advanced in either subject department studied beyond that of “survival”
and “persistence” except for a moment when the coach introduced “warm-up” activities at
Grallina, encouraging those teachers to bring back and reflect on their self as process in the
collaborative production of a social object – a new tactic, with their colleagues. Conversational
practice with the coach in the community of practice where shared meanings were transacted
about the relational aspects of mathematics teaching enabled teachers to access other ontologies
in the ongoing formation of their teaching identity. In was in this communal context that the
coach encouraged a collaborative approach to organisational learning. This collaborative
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approach encouraged exploration of what it meant to be a mathematics teacher and of teaching
itself in their context, of bridging the gap between hope and daily realities. For a period
encouraging teachers to move deeper into their community rather than to distance themselves
from it.
Lieberman and Miller (1990) argues that developing a “culture of teacher enquiry” described
here as a social constitutive process in a school is not as simple as is assumed in an
individualized coaching model which has been preferred by system “gate-keepers” who will
seek to subject, monitor and control the self improvement activities of teachers that may
undermine the institutional order. Change to a school’s culture must take place alongside such
individual intervention focused on continuous learning of teachers’ pedagogical content
knowledge in mathematics. Grallina teachers’ accounts of the encouragement and engaged
teacher commitment to the maths faculty PLT towards a local culture of learning, (organised
and led by Samantha the Regional Coach with the support of Mandy, the school-based coach)
speaks to the significance of social motivation in professional development time and
institutional space to reflect on shared practice. This social mediation encouraged shared
teacher learning of content in context, one that provided new opportunities for self improvement
by engaging networks from outside the school. It is in this way, that Lieberman and Miller
(1990) and Shulman and Shulman (2004) argue, that teachers may break primarily from their
isolation to create and work in a collective and collaborative “professional” world that
transcends the restricted discursive codes of Grallina. Lieberman and Miller (1990) contend
school leaders can influence teacher agency as reflective process ontology by reformulating the
identity of the subject department as a community of practice. Guskey makes this point
specifically, “… to be successful, professional development must be seen as a process, not an
event” (2002, p. 388).
Doig and Groves (2011) emphasise the importance that teacher learning and institutional
learning are bound together by discursive systems must be supported and sustained. This is the
virtue reported by the Japanese Lesson Study approach. The Japanese Lesson study model
demonstrates the
“… opportunity to develop professional communities of inquiry, with ownership of
the improvement effort, a commitment to inquiry, shared goals, and a sense of
reasonability to their colleagues and students” (Lewis et al, as cited in Doig &
Groves, 2011, p. 90).
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Huge cultural differences between substantivalist traditions (Harré, 2009) in the schools studied
no doubt would limit the effectiveness of any attempt at local adoption of the process centred
Japanese Lesson study model. However, emphasis on collaborative mentorship rather than
individual “coaching” in a professional development game plan not only sources local agency
but also “… enables teachers to build on their efforts to refine their understandings” (Doig &
Groves, 2011, p. 91). Teacher’s knowledge is developed socially within communities of
practice blending formal and informal narratives for as Shulman and Shulman (2004) contend,
this supports knowledge building and distributed cognition required to challenge old ways
encouraging a move to a committed grammar of school improvement. The DEECD coaching
policy had the reverse effect of subordinating teachers’ speech acts to a private monadic rather
than as dialogic order. The problem for an actor / agent, coach or teacher, subject to such a
cultural code arises when social reality consists of variations amongst actors (Heiskala. 2011).
Teacher improvement of practice is best served by means of conversational transactions in a
culture of “mutual intelligibility”, one where teachers project subjectivities and have these
reflexively recognised in the context of their classroom experiences. The current study suggests
a lesson study process grounded in local practice sustained in the institutional order and
undertaken by reflexive capable teachers to the improvement of practice as a way of navigating
the complexity of improving teacher skills and knowledge.
Unfortunately, most teachers in this study found the centrally administered coaching program
denied their epistemic and moral authority to explore their practice. Bullough (2008) too
contends that the notion of coaching reform as centralised is problematic for it is then
characterised as a remote, top-down authoritarian power structure, one that does not consider
that renewal is local, holistic, organic, and embedded in the teaching communities it serves.
Samantha perceived herself to be the villain in the teachers’ narratives reflected in the responses
she provided to the interview transcripts made available to her by the researcher. Two of
Samantha’s responses are provided below. The first, given in response to Mandy’s transcript
confirmed for Samantha her position as the coach and curriculum leader, in relation to the
institutional reform program. Samantha also references the difficulty she experienced in
meeting institutional role expectations as a coach as presented in the teacher narratives.
“It was surprising, once again to be seen as an ally who understood and
supported this teacher.
I was also glad to be seen as a “listener” as this is an important part of
coaching. The importance of professional trust and collaboration in the
coaching role was a key to some of the success with this teacher.”
150
Whilst she positioned herself as a mentor to Mandy, her response to Tony’s transcript was very
different. She positioned Tony as a problem in that he did not respond positively to the
coaching program, viewing it, she observed, only valuable as a traditional professional
development exercise.
“I was surprised by the negativity about coaching in general. There didn’t seem
to be any positives about the impact of the coaching except for the provision of
professional learning [to individuals].
It surprised me that the Scaffolding Numeracy program was seen as a set of
activities to engage students rather than an approach [which addressed] the
various needs of students from the evidence collected.
Some good ideas about providing time with coaches emerged.”
Despite this, Samantha recognised that Tony made an important suggestion that hinted at the
absence of a constitutive practice, one viewed as unimportant in an institutional order that
imposed “… the Scaffold Numeracy program…” (DEECD, 2012).
Samantha’s response also suggests that overcoming teacher resistance to change is the defining
aim of coaching. The underlying assumption is that self-improvement will arise naturally in the
context of new resources being provided and individuals knowing how to use them. In the
person of Mandy, this was naïve at best for whilst others perceived Mandy in the maths and
science department at Grallina as their default leader, she experienced ambivalence in the role
of school-based coach. For example, whilst Mandy accepted endorsement of school-based
coach as a promotion, she experienced feelings of apprehension at losing affinity with her
colleagues and or the mutual esteem or institutional identity she had established with the
school’s administration. Alternatively, whilst the coaching program benefitted novice teachers,
others conceivably felt they were being punished as a consequence of having the coaching
program forced upon them. Policy workers are not aware of the difficulties of teaching whilst
Mandy’s colleagues on the other hand, are all too familiar with these realities.
Samantha’s responses as with the narrativized “accounts” provided by teachers in this study
offers a further insight into the narrative nature of emotions located in a time and place and as
such provides access to an actor’s world. Thought and emotion are embodied and made
comprehensible from a social perspective; a “situatedness”. This “situatedness” of the “past-
present” practice of mathematics teaching in this study was, in part, reactive and defensive.
Perhaps brought on by a means of surviving tensions between the duties of “rule” following and
151
the responsibilities of pedagogical innovation that teachers were socialized to accept at both
Grallina and Lambertia. The issue of class control, student disengagement or having to get
through the curriculum in the limited time was signed in the teacher narratives before level of
understanding or interest in the subject matter. Teacher “civil inattentiveness” (Segal, 1998),
disengagement or conservativism in relation to professional practice indexed their perception of
their place in the institutional order. Alienated, they had come to know and accept a form of
teaching that enabled them to cope with their situated circumstance where they were unable to
express a moral commitment or teacher agency to develop beyond the restrictive space in which
they taught.
Conversational narrative structures such as anger, comedy, romance, helplessness and tragedy
were employed in their “accounts” of their agency in working with the coach where each type
of emotion narrative configured teacher agency in specific ways. For example, Josh Ryan’s
anger narrative at Lambertia College expressed his shame or guilt at having to be coached and
may be viewed narratologically as diluting his self’s agency. Or in the case of Ray Bush, his
narrative of frustration, of little support, of inadequate resourcing as a first year teacher in the
face of a syllabus that he had to get through also indexes his agential isolation and insecurity. A
narrative of helplessness may index a non-agentive teacher made immobile by way of repeated
personal professional suffering, loss of self esteem, honour in the expressive order of teaching.
Evident in Tony’s “account” of his school’s previous respect of him as a coach. Teachers in
this study either confirmed or disconfirmed their agency in their own biographies based on past
practices or future causes in the “past-present” culture of the school community. The
construction of teacher identity as such, and that of the coach were attributable to narrative
emotional forms that emanate from the social worlds to which they belonged, rather than as
reified objects, objects to be manipulated in some way by an institutional order. The state
policy platform, which proposed a coach, could instruct teachers in pedagogical content
knowledge that would raise their skill, elicited indifference or alienation among the teachers.
By asking, what sustains poor teaching practice in a school indexed as “underperforming”,
policy workers may perhaps attend to the concerns expressed in this current research. For
example, Farr and Moscovici (Eds) (1984) argue that “underperformance” is a “social
representation” that teachers come to know and accept as “the way things are done and have to
be done around here”. Harré (2009) is critical of the reification of the notion of social
representation as an explanation of the reproduction of poor teaching in these schools. He
suggests after Peirce that social representations are embedded in cultural artefacts and it is in the
collaborative production or socialisation of social objects that the culture is transformed. For
152
“…[t]he apprentice is learning the “rules of the game” [in] acquiring a social
representation of what to do and how to recognize when to do it, and with whom
in a “conversational” process, that is in a social setting with people showing or
telling what to do, supplementing the learner’s attempts” (Harré, 2009, p. 470).
Schools indexed as failures as an institutional order historically socialize teachers, students and
school communities as failures. After a history of being labelled failures it is absurd to attempt
to regenerate teacher beliefs by simply asking them to subscribe to a grammar of good practice.
The story of the teachers in this study suggest the shared meaning the coach could hope to
establish can only be achieved in a constitutive order of collaborative practice, one that takes
into account the narrative emotion of “past-present” practice. With sufficient time and ongoing
support, a project based prospective accounting of the type the coaching program sought to
achieve may have been pursued. A research project that accompanies such a program may
better describe how individual agents act collectively to generate artefacts and in doing so layers
of “rules” and meanings that emerge. Such a project, for example, could focus on the teaching
of algebra as a complex semantic field that requires an explanatory pedagogical framework and
as such cannot be reified on the basis of a known truth. Rather an explanatory format is called
for, one that relies on language in use to explore, describe and explain regularities and or
irregularities based on possibilities. In the local moral order of the schools studied, the coaching
paradigm of school reform attempted to make a transformation based on the universal truth of
the authority of an institutional order. The basic philosophical concern advanced in this thesis is
that teacher identity is transient and cannot be reified as a social entity.
The social world is the result of a continuous process where active individuals acting according
to shared rules generate artefacts. Schools consist of people with a shared body of knowledge
and understandings that include rules and conventions both tacit and explicit, which are
followed resulting in a coordinated system of practices. Conversations unfold according to
convention and as such result in changes to a teacher’s material world. In order for a school to
change, practices of which it consists must also change. A change in structure is therefore made
available from a change in practices and not by administrative fiat. The regularity, continuity
and uniformity within social practice is due to a shared body of knowledge achieved and
maintained through discursive practices in communities of practice. It is in the confines of
discursive practice, in subject departments, that a foothold to change a prevailing structure may
be provided. As Rawls argues, a constitutive practice
“… based on the requirements of social action and collaborative sense making
(not on [concepts of fused] beliefs [or] ritualized practices) [is] needed to replace
153
the more artificial and “mechanical” social orders of the past which created a
cooperative social context by forcing people to share beliefs and a ritualized way
of life.” (Rawls, 2011, p. 399).
Membership of a community of practice offers a prospect of collaborative, constitutive and self-
organising way of life that encourages a move away from individual habits, beliefs and
institutional rule following. The internal narratives attached to private institutional practices
may be challenged when replaced by a “… sequential, and reflexive practice of conversational
turn taking…” (Rawls, 2011, p. 399). The emergent local constitutive order Rawls (2011)
describes, operates independently from initial diverse individual beliefs and or an institutional
order in the form of vague, predefined global guidelines or “good ideas”. Unless habits of
belief are shared by a group of individuals and habits of interpretation negotiated, they can be
expected to play a limited role in organising the coherence of what curriculum policy guidelines
mean for teachers in a school, particularly for those new to the vocation. It is in a constitutive
order where individuals co-construct narratives that embody meaningful social objects (such as,
the Grallina version of the “warm-up” strategy) that represents a narrativized emotional
intelligibility of meaning making to teachers that is reflexive and situated. Rawls’ constitutive
order encompasses both the practical and expressive orders of teachers’ social activity in which
professional failure and success are reproduced or transformed.
In describing the TMSA of teachers in this study their professional identity formation was
ascribed to a dual praxis of structure and agency, a dialectic between self as social product and
self as producer of the social. A self as process metaphysics, after Whitehead (1929), was
applied to Bhaskar’s critical realist position to explore the social world of the teachers in
“underperforming” schools. In this approach, social existence is best understood as processes or
modes of change in which social entities such as “good teaching” and mathematics curriculum
“policy” are not fixed and are not self-identical over time. The coaching paradigm views
organisational learning as locked into a behavioural process of individual problem solving that
is intended to ensure institutional efficiency against external standards. As Nonaka (1994)
argues, a passive and static view of organisational learning in schools has done little to liberate
agency but rather relies on an “input-process-output” system of change without due
consideration of what is created and why. Ross (2005) further contends, just as the mathematics
textbook is created without direct reference to local experience, professional development in
education policy in the traditional organisational paradigm does not draw on the local
experience or epistemological authority of teachers. These approaches do not perceive a local
constitutive view of transformation of a teacher actor’s social activity, which has an expressive
154
as well as a practical function. Recommended practices that precede conversation in
transformations are rejected particularly if they don’t attend to redefining transformation as
emanating from the local moral order. Such a constitutive order requires recognition of the
moral authority of the subject department as a community of practice as affording a practice-
based reconceptualisation of the structure-agency debate, one in which transformation of
practice is based on the agency of actors. It is only with teachers’ claims to epistemic and
ontological authority comes a corresponding challenge to aging organisational capacity.
155
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Appendix 1
Appendix 2
Whole school survey
Personal details
1. Gender
Male [ ] Female [ ]
2. Total years of service
Years __________
3. Faculty areas in which you work
Faculty Area 1 ________________________
Faculty Area 2 ________________________
Faculty Area 3 ________________________
4. Position held. Please tick.
Classroom teacher………………………... [ ]
Classroom teacher with responsibility…... [ ]
Leading Teacher………………………...... [ ]
Teacher learning
Use the following scale to indicate frequency as it relates to each respective question.
1 = not at all; 2 = very little; 3 = a moderate amount; 4 = quite a lot; 5 = a very great deal
Within the last five years at this school, to what
degree did you personally:
Place a ü in the corresponding bracket [ ]
1 2 3 4 5
5 attend off-site workshops? [ ] [ ] [ ] [ ] [ ]
6 provide professional development to colleagues
at either a faculty level or to the whole school?
[ ] [ ] [ ] [ ] [ ]
7 research teaching and learning ideas from the
Internet?
[ ] [ ] [ ] [ ] [ ]
8 reflect on learning outcomes in order to think
about improving your teaching practice?
[ ] [ ] [ ] [ ] [ ]
9 source professional development in specific
areas?
[ ] [ ] [ ] [ ] [ ]
10 use on-line resources such as the Mathematics
Continuum P-10 to improve practice?
[ ] [ ] [ ] [ ] [ ]
11 explore teaching approaches that targets
learning for a cohort of students?
[ ] [ ] [ ] [ ] [ ]
12 share teaching approaches / lesson ideas with all
colleagues in your faculty?
[ ] [ ] [ ] [ ] [ ]
13 plan lessons and or units of work with
colleagues?
[ ] [ ] [ ] [ ] [ ]
14 engage in professional reading? [ ] [ ] [ ] [ ] [ ]
15 consider that professional development changes
your teaching and learning practice?
[ ] [ ] [ ] [ ] [ ]
16 attend optional professional development
offered by the school?
[ ] [ ] [ ] [ ] [ ]
17 seek the support of a coach / mentor / critical
friend?
[ ] [ ] [ ] [ ] [ ]
18 source and use material from journals published
by subject associations?
[ ] [ ] [ ] [ ] [ ]
19 invite a colleague to experience your classroom
teaching practice?
[ ] [ ] [ ] [ ] [ ]
Appendix 2
20 find subject associations useful as a source of
professional development?
[ ] [ ] [ ] [ ] [ ]
21 share and discuss student work? [ ] [ ] [ ] [ ] [ ]
22 align professional development activities to the
priorities of the school?
[ ] [ ] [ ] [ ] [ ]
23 consider that professional development leads to
improvement in student learning outcomes?
[ ] [ ] [ ] [ ] [ ]
24 use ICT resources to improve practice? For
example, interactive white boards.
[ ] [ ] [ ] [ ] [ ]
25 moderate student outcomes with colleagues? [ ] [ ] [ ] [ ] [ ]
26 share and discuss what you learnt / experienced
at a workshop with colleagues at the faculty
level?
[ ] [ ] [ ] [ ] [ ]
27 use a journal to record and reflect upon teaching
experiences?
[ ] [ ] [ ] [ ] [ ]
28 trial new approaches / initiatives learnt from off
site workshops? For example, the e5
instructional model.
[ ] [ ] [ ] [ ] [ ]
29 team teach? [ ] [ ] [ ] [ ] [ ]
30 use data to adjust your teaching in order to
improve student learning outcomes?
[ ] [ ] [ ] [ ] [ ]
31 share and discuss research on instructional
practice at a faulty level?
[ ] [ ] [ ] [ ] [ ]
32 feel supported in this school and empowered to
improve?
[ ] [ ] [ ] [ ] [ ]
School learning
Use the following scale to indicate frequency as it relates to each respective question.
1 = not at all; 2 = very little; 3 = a moderate amount; 4 = quite a lot; 5 = a very great deal
Within the last five years, to what degree has the
culture at this school encouraged staff to:
Place a ü in the corresponding bracket [ ]
1 2 3 4 5
33 develop an understanding that a ‘performance
and development culture’ exists?
[ ] [ ] [ ] [ ] [ ]
34 model teaching practice to others? [ ] [ ] [ ] [ ] [ ]
35 engage in self-reflective practice? [ ] [ ] [ ] [ ] [ ]
36 develop leadership capacity and capabilities in
order to professionally develop others?
[ ] [ ] [ ] [ ] [ ]
37 engage in group reflective practice? [ ] [ ] [ ] [ ] [ ]
38 engage in a reflective process of progressive
problem solving led by teachers working with
others in teams to improve practice?
[ ] [ ] [ ] [ ] [ ]
39 develop an understanding that coaching
encourages improvements in teaching and
learning performance?
[ ] [ ] [ ] [ ] [ ]
40 plan lessons collectively and collaboratively? [ ] [ ] [ ] [ ] [ ]
41 support innovative approaches to teaching and
learning?
[ ] [ ] [ ] [ ] [ ]
42 develop an understanding that data gathering
and analysis leads to improvements in student
outcomes?
[ ] [ ] [ ] [ ] [ ]
43 engage in discussion on topics that assist to
improve practice?
[ ] [ ] [ ] [ ] [ ]
44 value coaching as an effective professional
development model that improves practice?
[ ] [ ] [ ] [ ] [ ]
45 apply new found knowledge? [ ] [ ] [ ] [ ] [ ]
46 discuss and explore episodes of teaching and
learning?
[ ] [ ] [ ] [ ] [ ]
47 take risks? [ ] [ ] [ ] [ ] [ ]
Appendix 2
48 source feedback from students in order to
improve their own teaching and learning
practice?
[ ] [ ] [ ] [ ] [ ]
49 focus their professional learning on student
outcomes?
[ ] [ ] [ ] [ ] [ ]
50 share teaching and learning approaches with
others?
[ ] [ ] [ ] [ ] [ ]
51 share learning gained from attending an off-site
professional development program to all staff
or faculty colleagues?
[ ] [ ] [ ] [ ] [ ]
52 develop an understanding that school based
professional development delivered by teachers
from this school supports improvement?
[ ] [ ] [ ] [ ] [ ]
53 appreciate professional development as
ongoing, supported and fully integrated into the
culture and operations of the school?
[ ] [ ] [ ] [ ] [ ]
54 collaborate on teaching and learning projects? [ ] [ ] [ ] [ ] [ ]
55 use literature to inform improvement to
teaching and learning?
[ ] [ ] [ ] [ ] [ ]
56 use data on student outcomes to encourage
improvement?
[ ] [ ] [ ] [ ] [ ]
57 encourage opportunities for mentoring and
coaching colleagues?
[ ] [ ] [ ] [ ] [ ]
Appendix 3
Survey structure
The survey was constructed to elicit information on improvement to teacher professional
practice. Questions posed encouraged teachers to reflect on their professional practice and the
degree to which the culture of the school encouraged their professional development.
The survey was divided into two areas “Teacher learning” and “School learning” and a series of
questions was constructed that pertained to each. Questions were categorized as relating to an
aspect and randomly presented in the survey for participants to complete. The purpose of this
was to evaluate the degree of consistency in the responses provided.
The areas, and questions within each category are presented below.
Teacher learning
Report 1 - Collaborative approach to professional development
13 plan lessons and or units of work with colleagues?
19 invite a colleague to experience your classroom teaching practice?
25 moderate student outcomes with colleagues?
29 team teach?
32 feel supported in this school and empowered to improve?
Report 2 - Giving of yourself to assist others
6 provide professional development to colleagues at either a faculty level or to the whole school?
12 share teaching approaches / lesson ideas with all colleagues in your faculty?
21 share and discuss student work?
26 share and discuss what you learnt / experienced at a workshop with colleagues at the faculty level?
31 share and discuss research on instructional practice at a faulty level?
Report 3 - Source professional development
5 attend off-site workshops?
7 research teaching and learning ideas from the Internet?
9 source professional development in specific areas?
11 explore teaching approaches that targets learning for a cohort of students?
14 engage in professional reading?
16 attend optional professional development offered by the school?
18 source and use material from journals published by subject associations?
20 find subject associations useful as a source of professional development?
22 align professional development activities to the priorities of the school?
Report 4 - Self-reflective practice
8 reflect on learning outcomes in order to think about improving your teaching practice?
15 consider that professional development changes your teaching and learning practice?
23 consider that professional development leads to improvement in student learning outcomes?
27 use a journal to record and reflect upon teaching experiences?
Report 5 - Using resources to improve practice
10 use on-line resources such as the Mathematics Continuum P-10 to improve practice?
17 seek the support of a coach / mentor / critical friend?
24 use ICT resources to improve practice? For example, interactive white boards.
28 trial new approaches / initiatives learnt from off site workshops? For example, the e5 instructional model.
30 use data to adjust your teaching in order to improve student learning outcomes?
Appendix 3
School learning
Report 6 - Collaborative approach
34 model teaching practice to others?
40 plan lessons collectively and collaboratively?
46 discuss and explore episodes of teaching and learning?
50 share teaching and learning approaches with others?
54 collaborate on teaching and learning projects?
Report 7 - Culture (feedback, risk taking, innovation, teacher reflective practice…)
33 develop an understanding that a performance and development culture exists?
35 engage in self-reflective practice?
37 engage in group reflective practice?
39 develop an understanding that coaching encourages improvements in teaching and learning performance?
41 support innovative approaches to teaching and learning?
43 engage in discussion on topics that assist to improve practice?
45 apply new found knowledge?
47 take risks?
49 focus their professional learning on student outcomes?
51 share learning gained from attending an off-site professional development program to all staff or faculty colleagues?
53 appreciate professional development as ongoing, supported and fully integrated into the culture and operations of the school?
38 engage in a reflective process of progressive problem solving led by teachers working with others in teams to improve practice?
36 develop leadership capacity and capabilities in order to professionally develop others?
57 encourage opportunities for mentoring and coaching colleagues?
Report 8 - Use data to improve practice
56 use data on student outcomes to encourage improvement?
42 develop an understanding that data gathering and analysis leads to improvements in student outcomes?
48 source feedback from students in order to improve their own teaching and learning practice?
Report 9 - Use resources to improve practice
55 use literature to inform improvement to teaching and learning?
44 value coaching as an effective professional development model that improves practice?
52 develop an understanding that school based professional development delivered by teachers from this school supports improvement?
Appendix 4
Teacher learning
Report 1 – Collaborative approach to professional development
Gender
Plan lessons and or units of work with colleagues?
Invite a colleague to experience your classroom teaching practice?
Moderate student outcomes with colleagues?
Team-teach? Feel supported in this school and empowered to improve?
Male Mean 3.80 3.30 3.40 3.00 3.30 N 10 10 10 10 10 Std. Deviation .632 1.418 .966 1.333 .949
Female Mean 2.82 2.27 2.55 2.73 2.55 N 11 11 11 11 11 Std. Deviation .874 1.009 1.128 1.489 1.128
Total Mean 3.29 2.76 2.95 2.86 2.90 N 21 21 21 21 21 Std. Deviation .902 1.300 1.117 1.389 1.091
Survey results: Lam
bertia College
Report 2 – Giving of yourself to assist others
Gender
Provide professional development to colleagues at either a faculty level or to the whole school?
Share teaching approaches / lesson ideas with all colleagues in your faculty?
Share and discuss student work?
Share and discuss what you learnt / experienced at a workshop with colleagues at the faculty level?
Share and discuss research on instructional practice at a faulty level?
Male Mean 3.60 4.30 4.10 3.50 3.50 N 10 10 10 10 10 Std. Deviation .843 .823 .994 1.080 1.080
Female Mean 3.18 4.18 3.45 3.18 3.00 N 11 11 11 11 11 Std. Deviation 1.168 .603 1.036 .982 1.183
Total Mean 3.38 4.24 3.76 3.33 3.24 N 21 21 21 21 21 Std. Deviation 1.024 .700 1.044 1.017 1.136
Appendix 4
Report 3 – Source professional development
Gender
Attend off-site workshops?
Research teaching and learning ideas from the Internet?
Source professional development in specific areas?
Explore teaching approaches that targets learning for a cohort of students?
Engage in professional reading?
Attend optional professional development offered by the school?
Male Mean 2.50 2.70 3.30 3.10 3.10 3.10 N 10 10 10 10 10 10 Std. Deviation .707 1.059 .675 .994 1.287 .568
Female Mean 2.36 3.00 3.36 2.82 2.91 2.45 N 11 11 11 11 11 11 Std. Deviation .674 1.095 1.027 .982 1.044 1.128
Total Mean 2.43 2.86 3.33 2.95 3.00 2.76 N 21 21 21 21 21 21 Std. Deviation .676 1.062 .856 .973 1.140 .944
Report 3 – Source professional development (Continued)
Gender
Source and use material from journals published by subject associations?
Find subject associations useful as a source of professional development?
Align professional development activities to the priorities of the school?
Male Mean 2.70 2.90 3.40 N 10 10 10 Std. Deviation 1.160 1.197 .699
Female Mean 2.45 3.00 3.27 N 11 11 11 Std. Deviation .688 .894 .905
Total Mean 2.57 2.95 3.33 N 21 21 21 Std. Deviation .926 1.024 .796
Appendix 4
Report 4 – Self-reflective practice
Gender
Reflect on learning outcomes in order to think about improving your teaching practice?
Consider that professional development changes your teaching and learning practice?
Consider that professional development leads to improvement in student learning outcomes?
Use a journal to record and reflect upon teaching experiences?
Male Mean 4.10 3.50 3.70 2.80 N 10 10 10 10 Std. Deviation .738 .707 1.059 1.398
Female Mean 4.09 3.64 3.73 2.82 N 11 11 11 11 Std. Deviation .701 .809 .786 1.079
Total Mean 4.10 3.57 3.71 2.81 N 21 21 21 21 Std. Deviation .700 .746 .902 1.209
Report 5 – Using resources to improve practice
Gender
Use on-line resources such as the Mathematics Continuum P-10 to improve practice?
Seek the support of a coach / mentor / critical friend?
Use ICT resources to improve practice? For example, interactive white boards.
Trial new approaches / initiatives learnt from off site workshops? For example, the e5 instructional model.
Use data to adjust your teaching in order to improve student-learning outcomes?
Male Mean 3.60 3.60 3.50 3.40 3.30 N 10 10 10 10 10 Std. Deviation 1.075 1.075 1.269 .966 .675
Female Mean 2.73 3.45 2.64 2.45 3.36 N 11 11 11 11 11 Std. Deviation 1.348 1.128 1.120 1.036 .924
Total Mean 3.14 3.52 3.05 2.90 3.33 N 21 21 21 21 21 Std. Deviation 1.276 1.078 1.244 1.091 .796
Appendix 4
School learning
Report 6 – Collaborative approach
Gender
Model teaching practice to others?
Plan lessons collectively and collaboratively?
Discuss and explore episodes of teaching and learning?
Share teaching and learning approaches with others?
Collaborate on teaching and learning projects?
Male Mean 3.60 3.20 3.40 4.20 3.40 N 10 10 10 10 10 Std. Deviation .966 1.229 1.075 .919 .516
Female Mean 2.45 2.45 3.27 3.45 3.00 N 11 11 11 11 11 Std. Deviation 1.036 1.036 .786 .820 .894
Total Mean 3.00 2.81 3.33 3.81 3.19 N 21 21 21 21 21 Std. Deviation 1.140 1.167 .913 .928 .750
Report 7 – Culture (feedback, risk taking, innovation, teacher reflective practice…)
Gender
Develop an understanding that a 'performance and development culture' exists?
Engage in self-reflective practice?
Develop leadership capacity and capabilities in order to professionally develop others?
Engage in-group reflective practice?
Develop an understanding that coaching encourages improvements in teaching and learning performance?
Support innovative approaches to teaching and learning?
Male Mean 3.40 3.70 3.70 3.20 3.10 3.30 N 10 10 10 10 10 10 Std. Deviation .516 .949 1.160 1.135 .876 .949
Female Mean 3.73 3.45 3.09 3.45 2.55 3.09 N 11 11 11 11 11 11 Std. Deviation 1.191 .934 1.044 .820 .934 1.044
Total Mean 3.57 3.57 3.38 3.33 2.81 3.19 N 21 21 21 21 21 21 Std. Deviation .926 .926 1.117 .966 .928 .981
Appendix 4
Report 7 – Culture (feedback, risk taking, innovation, teacher reflective practice…) (Continued)
Gender
Engage in discussion on topics that assist to improve practice?
Apply newfound knowledge?
Take risks? Focus their professional learning on student outcomes?
Share learning gained from attending an off-site professional development program to all staff or faculty colleagues?
Male Mean 3.80 3.90 4.00 3.50 3.30 N 10 10 10 10 10 Std. Deviation .789 1.101 1.247 .707 1.252
Female Mean 3.27 3.18 2.91 3.55 3.09 N 11 11 11 11 11 Std. Deviation 1.009 .874 1.221 .688 .701
Total Mean 3.52 3.52 3.43 3.52 3.19 N 21 21 21 21 21 Std. Deviation .928 1.030 1.326 .680 .981
Report 7 – Culture (feedback, risk taking, innovation, teacher reflective practice…) (Continued)
Gender
Appreciate professional development as ongoing, supported and fully integrated into the culture and operations of the school?
Encourage opportunities for mentoring and coaching colleagues?
Male Mean 3.20 3.80 N 10 10 Std. Deviation .632 .919
Female Mean 3.18 3.09 N 11 11 Std. Deviation .982 1.044
Total Mean 3.19 3.43 N 21 21 Std. Deviation .814 1.028
Appendix 4
Report 8 – Use data to improve practice
Gender
Develop an understanding that data gathering and analysis leads to improvements in student outcomes?
Source feedback from students in order to improve their own teaching and learning practice?
Use data on student outcomes to encourage improvement?
Male Mean 3.90 4.00 4.00 N 10 10 10 Std. Deviation .568 .471 .471
Female Mean 3.27 3.45 4.00 N 11 11 11 Std. Deviation 1.009 .934 .000
Total Mean 3.57 3.71 4.00 N 21 21 21 Std. Deviation .870 .784 .316
Report 9 – Use resources to improve practice
Gender
Value coaching as an effective professional development model that improves practice?
Develop an understanding that school based professional development delivered by teachers from this school supports improvement?
Use literature to inform improvement to teaching and learning?
Male Mean 3.30 3.20 3.30 N 10 10 10 Std. Deviation 1.059 .789 1.160
Female Mean 3.00 3.27 2.64 N 11 11 11 Std. Deviation 1.000 .647 .809
Total Mean 3.14 3.24 2.95 N 21 21 21 Std. Deviation 1.014 .700 1.024
Appendix 5
Teacher Learning
Report 1 – Collaborative approach to professional development
Gender
Plan lessons and or units of work with colleagues?
Invite a colleague to experience your classroom teaching practice?
Moderate student outcomes with colleagues?
Team-teach? Feel supported in this school and empowered to improve?
Male Mean 3.38 2.69 3.08 2.62 3.85 N 13 13 13 13 13 Std. Deviation 1.121 1.109 1.115 1.044 .987
Female Mean 4.25 3.78 4.21 3.30 3.96 N 24 23 24 23 24 Std. Deviation .897 .850 .721 1.222 .859
Total Mean 3.95 3.39 3.81 3.06 3.92 N 37 36 37 36 37 Std. Deviation 1.053 1.076 1.023 1.194 .894
Survey results: Grallina C
ollege
Report 2 – Giving of yourself to assist others
Gender
Provide professional development to colleagues at either a faculty level or to the whole school?
Share teaching approaches / lesson ideas with all colleagues in your faculty?
Share and discuss student work?
Share and discuss what you learnt / experienced at a workshop with colleagues at the faculty level?
Share and discuss research on instructional practice at a faulty level?
Male Mean 2.46 4.08 3.54 2.69 2.92 N 13 13 13 13 13 Std. Deviation 1.266 .641 .967 .751 1.038
Female Mean 3.04 4.46 4.21 3.75 2.92 N 24 24 24 24 24 Std. Deviation 1.367 .588 .588 1.032 1.213
Total Mean 2.84 4.32 3.97 3.38 2.92 N 37 37 37 37 37 Std. Deviation 1.344 .626 .799 1.063 1.140
Appendix 5
Report 3 – Source professional development
Gender
Attend off-site workshops?
Research teaching and learning ideas from the Internet?
Source professional development in specific areas?
Explore teaching approaches that targets learning for a cohort of students?
Engage in professional reading?
Attend optional professional development offered by the school?
Male Mean 3.00 3.31 3.23 3.31 3.38 3.31 N 13 13 13 13 13 13 Std. Deviation .707 .947 .832 .947 1.193 1.377
Female Mean 2.79 3.50 3.71 3.79 3.50 3.75 N 24 24 24 24 24 24 Std. Deviation 1.179 1.142 1.042 .977 1.142 1.152
Total Mean 2.86 3.43 3.54 3.62 3.46 3.59 N 37 37 37 37 37 37 Std. Deviation 1.032 1.068 .989 .982 1.145 1.235
Report 3 – Source professional development (Continued)
Gender
Source and use material from journals published by subject associations?
Find subject associations useful as a source of professional development?
Align professional development activities to the priorities of the school?
Male Mean 2.38 2.62 3.23 N 13 13 13 Std. Deviation 1.044 1.044 .725
Female Mean 2.92 3.29 3.83 N 24 24 24 Std. Deviation 1.176 1.122 .963
Total Mean 2.73 3.05 3.62 N 37 37 37 Std. Deviation 1.146 1.129 .924
Appendix 5
Report 4 – Self-reflective practice
Gender
Reflect on learning outcomes in order to think about improving your teaching practice?
Consider that professional development changes your teaching and learning practice?
Consider that professional development leads to improvement in student learning outcomes?
Use a journal to record and reflect upon teaching experiences?
Male Mean 4.00 3.62 3.62 2.38 N 13 13 13 13 Std. Deviation .577 1.044 .768 1.502
Female Mean 4.29 3.96 4.17 2.92 N 24 24 23 24 Std. Deviation .690 1.083 .778 1.381
Total Mean 4.19 3.84 3.97 2.73 N 37 37 36 37 Std. Deviation .660 1.068 .810 1.427
Report 5 – Use resources to improve practice
Gender
Use on-line resources such as the Mathematics Continuum P-10 to improve practice?
Seek the support of a coach / mentor / critical friend?
Use ICT resources to improve practice? For example, interactive white boards.
Trial new approaches / initiatives learnt from off site workshops? For example, the e5 instructional model.
Use data to adjust your teaching in order to improve student-learning outcomes?
Male Mean 2.38 3.69 3.54 2.92 3.08 N 13 13 13 13 13 Std. Deviation 1.121 .751 1.330 .954 .954
Female Mean 3.13 4.08 4.04 3.37 3.54 N 24 24 24 24 24 Std. Deviation 1.329 .881 .999 1.313 .779
Total Mean 2.86 3.95 3.86 3.22 3.38 N 37 37 37 37 37 Std. Deviation 1.294 .848 1.134 1.205 .861
Appendix 5
School learning
Report 6 – Collaborative approach
Gender
Model teaching practice to others?
Plan lessons collectively and collaboratively?
Discuss and explore episodes of teaching and learning?
Share teaching and learning approaches with others?
Collaborate on teaching and learning projects?
Male Mean 3.38 3.00 3.46 3.69 3.23 N 13 13 13 13 13 Std. Deviation .870 1.155 .967 .630 .725
Female Mean 3.83 3.58 4.04 4.30 3.79 N 24 24 24 23 24 Std. Deviation 1.129 1.100 .999 .765 1.103
Total Mean 3.68 3.38 3.84 4.08 3.59 N 37 37 37 36 37 Std. Deviation 1.056 1.139 1.014 .770 1.013
Report 7 – Culture (feedback, risk-taking, innovation, teacher reflective practice…)
Gender
Develop an understanding that a performance and development culture exists?
Engage in self-reflective practice?
Develop leadership capacity and capabilities in order to professionally develop others?
Engage in-group reflective practice?
Engage in a reflective process of progressive problem solving led by teachers working with others in teams to improve practice?
Develop an understanding that coaching encourages improvements in teaching and learning performance?
Male Mean 3.62 3.62 3.38 3.00 3.00 3.69 N 13 13 13 13 13 13 Std. Deviation .870 .650 1.044 1.080 1.225 .751
Female Mean 3.88 3.92 3.79 3.63 3.71 4.00 N 24 24 24 24 24 24 Std. Deviation .900 .881 1.062 1.209 1.042 .978
Total Mean 3.78 3.81 3.65 3.41 3.46 3.89 N 37 37 37 37 37 37 Std. Deviation .886 .811 1.060 1.189 1.145 .906
Appendix 5
Report 7 – Culture (feedback, risk-taking, innovation, teacher reflective practice…) (Continued)
Gender
Support innovative approaches to teaching and learning?
Engage in discussion on topics that assist to improve practice?
Apply newfound knowledge?
Take risks? Focus their professional learning on student outcomes?
Share learning gained from attending an off-site professional development program to all staff or faculty colleagues?
Male Mean 3.62 3.46 4.00 3.42 3.46 3.31 N 13 13 13 12 13 13 Std. Deviation .650 .877 .577 .793 .776 .855
Female Mean 3.96 4.25 4.17 3.83 3.88 3.62 N 24 24 24 24 24 24 Std. Deviation 1.083 .737 .565 .761 1.035 1.173
Total Mean 3.84 3.97 4.11 3.69 3.73 3.51 N 37 37 37 36 37 37 Std. Deviation .958 .866 .567 .786 .962 1.070
Report 7 – Culture (feedback, risk-taking, innovation, teacher reflective practice…) (Continued)
Gender
Appreciate professional development as ongoing, supported and fully integrated into the culture and operations of the school?
Encourage opportunities for mentoring and coaching colleagues?
Male Mean 3.85 3.38 N 13 13 Std. Deviation .899 .506
Female Mean 4.13 4.17 N 24 23 Std. Deviation .850 .937
Total Mean 4.03 3.89 N 37 36 Std. Deviation .866 .887
Appendix 5
Report 8 – Use data to improve practice
Gender
Develop an understanding that data gathering and analysis leads to improvements in student outcomes?
Source feedback from students in order to improve their own teaching and learning practice?
Use data on student outcomes to encourage improvement?
Male Mean 3.69 3.00 3.15 N 13 13 13 Std. Deviation .947 .913 .987
Female Mean 4.12 3.67 4.00 N 24 24 24 Std. Deviation .741 1.007 .885
Total Mean 3.97 3.43 3.70 N 37 37 37 Std. Deviation .833 1.015 .996
Report 9 – Use resources to improve practice
Gender
Value coaching as an effective professional development model that improves practice?
Develop an understanding that school based professional development delivered by teachers from this school supports improvement?
Use literature to inform improvement to teaching and learning?
Male Mean 3.77 3.46 3.23 N 13 13 13 Std. Deviation 1.092 .660 .599
Female Mean 4.17 3.96 3.33 N 24 24 24 Std. Deviation .816 .908 1.239
Total Mean 4.03 3.78 3.30 N 37 37 37 Std. Deviation .928 .854 1.051
Appendix 6
Interview schedule – Coach
Opening
The Department of Education and Early Childhood Development positioned you as coach in
this school to improve student outcomes in mathematics. The intention of this interview is to
explore your perceptions of the coaching program.
1. Describe your work history before you became a coach?
2. What does it mean to teach?
3. What does it mean to learn?
4. Share an experience you had in working with
a. the management team at the regional level,
b. the school administration,
c. teachers, and
d. students.
5. What does it mean to you to be a coach?
6. Reflect over the period in which you worked as a coach, what was the most
a. confusing,
b. rewarding, and
c. overwhelming aspect of the program?
7. How were you changed by the experience of working as a coach?
8. Describe a situation where you felt success and where the experience in working
with a teacher was made all the more worthwhile?
9. What seems most “on target” about what you did in relation to the school’s needs
and objectives?
10. Do you believe the coach program will benefit schools?
Appendix 7
Interview schedule – Principal
Opening
Your school was invited by the Department of Education and Early Childhood Development to
receive a Teaching and Learning Coach to improve student outcomes in mathematics. The
intention of this interview is to explore your perceptions and responses to the coaching program.
1. Who was involved and what were the concerns raised in deciding that a Teaching and
Learning Coach would be positioned in your school and be made part of the leadership team
to improve student learning outcomes?
2. What did it mean to you to have a Teaching and Learning Coach allocated to your school to
work at improving student learning outcomes?
3. What was confusing, exciting or overwhelming with the idea that you and your school
would be participating in a coaching program to improve student-learning outcomes?
4. What positive and negative implications came about from the experience in having the
DEECD position a Teaching and Learning Coach in your school?
5. How has the Teaching and Learning Coach contributed to school reform?
6. Has working with a Teaching and Learning Coach assisted and or challenged your approach
to leadership?
Appendix 8
Vladimir Propp’s Theory (1928/1969)
CHARACTERS
1. The hero (seeks something)
2. The villain (opposes the hero)
3. The donor (helps the hero by providing a magic object)
4. The dispatcher (sends the hero on his way)
5. The false hero (falsely assuming the role of the hero
6. The helper (gives support to the hero)
7. The princess (the reward for the hero but also needs to be protected from the villain)
8. Her father
NARRATIVE FUNCTIONS
Orientation/Initial situation
0. Actor’s biography
Preparation (1st sphere: the introductory sequence)
1. A member of the family leaves home
2. A prohibition or rule is imposed on the hero
3. The prohibition or rule is broken
4. The villain makes and attempt at reconnaissance
5. The villain learns something about his victim
6. The villain tried to deceive the victim to get possession of his/her belongings
7. The victim unknowingly helps the villain by being deceived or influenced by the
villain
Complication (or 2nd sphere: The body of the story)
8. The villain harms a member of the family
9. A member of the family lacks or desires something
10. This lack or misfortune is made known; the hero is given a request or a command and
he goes on a mission or quest
11. The seeker (often the hero) plans action against the villain
Transference (or 3rd sphere: The donor sequence (magic agent is obtained)
12. The hero leaves home
13. The hero is tested, attached, interrogated and, as a result, receives either a magical
agent or a helper
14. The Hero reacts to the actions of the future donor
15. The hero uses the magical agent
16. The hero is transferred to the general location of the object of his mission or quest
Struggle (or 4th sphere: The hero’s return)
17. The hero and the villain join in direct combat
18. The hero is branded
19. The villain is defeated
20. The initial misfortune or lack is put right
Return
21. The hero returns
22. The hero is pursued
23. The hero is rescued from pursuit
24. The hero arrives home or elsewhere and is not recognised
25. A false hero makes false claims
26. A difficult task is set for the hero and the task is accomplished.
Recognition
27. The hero is recognised
28. The false hero/villain is exposed.
29. The gales hero is transformed
30. The villain is punished
31. The hero is married and crowned.
Teacher interview data and analysis
Lambertia College
Appendix 9
Josh Ryan, Lambertia College1
Josh, a science undergraduate, completed his teacher training in 2008. He was employed the
following year at Lambertia, on a one-year contract teaching science and junior mathematics.
Josh initially viewed his teacher identity as one framed within a paradigm of creatively
engaging students with their learning, using a variety of pedagogical techniques. His university
teacher-training program juxtaposed against the didactic approach he experienced as a student
fostered this belief in teaching. The powerful specific local exigencies and contingencies of the
classroom reshaped this idealistic notion of teaching to one that was more traditional in scope.
This more traditional approach enabled Josh to cope with issues of student management while
delivering curriculum in the suggested time frame.
Josh was a member of the team of teachers who taught junior mathematics and therefore part of
the coaching program. Josh felt that working with a coach was somehow associated with
failure, of being ineffective perhaps jeopardizing his chances of getting reemployed and as a
result he distanced himself from the coach. Despite this feeling of apprehension, Josh
accommodated aspects of change, particularly with respect to the Mathematics Lesson Structure
introduced by the coach. By the end of the 2009 academic year, the Mathematics Lesson
Structure and the coaching program provided a framework from which Josh’s teacher identity as
a maths teacher reemerged in the moral order at Lambertia, all the while, still framed between
the contingent and local specific exigent realities of the classroom.
1 Interview 1 – 10/11/09. Interview 2 – 23/11/09. Interview 3 – 11/12/09.
Josh’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
Young, tall, white male.
Novice teacher in his first year of teaching. Josh is on contract and his contract terminates at the end of the 2009 academic year.
He will need to reapply for the position if he wants to work as a maths teacher in the following year.
He feels that he cannot reach out for support for he does not want to be labeled a failure.
Josh has a qualification in science (chemistry and psychology), which also makes him eligible to teach mathematics.
First year out novice teacher who applies himself competently and thoughtfully to his teaching role even though at times finds himself struggling with the contingent and exigent realities of the class.
He is viewed as new to the profession and afforded space to grow into the position.
Member of the science and maths faculty. Josh is part of the junior maths team of teachers and recognized as such.
Appendix 9
Orientation
Josh accepts a one-year contract as a teacher of science and mathematics at Lambertia College after graduating with a science degree at Suncrest University.
Theme
“I use to hate listening to the stories, [it] use to just annoy me… but at the same time, you know, I still asked her how it was…”
Semiotic analysis Positioning analysis
1/2 ... this is my first year of teaching and I’m 23… I went to high school in Neucomb just down the road... I got into Suncrest and did a Bachelor of Science… I didn’t really know what I wanted to do when I finished.… I knew I didn’t want to work in a lab and when I was at uni[versity] my sister had just begun teaching. It was her first year of teaching when it was my first year of uni, so she was at home… and I’d come home and I [would] always have to listen to… all her stories of, you know, this kid[’s] doing this and it used to annoy me and… my mum works in a school as well, as a librarian, so they… were working together and they were always talking about the same kid’s and what happened at school and I used to just, you know after a long day at uni I used to hate listening to the stories, [it] use to just annoy me… but at the same time, you know, I still asked her how it was and she… was struggling in her first year and it… didn’t really sell the job as much…. She tutored when
Education indexed emerging personhood. The interpretant at first is immediate, i.e., recognition of uncertainty progressing through to energetic for he is now a teacher.
Teaching as vocation indexed to his sister and mother’s “teacher talk” and also with tutoring.
Storyline of emerging personhood. Josh is positioned as the newcomer to teaching possibly as a result of the perlocutionary force / effect of his mother and sister’s “teacher talk”.
she was at uni and when I started uni she said, you know, why don’t you do this and gave me a few names who I can talk to… get a few tutoring jobs after hours for money... so I’d started tutoring probably in my second half of my first year at uni just maths and… science… and I was doing probably five or six hours a week just to get money to get through...
Summary:
Introduced to Josh’s moral world and how he negotiated uncertainty to enter teaching as a vocation.
Preparation
Josh confronts contradictions and barriers to realising his preferred approach to teaching.
Theme
“… when I was on [teaching] rounds there … was a maths… teacher… and his lessons… were the same, you know, examples on the board, do chapter 12a, do question one and two and that was his lesson plan…”
Semiotic analysis Positioning analysis
1/48 … now math… I just did… like… an elective where they just go over the basics from [years] 7 to 10. So you’re qualified to teach it but it’s not like a major. So my two areas of study… [are] chemistry and psychology, that’s what I spent most of my time in, you know look at the study design or the problems or the activities for those two subjects, but maths I just did second half of the year and we basically… went over, you know things that kids find difficult like decimals, they think the
Teacher training program focused on majors in undergraduate program.
Chemistry and psychology as social objects indexed to teaching these respective disciplines in secondary school. The interpretant is energetic.
However, a science degree also indexed to teaching mathematics for disciplines complement each other. The effect of which is logical however, Josh doesn’t feel that he has enough content
Josh positioned as a maths teacher. He realises the contradictory forces at play in the teaching of mathematics and the incompleteness of his university teacher-training program.
Appendix 9
longer the decimal is the bigger it is, like something like 0.756 would be greater than 0.8 just because it’s longer…. We knew how to change those ideas and teach in different ways but it didn’t really say much about how you do an effective maths class, like they gave lots of good ideas and lots of little games that you can throw in here and there to make it interesting and I remember like we’d have a two-hour tutorial and they’d throw in, you know a game or two each time and they[’d] say, you know you can do this with your kids and everyone used to love it cos it was, you know a game in a tutorial… but we never did anything like, “this is a unit of work, this is how you’d plan it, this is what you do at the start of a lesson and this is what work they’d do”… like things that now you wish they did do. Like there was a lot of content… like “this… is how you do this and this is how you teach it and this is what kids have trouble with and there’s this game” but nothing like, this is how you should run a lesson which you think… [they] kind of just assume, they just think you’ll do it however you want to do it. And most people know that when they were at high school they did it the same way; examples, kids did the questions and even when I was on rounds there… was a maths… teacher that I did rounds with at the same school and his lesson plans that I use to just read over
pedagogical content knowledge to teach mathematics for the mathematics training he received in his teacher training program was inadequate.
The teacher-training program as immediate object indexed to ineffectual training.
Josh is disappointed to learn that teaching mathematics is iconically related to the textbook. The traditional approach to teaching mathematics. The interpretant is logical for it indicates the possibility of an alteration to a traditional habit of teaching mathematics.
Whilst Josh appreciated the mathematical games taught in his teacher-training program, he feels he missed out on how to plan for an effective lesson. He distances himself from his current teaching situation.
Whilst Josh positions himself closely to his university colleagues / experience through pronoun grammar he also positions himself away from the traditional approach of teaching mathematics, for Josh finds the approach of lecturing students before instructing them to complete exercises from their text boring and ineffectual particularly for the students at Lambertia.
were the same, you know, examples on the board, do chapter 12a, do question one and two and that was his lesson plan, kind of thing, so I don’t, I just… find that boring… even though I learnt that way and I did pretty well at maths I don’t… think they, I don’t know, [it] has to be different for them, especially at this school.
In a final semiosis, Josh indexes the students as the social objects of not responding to the traditional approach of teaching mathematics. The effect is logical for Josh is thinking about altering a habit learnt from past experience.
2/114 ... I think the first time I was introduced to her was when we had… one of those first meetings and she kind of just ran the meeting and I thought oh, she’s like… the maths KLA (Key Learning Area) head or coach. I didn’t really see the difference between a coach and… someone who just ran the… meeting, so I wasn’t sure what… her role was and what we’d get from her, so yeah like I said she showed us a few activities that were pretty helpful at the start but I didn’t really know what I could get from the whole thing
The coach as a social object bears a symbol relationship to a head of department.
The coach hints to the dynamical dimension in that the coach is an object of reference in the world of mathematics leadership; a representation of maths teaching and related practice as presented by the coach.
Whilst Josh recognises the coach as somewhat significant there is a sense of uncertainty about her (immediate interpretant).
Josh is positioned as the one that is the recipient of pedagogical knowledge from the coach who is positioned as the one endowed with power and positioned to deliver it to the subject department.
Pronoun grammar indicates a positioning away from and resisting the coach’s advance all the while positioning himself closer to his colleagues.
Gifts in the form of the “warm-up” activities provided by the coach, whilst appreciated did not engender a closer relationship.
2/274 I think I could have sat down and listened to what she had to say and then I’d… have a[n] understanding of what she does and what she does is she come[s] into my class, whereas you know, I… wouldn’t ask her… if she said let’s have a meeting, let’s talk, I’d do that, cos you know that would be great, but you know, I haven’t gone out of my way to set that up, just because, you know so many other
The coach is indexed to authority charged with the improvement of practice.
The effect of which is energetic for Josh does not subscribe to the coaching paradigm for it questions his ability and may threaten his chance of reappointment. The interpretant becomes the
Pronoun grammar use indicates a distancing away from the coach as the one that has the authority / power to effect change.
Josh is resistant to the advance of the coach perhaps of his position as a first year out teacher on contract. Whilst a coach-initiated conversation would be welcome anything more would perhaps position Josh as
Appendix 9
things on my mind than that…
object of a further semiosis one where the coach is indexed to someone as a mentor.
an “underperforming” teacher in the local moral order.
Josh positions the researcher in agreement with his stance.
Summary: Although Josh had a clear vision of how he wanted to teach mathematics, the powerful specific local exigencies and contingencies of the class framed the way in which he approached his teaching. In addition, Josh is resentful of his teacher-training program for it did little to prepare him to teach mathematics. In light of this lack, when introduced to the Regional Coach Josh declines the offer to be coached, perhaps in response to protecting his institutional identity.
Complication
Josh comes to understand the complex nature of teaching at Lambertia and orients himself accordingly.
Theme
“… I… wanted to make everything different… when I first started…”
Semiotic analysis Positioning analysis
Context: Josh recounts his first experience of teaching maths.
1/32 Yeah, I think, the first topic we did was angles and measuring angles and obtuse angles and you know, the first topic and it… kind of annoyed me that I didn’t know anything about these kids, what they could do and here I am just teaching them angles like… it’s not maths to me, like straight away, I don’t know whether they know place value, whether they can add, whether they can times… all I know they can do is follow instructions using a… like all I was testing them on was whether they can follow the instructions to use a protractor or whether they could look at an angle and decide what it was, like it wasn’t really teaching at the start and I thought it was weird to start off, you know secondary maths with such a topic like that, you know a lot of the teachers were saying you know, it’s an easy one, it gets them confident at the start and I thought you know… we wasted four or five weeks just teaching them what I thought was basics anyway. So that was a little bit frustrating… and I…
Angles as a maths topic indexed to the introduction of teaching mathematics to Year 7 students. The logical interpretant is one of frustration for Josh doesn’t quite know the mathematical ability of his students.
Teachers of mathematics at Lambertia indexed to a syllabus. The logical interpretant hints to an alteration in a habit.
Josh is positioned; socio-culturally confined to an approach to teaching mathematics at the start of year 7 that he feels is inappropriate.
This traditional approach stultifies Josh’s agency in wanting to make a change to the way mathematics is taught at Lambertia.
Pronoun grammar use indicates that whilst Josh associates himself as belonging to teachers of mathematics he distances himself away from the “it”, i.e., the way maths is taught at Lambertia. Josh expresses his agency in wanting to break away from the traditional approach but feels that he cannot because of the powerful specific exigencies of the culture and of his position as a novice contract teacher at Lambertia.
Appendix 9
wanted to make everything different as well when I first started, you know when I was at high school it used to be the same lesson structure every time, you know you’ll write a few examples on the board, you show the kids how to do it and then you get them to do it in their… books and I just wanted to make everything different and it was just so hard with that… topic…
This experience hints to the intransitive dimension evoking memories of Josh’s experience when he was a student for the teaching of mathematics had not changed.
2/10 … I need to improve a lot in… you know, setting home work and getting them prepared every class, I think my main goal is to… you know get [th]em working for that one session and then, you know, I don’t know, haven’t really developed the skill of them going home and doing work and coming back and then asking questions it’s kind of all focused on that one lesson, you know getting through all the content in school cos they would, you know they struggle bringing their book[s] to class every day so how are they gonna, you know, go home, finish work, comeback, you know corrected themselves and stuff like that. So I think I try to make, tried to squeeze everything into a lesson rather than stuff at home so that’s what I’m all worried about because half of them don’t bring their books and you know they waste ten minutes trying to find a pen, so I think my style is even if they don’t have a textbook or
A teacher of mathematics as a social object is indexed to teaching and student learning. The effect of which is both a recognition and acceptance of the fact that students have a poor disposition to learning.
The logical interpretant leads to the next semiosis. Effective teaching indexed to students having the required materials at the ready.
Josh positions students as unresponsive to learning. He feels ineffective as a teacher in the prevailing storyline of teaching and of student learning. This is perhaps why Josh positions the coach away from him. He doesn’t want it be known that he is struggling and considered a failure in the local moral order.
He involves the researcher in agreeing to his “teacher talk” as he struggles (heroic cry from within) to come to terms with engaging students.
something there that they can take something out of that lesson …I think that’s turning out to be a bad thing because you know they’re not getting organised and they’re not preparing for later years but I think at this stage I just… try and minimise, you know, behavioral problems and kids acting up that I just, you know, set it all out at the start of the lesson on the board and hope that they’re working rather than, you know, bring your textbook, this is what we’re doing, so whether it’s just introducing with notes and then a worksheet, you know, all they need then is a pen and paper to get them going… so now… I’ve… dug myself in a hole with not worrying about them bringing equipment because they… kind of just get away with it every session. So you know, it’s hard to get that balance of getting them organised but then doing stuff differently…
The effect of this is energetic for Josh prepares lessons on the board and equips students with pen and paper to get the class underway. A response to the contingent realities of the classroom.
Josh’s practice indexed to socialising students to arrive to class without the required material. That is, students are not accepting responsibility for their own learning. Despite this, the effect continues to be energetic.
Josh develops his teacher identity as linked to the contingencies of the classroom. Josh speaks from the self, expressing frustration in engaging students and distances their poor learning disposition through us of third person plural.
Summary:
The umwelten at Lambertia stultifies transformational activity for it references behavioural norms that act as structural impediments to the improvement of practice particularly for a novice teacher.
Appendix 9
Transference
Professional development assists Josh to imagine the possibilities open to his practice as a teacher.
Theme
“… just seeing something different made me want to try my own kind of thing…”
Semiotic analysis Positioning analysis
1/34 … I don’t know, I just, I remember having older maths teachers, you know and they, you had to just sit there you’d copy the examples down, you do it, I mean that’s… okay for some people but, you know other people who don’t know how to do it and I… remember seeing on my [teaching] rounds, there was one of my supervisors [who] did things a lot differently where… instead of using the textbook they[’d] have like a booklet (refer 1/36 below) and they’d …all work at different levels according to them and you know they were all independent and it just worked a lot better than standing out in front of the class saying do this, this, this and then you try it.
Teaching indexed to engaging students with learning. The immediate object hints to the dynamical (ontological dimension).
The effect is logical for Josh recognises and accepts that the traditional didactic approach to teaching is not effective at engaging students.
Josh recognises the need to meet the learning needs of students in a differentiated way.
Josh positions himself based on a past experience. He recognises that a didactic approach is ineffective for it does not attend to their needs.
Pronoun grammar use indicates a distancing away from the traditional didactic approach and even the differentiated approach as presented by his supervisor in Josh’s teacher training program as perhaps inadequate for students at Lambertia.
Josh speaks from the authority of self and positions the researcher in agreeing with his “teacher talk”.
1/36 … it had… textbook kind of questions in it… it had puzzles, it had more activity-based kind of things and I remember just seeing something different made me want to try my own kind of thing and yeah with the Year sevens, I… don’t know, I just didn’t wanna get into that habit even though later on they’re gonna do that
Josh indexes innovative approaches to teaching mathematics to the social object of teacher.
The immediate object hints to the dynamical object, i.e., of past practices, of a possible reality (ontological dimension) and independent of Josh’s world.
Josh positioned in the socio-culture of a school structure that frustrates his agency to teach using an innovative approach to engage students with their learning.
anyway, but I always wanted to do something different. I remember… all through my course I was doing different things when I had, you know my supervisor’s classes, I’d do practical things, group activities… I don’t know just to be different and try and be more exciting cos, I don’t know, I just didn’t wanna go in and do the same thing that everyone’s been doing for years and years and I still try that now, I hate doing the same bor[ing]... like every now and then I’ll have to do examples and say questions, because you know you can’t plan every lesson perfectly, but every now and then I like to do something different because I think they, the kids need that and…. I think it was two or three weeks in, I went on a PD for the interactive whiteboards and I’ve being using that in my maths classes now as well, just getting kids up and using it in front of them it’s just, I don’t know, they find it a lot, a lot easier when they can get up and show their friends how to do things and I don’t know, it just needs to be different… especially in this school no kids gonna sit there quietly, watch you do something on the board, write it down, sit there for 10 minutes while you explain it and then do it themselves… you know, one single session… doesn’t allow for that, you know, structure I think. So that’s why next year we’re… doing this whole
The initial effect is a logical interpretant, i.e., reflecting on past practices strengthens his resolve to try different approaches to teaching.
The subsequent semiosis leads to an energetic interpretant, one where Josh attends a PD session on using the interactive whiteboard (IWB). The IWB indexed to innovative teaching; an approach that encourages students to come to the front of the class and enact the teacher narrative.
This narrative supports students in their learning engaging them as they articulate mathematical steps to solving problems using the IWB.
Pronoun grammar use indicates how Josh positions himself as wanting to step away from the teaching style of his past.
He demonstrates his agency in attending a professional development session on the EWB (illocutionary / performative force). The perlocutionary effect is the positioning of him and his students in an alternative practice which casts light on Josh’s emerging teacher identity.
This may be viewed after Propp (1968/1928). Josh “violates the interdiction” of keeping to the teaching storyline leaves the security of the traditional approach to teaching mathematics to save as many students as he can.
Appendix 9
different program with the maths...
Context: Off site regional PD run by Joel Hindrict for local primary and secondary school teachers of mathematics on the regional sanctioned lesson structure.
2/242 That was the focus of the one that I went to and I went to the last one where they summed it all up and gave us a lesson plan and we planned, we worked… in groups of three or four and we planned, they gave us a topic, ours was fractions, they gave us fractions and said… plan a 60 minute lesson right now what’s your “warm-up”… what’s your “reflection” activity, what’s your activity, like the whole thing [lesson plan] and we did that on… a piece of butcher’s paper and then presented it to everyone and said this is what we’re going to do.
Professional development indexed to improvement to practice. The immediate object whilst relatively independent of the present though hints to the real object of reference in the world.
The effect is energetic for Josh engages with colleagues to construct a lesson plan based on the structured lesson approach that is proposed for implementation in the following year.
Josh positions himself as an emerging teacher confronting the traditional didactic approach to teaching mathematics.
He positions himself as belonging to colleagues using first person plural “we” to design and present a classroom lesson based on the Mathematics Lesson Structure (“magical agent”).
Josh feels that the “magical agent” will prove successful in defeating the “villainous” effects, after Propp (1968/1928), the traditional approach to teaching has on students.
Summary:
Josh, realising the lack in the traditional approach to teaching mathematics, takes a risk and alters his teaching practice, which proves to successful. In doing so, he transforms his material activity and experiences first hand the positive effect it has on students thereby recasting his teacher identity.
Struggle
Lambertia stultifies Josh’s emerging identity thereby socially reconstructing what it means to be a teacher.
Theme
“… I… don’t know what she can offer me …”
Semiotic analysis Positioning analysis
2/94 … I got taken out of my year 12 class for that meeting to plan this whole Year seven, Larry Owen2 thing and… there was me, Tony, Pete and Samantha at the start and you know we… were all trying to get our head around this Larry Owen thing and we only had that one session and by the time, you know, we all finished period one and got together and started talking about it, getting resources… it wasn’t going anywhere and then the principal gave us, you know, double sessions here and there… to try and get this unit together and we eventually got, I think algebra was the first topic that we did it with, and we finally got it all together, and what we were going to do, and it was good for about three sessions. The first three that we put all the time into and then at the end of the unit [we]… just went back to teaching the old way because we didn’t have enough time, it took so much time to organise, you know [VELS] Level three, four and five, what activities that we’re gonna differentiate you know how
The Larry Owen differentiated approach (the immediate object) bore an iconic relationship to effective maths teaching.
The effect of which was logical for whilst Josh recognised and accepted the differentiated teaching approach the experience did little to strengthen his teaching practice.
The differentiated approach to teaching indexes an effective teaching practice that may benefit students because of their different ability levels.
The interpretant is perhaps logical at first but by the end of this differentiated approach to planning and teaching is demonstrated as energetic for the team of maths teachers abandon teaching to the differentiated approach returning back to their tried and tested approach to teaching mathematics.
The “it” refers to the Larry Owen differentiated approach to teaching mathematics.
Josh positioned in the local moral order along with colleagues directed by a coaching storyline of reform. The coach inscribed with power to implement a differentiated approach to the teaching of mathematics.
Josh positions himself as belonging with colleagues as expressed in first person plural pronoun use and positions the researcher in agreement with his groups decision to dismiss the differentiated program.
2 A mathematics consultant who brought a differentiated approach to teaching mathematics to the teachers of Lambertia College
Appendix 9
we’re going to assess them because we had all these great activities but how do we know who’s doing what and how much they know because. We’d open up the doors, have two classes working together and I’d be teaching some of Pete’s kids and helping them out but he wouldn’t know what I am seeing and it was just the whole thing was a mess we… put all this work into it and you know Tony and Pete and the people that have been here for awhile just thought we’re doing all this hard work and we didn’t see the point of it like Larry Owen had talked it all up but we didn’t see how it could work especially in our school… so everyone was a little bit reluctant and all this work went into it and we got halfway through the unit and we thought you know… what do they know, how much have we taught them… it didn’t go anywhere and with Samantha only being here once a, you know, every second week she’d help out for one week and then we wouldn’t see her for, you know two weeks and we couldn’t find out what she thought of it and it was just a mess, a complete mess so then… we did that one algebra unit and then… we didn’t have the time to sit down and do another one, I think we… it must have been measurement, we started with and we did it towards the end… of term and then we started the term doing the measurement unit we got
The coach offers support, one that brings experience and resources. A significant other indexed not only to moral authority but also to a moral capacity is absent when teachers most needed her assistance. That is, a story line likened to an absent mother figure that is absent and unable to care to the needs of her children.
The coach as significant other is instrumental to meaning making that encourages mutual
Josh positions the differentiated program as unworkable given that student learning and understanding was negligible given the effort that the group of maths teachers put in. This storyline was adopted in the absence of Larry Owen and the Samantha coach.
halfway through it and… we didn’t know what was going on and then… four or five weeks later we did another topic and then we, while we were doing that topic we said alright we’ll try it again with algebra and it was a little bit better but by that stage we just thought, you know it’s too much work… and you know, I don’t think anyone saw the need to do all this work and we couldn’t see the effects of it really.
intelligibility.
2/120 … I’ve had Tony coming [in]to my class a lot of times with… [the VIT] registration process and we have our little focus… each lesson when he’s… in but… I think the one thing that stood out was I think it might have been term two or three and I had a class over in the ‘M’ Block and where Samantha’s office is and… I could see her in the back and I had a Year eight maths class and we’re doing something and… I went off at the kids I just, they… [were] being really ratty that day and it was hard to tell a few kids off and then help the other half and I thought it would have been good if she could have just stepped… in and help[ed] out those ones who wanted help with the maths, you know, while I dealt with the other kids, it’s hard to, you know, deal with kids and then teach the other half who wanna learn and just seeing her that day… I don’t know if she
A mentor (object) is indexed to improvement of teaching practice. Tony as a mentor teacher and the VIT3 as social objects are both indexed to a requirement for inducting graduate teachers, i.e., conceptual model iconically related to teaching and learning. The effect of which is energetic.
Josh indexes the coach (immediate object) as one who can assist teachers in times of need, i.e., classroom management.
The effect is immediate for Josh doesn’t quite understand the relationship between the sign and the object. For example, Josh does not index the coach as intended by the DEECD but rather as someone who is there to support his teaching.
Josh positioned as a first year graduate teacher by the VIT and consequently has to complete an induction program that will position him with the right to teach through registration.
It is through this teacher registration process that Josh realises his emerging teacher identity as supported by his confidant / mentor who inducts and assists Josh to realise his teacher identity.
3 VIT – Victorian Institute of Teaching is a statutory authority to regulate the teaching profession established by an Act of the Victorian Parliament in 2001. Graduate teachers are required to undertake a structured induction program.
Appendix 9
noticed me… in there trying to deal with everything and I just thought and I went and spoke to Tony about it, I go… “what [do]… these coaches do, you know I… had a maths class right there, she saw it was maths, you know, she could have came in and helped”, and Tony’s like “na they’re not there to you know control your classes”, “I go, no not that, just, you know the people that needed help” and he’s like “yeah well, you know, she’s got work to do” and kind of, just an eye opening experience that, you know we’re in a maths class that there[’s] a coach, the word coach to me means you know help out in a maths class and she just … sat there so and then I don’t know, I just don’t feel… it feels like… if I asked for help I’m kind of struggling, you know what I mean, whereas you know I… don’t know what she can offer me that hasn’t been stated, what she can do I mean I’ve seen her helping out Raymond’s classes but whether that’s just because he want[s], needed an extra person in there and he wasn’t comfortable with his kids or, you know I don’t know I’m not sure what they, what they do I haven’t been told, you know.
In a subsequent semiosis following a discussion with Tony, Josh surmises that the coach is in fact someone that will improve his teaching practice. This storyline is juxtaposed against the private act of teaching competently as the sign symbolically represents the autonomous teacher as social object. The interpretant is energetic for Josh does not express a desire to engage the coach to improve his practice for he feels that he will be labelled as an ineffective teacher.
Josh indexes the coach as perhaps interfering with his emerging identity as a competent teacher in the local moral order. As a contract teacher, Josh perhaps perceives that being supported by the coach may be viewed negatively by the administration and detrimental to his effort in reapplying for his position at the end of the year.
Alternatively, the coach may be viewed as a mother figure (object) that attends to the cries of a struggling son; mother knows what’s best. Where Tony, the older sibling and mentor indicates that Josh now needs to stand on his own two feet for he is no longer a child unlike Raymond who is still in need of support.
The coach is positioned by the DEECD to improve teaching practice. Josh confused with the role of the coach comes to the realisation that the coach works with teachers who perhaps experience difficulty and as a consequence this may threaten Josh from obtaining his VIT registration (symbolic of teacher “hero” status and emerging teacher identity). Therefore, Josh resists the coach even though in a moment of dissonance he was prepared to accept her offer of assistance.
Pronoun grammar use indicates that Josh makes his position clear by distancing himself from the coach and positions the researcher in agreement with his “teacher talk”.
Summary:
The local moral order inhibits Josh’s emerging teacher identity. Firstly as a consequence of having to implement a differentiated program with little support from both Larry Owen and the coach. And secondly, Josh felt that to solicit support from the coach was an admission and recognition of failure as a teacher and that this would have a negative effect on his emerging teacher identity.
Appendix 9
Return
Josh points to the need to improve his practice.
Theme
“… I think next year I really want to get… into it… making the most of the coach…”
Semiotic analysis Positioning analysis
3/24 ... I don’t know, I guess… I saw it more of [as]… something you would… reach out for if you were struggling more so than doing it to improve… you know Raymond has had a… bit of a rough year so just maybe that was playing on my mind whether he was going to her for help to control his classes or whether it was you know a more… of a focus… you know, aiming at when they were coaching so I think that was probably what… threw me off at the start but… yeah I think next year I really want to get… into it because you see a loss of the older teachers that are reluctant to… go to meetings and all these numeracy PLTs4 you never see any of the older teachers there it’s usually four or five of us at most… [have] dropped off as the years gone on so I don’t wanna fall into… they’re stuck in their old ways and they don’t wanna improve so I wanna be the complete opposite of that so I think you know making the most of the coach next year, probably do that.
The coach is indexed to supporting and improving practice.
Josh indexes the coaching program to assisting teachers who struggle, unable to control their class and unable to teach effectively.
The effect initially was energetic for Josh did not go out of his way to seek the support of the coach.
This became the object of a subsequent semiosis for Josh now indexes the coach to improvement of practice. A sense of defiance in light of the old teaching habits of the past iconically related to the older teacher.
For older teachers are “… stuck in their old ways.” The effect of which is logical, i.e., a recognition and acceptance of the coach as one that improves practice by challenging old practices.
The “it” refers to the act of being coached.
Josh positioned as a new teacher to Lambertia and of wanting to improve his practice. At first he feel threatened by being associated with the coach for he feels that this is a sign of weakness. He realises that he does not want to represent the older teacher who doesn’t want to improve, stuck in their old practice.
Josh positions the listener in agreement to his “teacher talk” describing his emerging identity as he talks from the self to state his repositioning for the following year, recasting his identity in the process.
The “that” indexes the “… old ways…” of teaching.
4 Professional Learning Teams – a discourse community of teachers set up to assist and encourage teachers to talk about and share their practice thereby making improvement.
Summary:
Josh demonstrates agency in repositioning himself as one that wants to improve his practice accepting the role of the coach as one that will support his emerging teacher identity.
Appendix 9
Transformation
The “warm-up” as presented in the Mathematics Lesson Structure allows for a reconstruction of practice.
Theme
“… it takes five minutes, when you’ve finished it, everyone[’s] ready to go… whereas if…”
Semiotic analysis Positioning analysis
2/216 I think the warm-ups are really good… they get everyone switched on straight away, I thought when they… showed [th]em in the meeting, everyone was into it because we’re maths teachers and I thought you know this might or might not work. One of them was, you know [I] have between one and $500 in… [my] pocket and the kids get eight questions to figure out how much it is and I did that with my Year sevens and they were all, you know, they were fighting for being one of those people to answer… and that’s right at the start of a lesson and you’ve got everyone participating… it takes five minutes, when you’ve finished it, everyone[’s] ready to go… Whereas if you start a lesson and you know [you] start writing notes on the board, that five minutes is wasted with people trying to get their books out, so I found it really good to just get everyone straight onto it so there’s more of those warm-ups that we find out about…
“Warm-up” activity introduced at the start of the lesson indexed to student engagement and provides an indication of the real object of reference in the world, of student learning and experience in mathematics.
The effect of which is energetic for Josh incorporated the “warm-up” activity into his practice as a teacher and sees the relevance of it in engaging students with their learning.
Josh positioned as an emerging teacher in a meeting run by Joel Hindrict. It is in constitutive practice where teachers are able to make meaning, a process of mutual intelligibility. That is, meaning emerges for participants as a result of a mutual orientation towards a constitutive use practice; in this case it was the “warm-up” activity.
Josh speaks from the authority of self when he acknowledged the usefulness of the “warm-up” activity, not only improving his teaching practice, but also in assisting him to develop his identity and status as a teacher of mathematics.
Summary:
Josh demonstrates his newfound and emerging teacher identity as constituted by the coaching program and the “Mathematics Lesson Structure”. Both have assisted Josh to challenge preconceptions of teaching mathematics recasting his identity in the process.
Samantha’s response
“I was surprised by the lack of understanding of the role of a numeracy coach. The
expectation that a coach steps into a classroom to assist with discipline and management
oppose what we are taught as coaches.
Also surprisingly, this teacher still wants to improve his practice and sees some value in
some of the professional learning and lesson ideas.”
Appendix 10
Sarah Farqua, Lambertia College1
Sarah a senior teacher initially found the coaching program overwhelming. Sarah welcomed the
coach program for she genuinely felt that it would improve mathematics outcomes for all
students in the local community. She accepted her position as a school-based coach for the
following year sharing the position and journey with another of her colleagues, Lucy. Guided
by the Regional Coach and the professional development afforded to her, Sarah’s institutional
identity transformed as she became familiar with the myth promulgated by the Western
Metropolitan Regional office of the DEECD (DEECD, 2011). Her position as one of two
school-based coaches at Lambertia provided Sarah with recognition and an opportunity to
explore and expand her leadership capacity. She spoke enthusiastically of the coaching
program for the following year, articulating an approach to the improvement of maths teaching
that would position motivated Year 7 teachers teach to the Mathematics Lesson Structure; this
was the “game-plan”. The institutional order prevailed in transforming the structure of how
maths was taught and delivered at Lambertia, transforming teacher identity in the process.
Sarah’s account documents how an institutional order encouraged her through this process of
transformation.
1 Interview 1 – 5th Nov 2009. Interview 2 – 19th Nov 2009. Interview 3 – 14th Dec 2009.
Sarah’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
A woman of gentle character; married mother of two children.
A trained maths teacher. A senior maths teacher who has been selected along with another by the school administration to be the school-based coach for the following year.
A quietly spoken and articulate teacher who demonstrates an appreciation of mathematics and of teaching. She is recognised as such by her colleagues who on occasion seek her support.
A maths-trained teacher who teaches senior mathematics. Recognised as a maths teacher by the broader community and also by administrators who appreciate that she has epistemic authority to lead the change to the teaching of mathematics at Lambertia.
Appendix 10
Orientation
Sarah has taught for twenty-two years, sixteen at Lambertia College. At the time of this interview, Sarah was being trained to work as a school-based numeracy coach for the following year.
Theme
“… if you can do the work then you do maths science…”
Semiotic analysis Positioning analysis
1/2 … I became a teacher… I knew way back in Grade 3 that I wanted to be a teacher, I think I was very lucky that… I went to a very traditional primary school and we just had great teachers… very small in terms of we only had one class per year level and my Grade 3 teacher, I think was my hero… and so from there I decided that I would like to be a teacher. I think… [I]… fell into… maths science because of the subjects that I chose in secondary school… you know… that traditional push of, if you can do the work then you do maths science… I haven’t taken that push with my own children I’ve steered them away from that side because I think… it’s an area that you really have to love and either tends to lead you into research… or into… quality control type jobs with the science and not very much in between. So I think… which is fine if you just want to study it but to make a career out of it, I think it’s very…
Vocation of teaching indexed to a past teacher and experience in Grade 3. The effect of which was energetic.
Sarah indexes the disposition of a maths science student and the limited career paths available. She discourages her own children from maths / science. The interpretant is energetic.
Sarah positioned as a maths science teacher as a result of her upbringing.
She positions her own children away from maths science, as vocations for the career paths are limited in scope.
Sarah talks from the authority of self by using first person singular, positioning the researcher in agreeing with her “teacher talk”.
Summary:
Sarah loved studying maths and science discouraged by the limited career pathways available. She discourages her own children from studying maths and science.
Preparation
The coach bears the magical agent (mathematical know how) that will transform Sarah’s practice to one that will engage students.
Theme
“… Samantha, our coach has been quite an eye-opener for me…”
Semiotic analysis Positioning analysis
1/4 … I… wanted to teach but fell into teaching maths science… I’ve gravitated to the maths rather than the science… I find that much more practical for the kids and… you can see their understanding grow and that they value it more as ... something that’s useful to them. Science is probably a bit... easier to teach because it’s much more practical and... I find it a bit easier… to scale the work… so more kids seem to cope with science than with maths... and I think that’s where Samantha, our coach has been quite an eye-opener for me because, you know, reflecting back… on when we did method, you know... teaching methods at uni[versity], I think we spent three two-hour sessions and we got the “use the pizza to teach fractions” and that’s about it.
The coach is indexed to effective teaching of mathematics. The immediate object hints to the dynamical, of a world of teaching possibilities. The effect of which is logical for the coach has made the lack evident.
The lack represents the university teacher-training program. The teacher-training program as a sign indexes inadequate preparation to teach mathematics.
Sarah positions the coach as one that can provide her with an approach that would enhance her teaching of mathematics.
Pronoun grammar use indicates that Sarah enjoys teaching mathematics and believes in what it has to offer her students.
Sarah also positions the researcher in agreeing with her stance.
Summary:
Sarah appreciates the possibilities that the coach brings to enhance her teaching practice.
Appendix 10
Complication
The socio-cultural tradition of mathematics teaching is challenged
Theme
“… what we were doing wasn't working for our kids... they were coming in weaker…”
Semiotic analysis Positioning analysis
1/6 … well, you know, if you have a pizza and use that as an example to divide up… you know, for fractions, that’s the sort of thing that you would do… never got any of the background, the context… how kids learn, the stages that are critical to them making the next jump, you know, a lot of that sort of thing has… for me has come through Samantha... because traditionally maths was very much textbook... taught… and I guess, the structure of that appealed to me because I… teach very traditionally in terms of... you know, we talk about it I... give them some notes covering what it is that we’re doing in the example and then they… follow algorithms and then the problem, the worded problems allow you to then take it out into practical contexts that for some… kids, that was very difficult. So that was almost… a level of differentiation, but... with the work that Samantha’s been doing and exposing me to different resources… it’s given me a greater understanding of what they need to learn before they can move on… something I’ve found this year too in teaching Year sevens… is that the level of
University teacher training program indexed to teaching. The immediate effect reveals a lack for Sarah wasn’t exposed to a broad understanding of what it meant to teach well. Sarah’s once energetic interpretant that of what it meant to her to teach mathematics becomes the object of a further semiosis for Sarah realises the lack in her teaching practice.
The coach as the social object is indexed to improvement to teaching for she is resource rich and enthusiastic about her role. Sarah’s traditional approach (energetic interpretant) is put into question for the coach reveals the lack. Sarah questions her traditional approach in line with the dynamical object afforded by the coach.
The coach is positioned as the one that knows what it means to teach mathematics, whilst Sarah does not.
Sarah positions her training as ineffectual in teaching mathematics and is encouraged by the coach to improve through the myriad of activities on offer to engage her students. Students positioned as requiring assistance for they arrive with poor mathematical skills and understanding.
understanding that they come in with… is much... lower than I expected in terms of, you know, kids knowing things that I would take for granted, like tables and, you know, addition, subtraction, multiplication, their understanding of fractions is... quite poor. So this year we’ve had to do a lot of work in those areas... and that forces you to think about the learning steps that they’re going through… and also… the link between… not understanding [and] how that relates… to [their] behaviour… the proportion… of kids seems to be changing … whereas previously you’d have maybe three or four in the class now it may be the majority of the class. So then that forces you to go the other way in how you’re gonna cater for the kids that do understand it and not hold them back…
The coach as mother figure, perhaps Sarah’s Grade 3 teacher points to a new way of doing and saying casting a light on Sarah’s socio-cultural world of maths teaching. This provides Sarah with a self-actualising moment.
Sarah positions herself through first person singular as a traditional teacher one that adopts a teaching method that existed before her arrival and by which she herself was taught.
Sarah positions herself in the storyline of coaching for improvement to the teaching of mathematics aligning herself with the coach. Perhaps because she will be the school-based coach for the following year.
She positions her students’ lack of mathematical skill away from her, preferring that they should be skilled and ready for the next layer of learning. In addition, she positions the coaching approach also away from her, perhaps not quite sure if she is capable of making the transition from her current repertoire of teaching to the new coach directed way.
2/14 ... I think initially Samantha’s… enthusiasm and passion for… teaching... came across and as the coach she would, you know go off and find lots of different things on the [Inter]net and come back with these ideas… that you haven’t heard of… and then with the coaching... PDs that what’s happening this year, it… sort of exposed you to even more... the professional reading, research, as well as being
Coach indexed to improvement to teaching.
The effect of which is logical for Sarah strengthens her beliefs. The immediate object points to the dynamical, i.e., of the ontological dimension of mathematics, of teaching and learning and the inherent possibilities.
Sarah positions herself away from Samantha. Perhaps either hesitant to the impending change to her practice and or unsure of Samantha’s institutional identity.
Appendix 10
able to network with people and hear different ideas reinforced what Samantha was doing and Samantha was sort of also involved in some of those sessions run by region, so because we had someone back here that we could say, what about this... you had support to try different things so… I think it was just that whole new exposure and realising what we were doing wasn’t working for our kids... they were coming in weaker and that we really had to do something about it and I think in the past we didn’t really know what to do because often you know we relied on the textbook and modifying work by going to other textbooks…. So the whole coaching thing is it has… opened our eyes more to more practical... tasks that you could do in a maths classroom and more of that hands-on which allow kids to… get an understanding of what they’re doing and… also gives that realisation that… if you do something out of the ordinary they tend to remember that and it gives them something to hang on to so they may not remember the… maths initially but the activity may spark them and then the maths gets dragged along because that’s what the activity was about
The interpretant becomes the object of a further semiosis for the textbook and associated practices index a way of teaching that is ineffectual. The interpretant is logical for Sarah feels that practical tasks allow students to access mathematical learning.
The practical task that Sarah is referring to is the “warm-up” activity, for the activity is indexed to teaching that engages students, a strengthening and perhaps leading to a transformation of Sarah’s practice and identity
Through second person singular Sarah positions herself away from the coach and of the program that she represents.
Despite this positioning away, Sarah recognises that the traditional teaching approach is ineffectual and that change is inevitable. This is made evident for Sarah positions herself closely to her students.
Through first person plural “we”, Sarah aligns herself and belongs to the teaching staff. In addition, Sarah positions the researcher in agreeing with her “teacher talk”.
The positioning away from the coach and the regionally presented “structured lesson” approach to teaching perhaps indicates that Sarah is either overwhelmed or unsure of the emerging storyline as a school-based coach charged with implementing the new sanctioned lesson approach.
Summary:
The myth of reform offered by the coach offers Sarah an insight that she juxtaposes against the actualities of the everyday experience of teaching at Lambertia.
Transference
The realm of the possibility is where a transformation may occur.
Theme
“… if you… can improve their understanding… it’ll flow onto other parts of their schooling…”
Semiotic analysis Positioning analysis
Context: Sarah discusses her experience at the regional PD session to train up school-based coaches; her new position in the following year at Lambertia.
1/42 … the whole focus was improving numeracy in the region and… the western region has improved the numeracy so… she [the regional director] was pleased with that… it has had an effect and its made people focus on… what’s going on and then of course there’s that balance of are you just teaching to improve NAPLAN results because of league tables or [are] we actually looking at improving student’s understanding overall so that it actually has a flow on effect.… The idea for us is that it will, because then one of our big… charter goals is also to increase VCE results. So it’s… all linked and you know, if you… can improve their understanding… it’ll flow onto other parts of their schooling not just in maths and, you know, this year there’ve been conversations with geography and map reading and in… science and… graphs and all those sorts of things… and articulation of what you’re doing also helps those cross-curricular understandings and getting them to realise that you
The “she” as the Regional Director indexes improvement to student learning data as represented by the NAPLAN results. The effect of which is logical for Sarah’s understanding is strengthened, by defending the myth of school reform. She defends it with the logical argument that mathematics has a “flow on effect” in our lives.
It is this way that Sarah defends the current initiative. An apology for NAPLAN / league tables and arguing to hold the myth in good stead for mathematics is important to our everyday lives. The transcendental argument is invoked to strengthen the myth of mathematics.
The Regional Director (Western Metropolitan Regional Office of the DEECD) positions teachers of mathematics in line with the policy directive of improving numeracy.
Sarah positions the Regional Director using third person singular (“she”) and uses second person singular (“you”) to position teachers of mathematics and students away from her.
This perhaps indicates that whilst Sarah feels comfortable with the idea of improvement to teaching, she may feel overwhelmed by the expectation placed upon her by the Regional Director and resistance she may experience from teachers of mathematics she is expected to coach as part of her new role as school-based coach.
Appendix 10
don’t just draw a graph in maths that it does come up in other places and, you know, even… newspapers have graphs… it’s getting that broadening of… life for them and seeing how maths can help them understand their world and that the other… positive spin-off for us through the coaching has been that it’s primary and secondaries, so we’re meeting primary teachers and we [are] having those discussions over… the fractions issue… you know, some… do more than others, some… feel that their kids aren’t ready to tackle those concepts, some feel that it doesn’t come under their VELS levels and that they’re not expected to teach it. So, just having those discussions and… starting to work with them rather than, they come in here and they don’t know anything… so… for Behriana2 I think it’ll build more of a sense of Prep[aratory] through to 12… and everyone having an understanding of who’s doing what and how…
The interpretant becomes the object for a subsequent semiosis one that involves a constitutive practice of primary and secondary teachers indexed to the improvement of learning across the community.
Meaning or myth making is this account is derived from several objects all of which coalesce through conversation at a meeting of primary and secondary school teachers the Behriana encouraging mutual intelligibility of maths teaching.
Sarah positions herself as working closely with the other school-based coach “us” and “we”.
The storyline of student failure and how to overcome it becomes evident as a consequence of a constitutive practice encouraged by the coaching initiative for primary and secondary teachers of mathematics.
2/66 We… did... a few sessions… wasn’t as formal as sitting down together for a session… come out of class and if it’s recess or lunch we’d talk about it... so we did a few sessions like that... where she came in and had a focus on… what I was doing so, for example... one of the areas that we looked at was... giving instructions which
Sarah responds to the coaching narrative by being coached by Samantha.
Samantha indexes how to apply the Mathematics Lesson Structure to teaching junior students.
The interpretant is logical
Sarah positioned as a teacher being directed by the Regional Coach not as a teacher but as a school-based coach.
Sarah aligns herself closely with the coach through use of first person singular and plural (“I” & “we”) in accordance with her new role as school-
2 Lambertia College is located in the Shire of Behriana
may sound pretty trivial but with Year sevens... has a huge influence on the class and because I’d been teaching the seniors for a few years you don’t realise quite how much you assume that they know and how specific you need to be, so... we looked at that… in a class, she and I and we’d pick a few other things that she came in occasionally and… had a look at but it wasn’t a very formal coaching relationship…
for Sarah realises the difference between teaching the senior from the junior students.
Sarah iconically references her role with that of the coach as one of similarity, rather than who is her subordinate.
based coach.
Sarah’s emerging institutional identity reinforced by the coach’s affirmation of her capacity to respond to the coaching initiative.
Perhaps intimidated by the coaching experience, Sarah refers to the coach in the second person singular when she challenges the private nature of her teaching world.
Summary:
Sarah’s institutional identity as a school-based coach is strengthened through the professional development afforded to her by “head office”. Sarah aligns herself with the myth of school reform as bestowed upon her by the regional office of the DEECD. As part of the professional development offered by the region, the coaches at Lambertia meet with primary school teachers hints to a constitutive order that makes the lack apparent strengthening their coaching identities in the process.
Appendix 10
Return
The “game plan” is ready to take on the challenge.
Theme
“… once… they see that they can do it and can experience some success I think that’s where you… get them …”
Semiotic analysis Positioning analysis
3/76 … it gives Lucy (the other school-based coach) and myself another ally and another person who knows what they’re doing… and Samantha knows more than us so she’s a great support for us…. We also have a… graduate… next year… so that’ll be good because I’m… [hoping] to harness that enthusiasm as well and sort of get that momentum going for this program so… and then on top of that we’re also going to the… on-line assessment but what we found that… gives you an idea of… where the kids are at and sort of just confirms suspicions that you already have it’s not really going to make changes to how they learn and so that’s why the… lessons I think are so important and for them to be interactive and… engaging… because they… give… an access point… because once… they see that they can do it and can experience some success I think that’s where you … get them. Whereas the fun and games… can be fun but they get bored after ten minutes and they don’t think they’ve learnt anything so again in… Joel Hindrict’s… lesson
The coach as social object is indexed to improvement to teaching.
The effect is logical for Samantha’s expertise is important to developing the moral capacity of the school-based coaches.
The interpretant becomes the object of a further semiosis for the graduate (part of the “game-plan for reform) is indexed to enthusiasm (non resistant behaviour). The effect of which is logical, i.e., a strengthening of their plan to implement change.
The “game-plan” is iconically related to the mechanisms that have been put in place to effect the improvement of practice, i.e., the school-based coaches, assessment tools provided, graduate teacher who will teach to the Mathematics Lesson Structure…
Sarah positions herself closely to both the Regional Coach and Lucy who is the other school-based coach through use of first person plural “us”.
Sarah also positions a graduate’s “enthusiasm” as supporting the implementation of the “structured lesson” approach.
Sarah positions herself away from the impending change. She also positions students away from her all the while connecting to the “warm up” component of the Mathematics Lesson Structure, for she feels that it may be the solution to engaging students.
This account shows Sarah’s affective dimension, one of apprehensiveness in the face of a changing paradigm and perhaps the resistance from staff and students alike.
structure where the reflection… is so critical is that it makes them talk about what they’ve done and then you can bring out what the actual maths was…
Summary:
Sarah realises the resistance that comes from change and is encouraged by the support that she has. Despite this, she feels apprehensive of the ensuing confrontation that will occur in the following year.
Appendix 10
Transformation
Identity reformation.
Theme
“… something like that I never would have done last year, I would have stuck to the textbook…”
Semiotic analysis Positioning analysis
3/20 yeah... sort of thinking like when kids come in… from primary school into secondary and… some can… add and subtract and multiply and some can’t and… you know… you try to show them the way to do it and I guess this is sort of taking a step back of saying why are they doing it that way and what… are the underlying beliefs that they have that makes them think that that’s correct so I think that’s the shift in my teaching whereas before I would have just tried to show them the right way and given [th]em all… more of the algorithms to follow; now I’m sort of thinking okay so… why do they think that and how can we change… for me that’s a shift and… that’s a shift that I want to get across to the whole department…
Primary school as the object indexed to students’ inability to add and subtract. The interpretant is logical for Sarah considers a change to her practice one based on self-reflection of student learning needs.
The immediate object of a teaching practice using brings the lack to the surface. Reflexively hints to the ontological dimension of teaching and learning.
Sarah is encouraged by this experience.
Sarah imagines herself as coach, i.e., as the one that knows and is now in a position to effect change within her school and subject department.
Sarah positions the researcher in agreeing with her previous teaching approach as the only way of dealing with the exigencies and contingencies of the classroom.
Use of first person singular indicates that Sarah is talking from the self in describing a transformation to her identity as evident in the change to her teaching practice.
Summary:
Sarah comes to appreciate the myth of school reform enacted by the Regional Coach as challenging the traditional approach to mathematics. Sarah’s identity transformation is perhaps on course to develop new possibilities in the maths department at Lambertia.
Samantha’s response
“It was surprising to be identified as an “ally” when often the coaches are viewed as the
“enemy”. I was also pleasantly surprised with the depth of understanding of the importance of
growth for every child.
The having to “cover content” concerns are typical of most teachers but I would have hoped that
this teacher could have seen more connections between concepts.”
Appendix 11
Pete Milios, Lambertia College1
Pete, a part time teacher was not receptive to the coaching program. Whilst he applied himself
to the differentiated approach to the teaching of maths, prescribed by the principal and led by
the coach, he did not appreciate the “messy” nature of the task. Pete’s part time status was
important to him and whilst he saw the need for change it could only be achieved through a
concerted effort by all, only happy to experience it perhaps from the outside looking in. Pete
felt that the numerous programs implemented over the years to improve student outcomes had
little to no effect for they were never properly monitored and assessed for their effectiveness.
Change for Pete appeared as “change for change sake” and he seemed tired at the prospect of a
further disruption to his practice. This contributed to Pete’s desire to not teach maths and not be
included in the coaching program for the following year. The coach was therefore someone
distant and one who had little effect on Pete’s teaching practice. Rather, Pete preferred that the
coach be used to resource the needs of teachers instead. In addition, Pete felt that the primary
schools in the local community were not effectively meeting the needs of students who arrived
at Lambertia with below than average ability in mathematics. Accordingly, for Pete, the system
appeared to be failing students. Finally, Pete described Lambertia as a “difficult environment”
to teach in and that the “motley crew” of students were not interested in learning. As a
consequence, Pete felt that repetition, as a teaching practice was important for it instilled in
students the necessary skills and knowledge required.
1 Interview 1 – 5th Nov 2009. Interview 2 – 17th Nov 2009. Interview 3 – 8th Dec 2009.
Pete’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
Senior, tall male. Part time teacher of science and maths with the corresponding rules and responsibilities required from a teacher, i.e., preparing lessons / course, discipline and welfare….
Hesitant and cynical of “change for change sake” particularly without consultation.
Pete sees teaching science perhaps as a calling whilst teaching mathematics is more of an imposition.
Attends the science faculty meeting rather than that of mathematics.
Pete appreciates the idea that a coach viewed as a resource to support teaching akin to that of a teacher of science who has a laboratory assistant to support his/her delivery of a lesson.
Accordingly, Pete does not deviate from the norm by inviting change and or a coach into his class to improve his practice.
Pete view of the coach demonstrates that he belongs to the science department.
Appendix 11
Orientation
Pete is a part time teacher of science at Lambertia College where he has worked since 1988.
Theme
“… I’m a science teacher and every science teacher gets a maths class…”
Semiotic analysis Positioning analysis
1/4 ... I did [a] science degree, did a Dip. Ed. ... after taking a year off… wasn’t sure what I… wanting to do… but... after having a year off [I] decided… I’ll do a Dip. Ed (Diploma of Education)… did some youth… work prior to that [to] see how’d I’d go with secondary kids and I thought… I’ll give it a go and so I’ve been here… since [19]88, been doing it since 88, science, biology got into maths... purely by the fact that I’m a science teacher and every science teacher gets a maths class... you know… you’ve got a maths background usually... just about every year I’ve had a maths class… anything from [Year] seven to nine never had a ten, I had a year eleven for half a year when I came back from long-service… but… junior maths pretty much every year… a class or two on the odd occasion…. So it’s not my specialty but you know, I’ve always been thrown into it and yeah it’s always interesting to see different ways of teaching particular... topics… coming to [the] realisation that… not all kids learn the same way... bit of a challenge at times. This year has been a little bit
Science trained teacher iconically related to teaching mathematics. The immediate object represents a historical understanding that the two domains are accepted as related to each other in the world of teaching.
The effect of which is immediate for Pete teaches maths and therefore recognises and accepts the relationship between the two domains and responds by accepting the role of maths teacher.
Pete positioned in a master narrative of teaching and learning. Pete speaks from the authority of self through use of first person pronoun (“I”) and positions the researcher as in agreement to his “teacher talk”.
Pete is a part time teacher of science. In the teaching system of rights and duties Pete has a moral obligation to teach mathematics even though the performative force of his speech act indicates that he would prefer not to.
easy for me cos I’ve had the LEAP (Learning Acceleration Program) group which is a group that’s… filled with kids that are fairly talented.
Summary:
The moral order views science and maths as complementary and imposes a responsibility on Pete as a science trained teacher to teach mathematics even though he would prefer not to.
Appendix 11
Preparation
Pete is introduced to the coach.
Theme
“ ... I wasn’t sort of too keen on having someone come in and observe my classes…”
Semiotic analysis Positioning analysis
1/22 How she was introduced to the school, well… the… first day of the year she was introduced to us… and… then at a maths meeting…. Introduced there as well and you know, she introduced herself and was… pretty much open to anything that anyone needed her, anyone that needed any sort of ideas on how to teach particular aspects of maths and or just wanted her to come in to… observe how… we taught, to give… feedback as to how… we might have been going with our explanations… to the kids… any aspect at all…. If there were any particular resources and I remembered… on one or two occasions when I asked for… a few lists of things… I just didn’t have time… she was able to get them for me quite quickly… but being part-time… I often wasn’t there… for the maths meetings… because I only had one math class I often went to the science meetings and missed out on the maths… meetings. We never really had many numeracy meetings… last year but this year there’ve been more scheduled numeracy meetings
The coach as social object indexed to the improvement of teaching. The effect was immediate and became the object of a subsequent semiosis, one that included:
1. Pedagogical ideas. 2. Classroom
observation. 3. Resources.
The effect is at first immediate but later energetic for Pete rejects the coach’s offer to coach him in class and also rejects the differentiated approach. The only form of assistance Pete asks from the coach is for the provision of resources.
Principal and math’s
Pete is positioned as a teacher of science and mathematics in a storyline of failure and requiring assistance in order to improve student outcomes.
A coach is presented and the donor and positioned as facilitating improvement. Her allies are the maths coordinator and the new College principal introduce the differentiated approach to teaching mathematics. The differentiated program is the treatment agentry that will improve teaching practice and student performance.
Pronoun grammar use indicates that Pete distances himself away from and not belonging to the coach even though he uses the coach to resource one of his lessons. He instead positions himself closely to the science domain as demonstrated through use of first person singular “I”.
where… the numeracy coach… has been there either running it or been there to help out…. This year in particular… with the new principal… there was… more of a push to begin a program that… the previous math’s coordinator wanted to get going a few years ago, I believe she said… Larry Owens’s2… method of teaching, where… you… schedule the year seven maths classes on together, as many as possible, two or three and you open up the doors and it’s team teaching that occurs in a large area… more activity-based… we were thrown into at the start of the year…
coordinator indexed to the improvement of numeracy. The interpretant is immediate and becomes the object of a further semiosis linking the improvement of student performance to the Larry Owen differentiated program.
The interpretant is immediate, of a low-level recognition. Evident given Pete’s allegiance is to science rather than mathematics.
3/266 … initially I didn’t know what that would mean for me until you know Samantha says, “you know, you can use me in any way you want; coming into your classes and observe your classes and let you know… what it’s like and you know... things to maybe focus on....” I wasn’t sort of too keen on having someone come in and observe my classes but then when I found out we could use her in lots of other ways... getting… ideas... helping us find resources... and then you know when… I could see that you know she… would fall over herself [to] try to, you know, help us and send us e-mails with things that might be useful for the
Coach indexed to improvement to teaching practice. The effect of which was at first immediate, i.e., a recognition and acceptance of Samantha’s role within the school followed by a logical interpretant for Pete appreciated Samantha’s ideas and resources whilst rejecting her offer to observe him teach in his class.
Pete distances himself from and resists the offer by the coach to improve his teaching practice.
Pete’s use of pronoun grammar positions Samantha away as someone he does not belong to. He indicates this intention through use of first person singular “I” indicating his preference for not wanting to be coached in his classroom.
2 Larry Owen is a mathematics consultant who brought a differentiated approach to the teaching of mathematics at Lambertia College.
Appendix 11
topic we’re doing and... you know, a spreadsheet on this or that... then... I felt that yep this is a good thing.
Pete positioning the researcher in agreeing with his point of view.
Summary:
Pete displays an affinity identity with the science department over and above that of mathematics. Whilst Pete appreciates the out of class support provided by the coach, he does not subscribe to the proposed changes to his maths-teaching repertoire as presented by the Larry Owen differentiation numeracy program, nor to the offer from the coach to improve / change his classroom teaching practice.
Complication
Pete does not hold any hope for the future although he hints to a constitutive order as a means of improving practice.
Theme
“… there’s change for the sake of change and things don’t necessarily seem to get better…”
Semiotic analysis Positioning analysis
1/122 ... I’m all for teachers supporting one another and showing methods, ways of teaching a concept, new ways which might get it across to kids better... but when it’s something where that’s sort of bit left of centre... I’m not… a big fan of it… I’ll put it this way… I’m not keen on teaching year seven maths next year... and there’s a couple of reasons for that and that [is] partly because of the, you know, the work that’s gonna be required in order to bring in any of these new programs… what’s also being done is... the whole school is going to 60 minutes a session, instead of 48 and so it’s mainly because they say… it’s... important that maths does have 60 minutes... 10 minutes of an activity which gets the kids in and get[s] them sort of energised and an activity which gets their minds going, working and then you’re teaching them, you know talking to them for five minutes at the most getting them introduced… to what they’re going to do, then they do it and then 10 minutes at the end… [for a] reflection… where you ask them, okay what did you
Change to teaching practice indexed to the Mathematics Lesson Structure. The effect of which is energetic for Pete recognises but does not accept the new teaching approach to mathematics. This is symbolically represented as “left of centre”.
The interpretant becomes the object of a further semiosis one where a change brought about by the Mathematics Lesson Structure is too onerous. The energetic interpretant is that of not wanting to teach Year seven mathematics for the following year.
Pete positioned as teacher of mathematics in a storyline dominated by change to the school structure brought.
The coach and her allies have introduced this new approach to the teaching of mathematics.
Pete’s resists and positions himself away from the new structured lesson approach for it threatens his teaching world and his teacher identity in the process.
Pete’s speaks from the authority of the self to indicate a distancing away from the Mathematics Lesson Structure, positioning the coach, principal and maths coordinator at a distance (“they”).
Pete also positions the students (“them”, “you”) in his maths class also at a distance
Pete positions the researcher in agreeing with his point of view.
Appendix 11
learn today, what did you find interesting… today or whatever. So that’s actually what, they’re wanting us to do in every maths lesson…
2/12 … I do enjoy teaching maths to an extent… it’s not my, I feel I’m lacking in… presenting it in a way that… all kids understand I know some of the kids will… pick it up very quickly from explanations; I go through examples but other kids wouldn’t and you know… how do I get through to them, you know, it’s difficult when, you know, that they… haven’t had a good grounding in the basics [at] primary school so you got to go back and cover those... it’s hard when you haven’t got... kids focused at times in a classroom you’ve got [to] spend a lot of your time getting kids back on task that’s what I find frustrating... in this place it hasn’t been much of a problem this year with the LEAP group that I have. The year seven LEAP group, it’s actually been more enjoyable, I’ve enjoyed going in there... tried a few different things but not as much as I really probably would like to...
Teaching mathematics indexed to an effective teaching practice, one that assists students to understand. The coaching paradigm perhaps has strengthened this connection for Pete. The interpretant is logical.
The lack (poor student performance) is made known and indexed to the local specific exigencies and contingencies of the classroom. The interpretant is logical.
Pete positioned as a teacher of mathematics who recognises the lack both within himself and in the broader community.
Pete confirms through first person singular that his traditional approach to teaching mathematics does little to help his students understand.
Pete’s use of second person singular “you” positions himself away from his responsibility as a teacher teaching students who don’t respond accordingly or who arrive from primary school lacking the necessary skills.
Pete positions the researcher in agreeing to his “teacher talk”. Of his tragic teaching circumstance. That is, of students who arrive without the necessary maths skills, of student who don’t focus on their learning. All within a paradigm of school improvement.
2/88 … I can see that some kids just… [see it] as boring, laborious… I know that repetition does help you [to] remember things it help[s] you to go about… understanding or not understanding it so much straight away… it helps… a lot of kids… that haven’t
Students at Lambertia as the immediate object indexed to lacking basic maths skills. The effect is energetic for Pete believes that repetition, as a teaching practice is the key to providing students with the basics in order to
Pete positioned in a school system that has failing students. The students have failed because of the lack, of primary school teachers who don’t know how to teach mathematics and consequently students arrive at secondary school
got an understanding of the basics yet they just can’t do a lot of the work out of the textbook… a lot of the students at our school have got very poor skills and really they need to be taken back a number of steps and exercises out of… the class textbook which all of [th]em are suppose to have aren’t really relevant to [th]em, it’s not gonna help them to learn anything, cos they haven’t got the basic skills and unfortunately a lot of the primary school[s] haven’t been equipping them with these basic skills from the VELS which are in the VELS they don’t even realise, you know some of the things they’ve got to teach them they’re surprised when… they’re informed that okay you’re supposed to be teaching these things you know we expect [th]em to have an understanding of these… things when they get to secondary school and the… comment that… was…“oh really, I didn’t know that we, they had, we had to do that”, and I’ve also heard that… there are teachers at primary schools who aren’t confident with teaching science and aren’t confident with teaching maths so they don’t focus on it as much with their group of kids.
succeed at maths.
The effect becomes the object for a further semiosis. Students indexed to the lack of adequate primary school teaching of mathematics.
The lack of skills that students have as a consequence of inadequate maths training at primary school makes maths irrelevant to them. This is evident when students don’t have the prescribed text, for this too is ineffectual in meeting the challenge.
The effect is energetic, i.e., that repetition is important to the development of maths skills in students.
without the necessary skills in mathematics. Pete feels that repetition is a way of encouraging students to learn the basics.
Pete’s use of pronoun grammar positions himself away from students. In addition, he positions teachers at primary school as not being able to equip students with the basic skills. Finally, he positions the listener / researcher in agreeing with his moral position of a teaching practice that is necessary in dealing with the contingent realities of the classroom..
3/84 … there’s a lot of… scepticism, cynicism with... possible change and doing things in a different way… and people being taken out of their comfort zone and maybe having to do more work, you know. I know there’s some older people
Pete positioned in a difficult teaching environment.
Appendix 11
here who and I could also be put into that… boat… where it’s just like there’s change for the sake of change and things don't necessarily seem to get better… just… [seem] like… just extra work and… there’s already plenty of work with the nature of some kids around here in some of the classes, you know, banging your head against a brick wall and... a lot of kids in the class are suffering… you know, the... motley crew that... are there in some classes particularly at Year nine this year... so… I think there… are a lot of people here that have got… you know [an] idea that [they] would like to see improvement in the student’s learning and would wanna try something that’ll help them to improve but… there’s underlying cynicism there, I think… that’s a natural reaction in a place like this and we just go ahead and you know give things a go anyway.
The metaphor “…change for the sake of change…” iconically related to the immediate object of the coach
The effect of which is logical for Pete is reluctant to move away from his comfort zone, i.e., a strengthening of a habit.
The interpretant above becomes the object of a subsequent semiosis. Students at Lambertia indexed to difficult learning experiences. The interpretant is energetic, a “… a natural reaction in a place like this…”
Pete feels positioned in this way because of a storyline of difficult students who negate teaching efforts fuels a culture of cynicism amongst staff that appears to have given up trying.
The coaching program is another message from “head office” to encourage teachers not to give up. The request is met with resistance for Pete together with his colleagues are already working heroically. Any move away would disturb the sense of equilibrium (“comfort zone”); perhaps disrupt the ground they have maintained.
Pronoun grammar indicates Pete positions himself away from students, his colleagues and with the reform agenda.
Pete involves the researcher in why he has taken the position that he has.
3/288 … it’s all about improving students learning… and if, you know, if it’s something that people genuinely believe is gonna help then… if it’s a program that’s… going to help them if we go ahead and choose to do that program then it needs to be a wholehearted effort where everyone’s… involved in it and that everyone’s gonna give it a go and everyone’s gonna support one another so… okay we’ve got to give it a try… everyone’s got to be
Student improvement indexed to a collective approach by staff to apply a program that engages students with their learning.
The immediate hints to a dynamical object that speaks of a civic / democratic approach to change, of a constitutive order.
The “it” refers to the Mathematics Lesson Structure.
Use of pronoun grammar positions Pete as belonging to his colleagues in giving “it” a go.
Despite this he positions himself as not belonging to the “it” nor to his students.
convinced that… this is a good way to go, bit of debate doesn’t hurt, not much of that happens around here as… it used to years ago… but anything that’s gonna help to improve students’ learning that… looks like it may work yep go for it but as soon as there’s signs that okay it’s not working and it’s gotta be reviewed and looked at as soon as possible and not just dragged out where you know it’s just organised chaos and the kids aren’t getting anything out of it the teachers’ aren’t finding that… it’s helping their classroom management and you know, people going back and resorting to their old ways so its gotta be all in or none, everyone’s gotta be convinced that yep this is the way to go and from the sounds of it, even though I wasn’t there… the program of how the sixty minutes maths lesson will work using… Joel Hindrict’s… method… of running a lesson, a lot of people… seemed to be… encouraged by it so it’ll be interesting to see how that goes… on the outside looking in.
The effect of which is logical for it is based on a number of conditions.
The object becomes the object for a further semiosis, of disruptive students who disrupt learning causing concerns with classroom management.
The effect is now energetic for whilst Pete is encouraged by the sense of change brought by the Mathematics Lesson Structure, he doesn’t want to be involved.
Pete describes a collaborative and calculated assault to the improvement of student performance using the Mathematics Lesson Structure.
Pete expresses his interest in evaluating the collaborative effort of his colleagues in the implementation of the Mathematics Lesson Structure through the eyes of a strategist, i.e., as a person “…on the outside looking in.” Perhaps in proving that it will not work.
Pete positions the researcher in agreeing with his position as a teacher at Lambertia.
Summary:
Pete has ceased to be responsive to his teaching responsibilities, perhaps as a result of teaching to the same cohort of students since 1988. The account provides an insight into the exigent and contingent realities of the classroom and the effects that this has on Pete.
Appendix 11
Transference
Pete’s institutional identity positions him as belonging with his colleagues and to their growing appreciation for the Mathematics Lesson Structure.
Theme
“… it was something that… we used to talk about years ago… you know, get the kids hooked in with…”
Semiotic analysis Positioning analysis
Context: In this account Pete talks about the differentiated program that Larry Owen introduced to Lambertia College and with the support from both the coach and the maths coordinator the program was introduced.
1/38 … we didn’t let them decide themselves which group to go to, but… Larry Owen suggests… that’s the way of doing it, he said kids are usually pretty hard on themselves and they’ll put themselves into the group that they think they belong in, but… we did it, we got together after doing the initial activity at the start of the topic and had a look at all our kids and said okay this one in this group, this one in that group and then… when they lined up for… the next lesson we just sorted them into different parts of the room. That took some time, it was a bit messy, at times… and then, you know, to get the kids to all settle down and for them to listen and speak to them in a much larger room sometimes we would say okay this is what we’re doing then we’d close the rooms up a bit so that, you know, one teacher could focus on this group, another teacher would focus on that group and the other, but we’d have the doors open slightly to see whether we were all at, it might be…
Improvement to teaching practice indexed to the differentiated program (immediate object) that was presented in an open learning environment where students from a number of maths classes were encouraged to work on a maths task that met their learning needs.
The effect is immediate for Pete is uncertain and apprehensive as are the other teachers’ trialling the differentiated approach.
In a subsequent semiosis, the students are indexed to concerns related to classroom management. The effect is energetic for Pete and his colleagues respond by closing doors in the open-learning centre in an attempt to separate and control the behaviour of students.
This was made evident when teachers sorted students into ability groups rather than allowing students to find their own group as Larry
Pete positioned in moral order directed by the coach to perform to a new teaching and learning practice.
The contingent realities of the classroom, i.e., the behaviour of the students are brought into sharp relief when teachers firstly position students into ability groups and then close them off from each other in the “open-learning” space.
Pronoun grammar use indicates that Pete positions himself closely with his colleagues whilst distancing himself away from the students and the coach.
rotating activities…and at times the numeracy coach because she spends half the time here, one week here, one week at Grallina… didn’t always work that she could be with us, so we [would] have an extra teacher amongst the three classes… when she was here she helps out.
Owen suggested.
Finally, Pete indexes the coach to her role as a helper / teacher.
In addition, Pete positions the researcher in agreeing with his feelings about the activity in that it was “messy” perhaps in contrast to just teaching / controlling his own students in his own classroom environment.
3/20 ... one thing that I found quite useful particularly this year, didn’t know it was around and… she introduced it is to us… which was the VCAA maths online testing and [Samantha] took us through how to do that and particularly with my Year seven group this year I found it very useful in knowing where they were at… and comparing it to the results that I’ve got for them myself and tests and worksheets and book work and assignments that was good, I found that a useful tool… also with just looking at how to teach… certain topics like the algebra one comes to mind that we... were working on… presenting it in the Larry Owen way we looked at… misconceptions that students have and that teachers have in teaching students algebra with the pro-numerals that are used and how… they’re represented… she made us… she helped me to look at… we need to correct some of the things that… we’ve been teaching… algebra… so that as well and just intro with trying to come up with innovative ways of making… topics
The coach as the immediate object is indexed to improvement to teaching and learning.
The VCAA online testing referred to as the “it” indexed to assessment. The interpretant is logical for it strengthens Pete’s habit with regards to assessment.
The interpretant becomes the object for a subsequent semiosis, also strengthening his practice with respect to teaching algebra using an activity sources from Larry Owen.
Pete positioned in the storyline of improvement to teaching practice is encouraged by the “it” (VCAA online testing). The “it” together with the “warm-up” type activities are useful tools / magic provided by the donor to make his teaching
Pete aligns himself closely with his colleagues through first person plural “we”, and also hints to speaking from the self (“me”) whilst positioning the coach and his students at a distant.
Appendix 11
more fun introducing... activities that can help to break up a lesson or start a lesson off to get the kids warmed up and thinking, something that I hadn’t been doing a real lot in recent times but you know it was something that… we used to talk about years ago and try and do in science, you know get the kids hooked in with some sort of, you know… mind type exercise, you know it’s not necessarily related to the topic we’re doing and this is… where the maths department is going next year… with the Joel Hindrictwho… came and… we had that staff… I wasn’t here, it was on a Monday when I wasn’t here, an in-service on teaching sixty minute sessions of maths and always opening with [a]… five to ten minute activity… and then getting into the main part of the lesson and then summing up and finding out from the kids what they’ve learnt from the lesson…
Pete references the “warm-up” aspect of the Mathematics Lesson Structure as the “it”. The interpretant is logical for Pete recalls a period in his teaching career when the “warm-up” type activities were used to engage (“hook”) students with their science learning.
Finally, Pete positions the researcher in agreeing with his perspective on the use of the “warm-up” type activities that were used early on in his science teaching.
Whilst Pete warms to the ideas presented by the coach and the sanctioned lesson structure, he is retelling the coaching narrative through his colleagues (“we”) in absentia. This is hinted to with use of first person pronoun (“I”).
Summary:
Pete appreciates some of the ideas presented by the coach linking them to the improvement of his practice. He is encouraged by his colleagues’, whom he feels close to, in their positive response to the implementation of the Mathematics Lesson Structure for the following year. Pete recalls a past practice, when describing the Mathematics Lesson Structure. However, the hollow presentation, spoken through the excitement of his colleagues, masks his absence, revealing a surface attempt to improve his practice.
Struggle
Pete shares his experiences of teaching in a paradigm of change.
Theme
“… when you've got teachers that, I don’t know, I just wasn’t in the zone at times… it was a bit messy.”
Semiotic analysis Positioning analysis
1/114 … it was a bit messy this year trying the Larry Owen program, particularly with not all the resources and one topic was more difficult… to do then the other… it’s gotta be well structured, it’s not something we [were] expected to do, we were thrown into it by the principal basically, new principal yep, she’d had experience with the Larry Owen method down at Kanamirik College and yep it’s great, we gotta do it ourselves. So without even consulting us, we weren’t consulted and Samantha basically, you know the maths coordinator Sarah just said “oh yep, looks like we’re doing it.” No consultation and you know, you, the people, the teachers that… are teaching your Year sevens, you know at least you gotta say okay what you think about doing this, not okay, why are we all timetabled on together in three rooms next to one other, what’s going on? “Oh, the principal’s decided that, you know we’re gonna try this Larry Owen method of teaching.” So, Samantha did a lot to you know help out with, you know getting… the… PD
Principal indexed to directive. The effect of which was an acceptance (logical) because Pete together with his colleagues had no other choice but to work with the coach and maths coordinator implement the differentiated approach.
The interpretant becomes the object for a further semiosis in that the differentiated approach to learning (Larry Owen) indexed to improvement to teaching mathematics.
The interpretant is logical for the experience has weakened Pete’s approach to the principal’s directive.
The coach and maths
Pete’s position and institutional identity in the local moral order was altered without consultation. Pete resistant to repositioning by the principal.
Pronoun grammar use indicates that the “it” (the differentiated approach) took Pete and others in his team by surprise.
Pete positions himself closely with his colleagues and distances himself from the coach, maths coordinator, principal, the Year seven differentiated program and at one stage the researcher.
Pete positions the researcher as agreeing with stance taken.
Appendix 11
organised… helping out with resources, but when you’ve got teachers that, I don’t know, I just wasn’t in the zone at times, it was, it was a bit messy.
coordinator are iconically related to the social object of principal. Logical interpretant further weakening Pete’s teaching habit.
1/132 Just the smart alec response that you might get, “oh that’s boring or that was crap, I didn’t learn anything”, you know, your gonna get kids saying that and that’s what I don’t, I just get disheartened by that sort of thing so I’d rather avoid the situation and just assume, yep we did some good stuff today… but, na look, I’ve… gotta give it a go I suppose… look… the… activities which use skills that they’ve learnt [by] playing games, card games, board games… you know, getting a piece of string, getting the book… where they think the numbers should go on a decimal line or a number line or fraction line or whatever, that sort of stuff yeah, I’m all for that if it’s gonna help them understand concepts that… we’re trying to get through. Reflections side of thing, look, it is important to get feedback from them, I’m just worried about with some… of the kids, the crap that they’re gonna give you at the end that’s all, but that’s just me and I’m probably being too negative.
The Reflection component of the Mathematics Lesson Structure indexed to receiving negative comments from students. the interpretant is energetic for Pete does not want to encourage this practice in his class for he fears comments students may make.
In interpretant becomes the object for a subsequent semiosis. The “warm-up” activity indexed to student learning. Logical interpretant for it strengthens his teaching practice.
The “warm-up” component indexes improvement to learning and hints to the dynamical to the possibilities of improvement to teaching mathematics and remains an influence upon semiosis, e.g., Pete contrasts the “warm-up” activity with the Reflection.
Students indexed to not taking their studies seriously. The energetic interpretant is to control student behaviour rather than provide them with an opportunity to express it by way of reflection.
Storyline of coaching for improvement teacher practice using the Mathematics Lesson Structure.
Pete positioned as teacher who describes the positive attributes and shortcomings of the sanctioned lesson structure. On the one hand, Pete believes that the “warm-up” activity engages students. Whilst on the other hand, students may not take the reflection activity seriously thereby challenging his institutional identity.
2/14 There are some kids in there who… aren’t as… adept with their maths as most of the rest, yeah I’ve… [tried] different things, trying to enhance… the maths that they’re getting give [th]em more problem-solving type tasks… but… you’ve got to get through a lot of material doesn’t allow you to do that at times but then I become a little flexible and not worry so much about the… course on occasions not worry too much about getting through it… as much as maybe other people have.
Syllabus indexed to teaching mathematics.
The effect of which is immediate and becomes the object for a further semiosis for students are indexed to not being able to cope for they don’t have the skills to complete the requirements of the Year 7 curriculum.
The effect is energetic for Pete modifies his approach to getting through the curriculum in the time available. This represents the exigent and contingent reality of the classroom
Pete positions his students as not able to cope with the curriculum. Pete also positions himself as not belonging to the prescribed syllabus referring to it in the second person. Pete shows his agency by modifying the program to suit the cohort he is teaching mathematics to.
2/136 ... some things gotta make a difference… It is possible to change things… It’s gotta be a combined effort. I think all these programs can come in, sure but you gotta have the people that are willing to do it and try it and others to help support it, to see, to make a fist of it and see if it works and in the past you know, lots of programs that we’ve tried in this school to improve student understanding, student learning, student outcomes… they haven’t really been followed through in reviews… At times we get caught up in lots of other things and other programs and we forget to do some of these reviews as to what’s worked what hasn't worked and that’s… disconcerting.
Improvement to student outcomes indexed to educational programs and expertise that isn’t readily available.
Immediate interpretant is \ a recognition of the exigent and contingent realities of the classroom.
Pete positions himself as belonging to his colleagues but away from the “it”, i.e., any program not administered well.
Pete overwhelmed with the numerous programs in the past positioned as a failure when underperformance attributable to the failure of administrators.
Summary:
Pete appears spent as a consequence of a history of unreviewed administrative change, student learning difficulties and a curriculum that does not meet the needs of his students.
Appendix 11
Samantha’s response
“It surprised me that although this teacher found the new Year 7 program fairly negative he/she
still insists on having a go at things that might improve student learning.
The need for consultation with staff is a basic component in managing change and, yes, this was
missing from the process. The need for focus on the important things comes through in this
reflection.”
Teacher interview data and analysis
Grallina College
Appendix 12
Ray Bush, Grallina College1
Ray, the “senior-graduate” teacher worked in industry for several years before deciding to
change his vocation. He initially found the teaching experience frustrating because of the
limited curriculum resources that were available at Grallina. Despite this lack, Ray pressed on
using whatever resources he could find, supplementing these with what was available on the
Internet and also from his teacher education program. The coach and the coaching program also
developed Ray’s teaching repertoire. This was achieved primarily through his active
participation in the PLT meeting with the coach held every fortnight. Ray applied “warm-up”
activities, encouraged by the coach, to his Year 7 maths class reporting his experience back to
the other teachers of junior maths in the PLT. The PLT and the Mathematics Lesson Structure
thus provided Ray with a foundation to his teaching practice and for dealing with the local
specific exigencies and contingencies of the classroom. For example, whilst Ray experienced
difficulty in delivering the set curriculum in the available time he used an assignment approach
to teaching mathematics for it afforded him the best opportunity to engage his students and
deliver the curriculum in the time required. The idea had merit, particularly because it was
developed from the PLT. The coach-led PLT encouraged teachers to apply key mathematical
knowledge using a variety of techniques that incorporated a number of mathematical skills into
the one activity. The PLT as a constitutive practice allowed for this imagination, where teachers
responded to ideas presented by way of mutual intelligibility.
1 Interview 1 – 7 Oct 2009. Interview 2 –22 Oct 2009. Interview 3 – 7 Dec 2009.
Ray’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
Mature-aged male teacher
First year mature age teacher who worked in industry as a manager. Perhaps viewed as an emerging leader by the School Administrators.
Ray viewed by others as focused and competent. For example, Ray incorporated ICT (Audience response technology) into a junior maths lesson. Ray sourced the technology from another school and used the technology with effect.
Ray presented his approach and findings to colleagues. The School’s administration was encouraged to purchase the technology for the school.
Ray presented one of the many “warm-up” activities to his colleagues at a PLT.
He identifies himself as a teacher of mathematics one who belongs to the maths department.
Ray shares his experience in using the coach inspired “warm-up” activities with his peers, both in the year 7 PLT and with colleagues in the maths department.
Appendix 12
Initial situation Ray after years of working in the corporate world decides on a career change after raising his two children. Theme “So I decided I want to make a difference …”
Semiotic analysis Positioning analysis
1/2 Okay, well first year teaching… and a mature age person. Married for 15 years and decided to start a family… and so I gave up my day job which was, I was a… corporate manager… and… we made the decision we don’t have children to give them to childcare, so I gave up work, I was a stay at home dad… thought well what can I do once Alex gets up to school age, I’ve got to have something to go back to I am not going to go back to [a] day job. So I decided I want to make a difference… and just talking to people they think, oh, you would make a good teacher… so I went back to uni[versity], did the uni course for four years and brought up Alex and our other son Scott and here I’m being a teacher…
The sign of teacher has an iconic relationship to its object for the metaphor “to make a difference” mediates between the sign and the object and manifests itself in the correct understanding of the sign. The sign is internalized for it is defined by its tradition (dynamical object). The effect of which is energetic, for Ray undertakes the university course and becomes a teacher.
Ray morally repositions himself from corporate manager to teacher through the presentation of a storyline; a father and stay at home dad who is opposed to giving up his children to child care in order to go back to a daytime job. Ray’s moral purpose (illocutionary force) to make a difference supports and guides his repositioning.
Summary: Ray’s moral purpose is encapsulated in the metaphor of… “want[ing] to make a difference…” that encourages a transformation to his material practice. Teaching affords Ray this opportunity.
Preparation The rules developed by the teacher-training program are broken creating a moment of conflict in Ray’s moral world. Theme “… they said...“no, we’re working out of the book, the maths textbook…”
Semiotic analysis Positioning analysis
1/44 … the maths at uni was really focusing on primary maths and they were all about concrete materials, you know, you can’t deny them that, yes, get concrete materials in, you know, your MAB (Multi-based Arithmetic Blocks) blocks… the blocks of 1000, flats of 100, strips of 10… they were focusing on all the activities that you can do for junior… primary school, the beginning maths… and then when we were at the school placements we would then put lessons together for area and perimeter specifically for our primary school placements and then when we got to [our] secondary school placements… they said... “no, we’re working out of the book, the maths textbook and we’re up to Chapter 10 and you’ll be taking it from there.”
The use of concrete materials indexed to effective teaching of mathematics. The effect of which is energetic, for Ray sets about framing his teaching practice to that outlined by the university teacher-training program. The practice of using concrete materials indexed to primary teaching hints to the dynamical object of past experience. However, this practice is contradicted in his secondary school placement where the paradigm of secondary maths teaching created a sense of uncertainty (immediate interpretant).
Ray positions himself in an emerging storyline of teacher and of teaching. Ray’s use of third person plural (“they”) positions the teachers in his teacher-training program as perhaps the ones to which he feels distant to for “they” are positioned as the ones that know whilst he is the one that doesn’t. In contrast, Ray felt closer to the other teachers (“we”) when framing lessons in line with course expectations. Ray positions himself closer to primary rather than to secondary teaching for the textbook contradicted his emerging practice.
Summary: Ray notices the disparity between primary and secondary school systems and to the possible role that he must play in coming to terms with teaching in a secondary school.
Appendix 12
Complication Ray secures a position as a secondary school teacher and is overwhelmed in his first year of teaching for Grallina lacks a well structured and well-resourced mathematics curriculum. The lack is therefore made known and Ray is requested to assist in overcoming this concern. Theme “… frustration... hang on this is my first year guys…”
Semiotic analysis Positioning analysis
1/70 … perhaps the teachers are… keeping the materials to themselves and putting up the outside framework… up on the system and so when you look at the stuff that’s been and gone before, okay that’s great, there’s some pointers but what is the detail of the plan…. So it’s first year people out who are then expected to come in first week and… plan out things in detail… just by yourself and sometimes it… feel[s] that way, but other times you look for another thing that’s on the… staff share folders, oh, that’s great, that’s complete, that’s fine just grab that and go okay that’s good and then you just adapt it to yourself and then make sure they’re doing that outcome, yes, that meets that VELS… standard…
Teaching effectively is to use a curriculum guide for this represents a teaching method as adopted by past members of a community of practice. In this instance, it is related iconically to a representamen of the resources on the school’s intranet computer system. The effect on the one hand is a logical interpretant for it weakens Ray’s practice when he is unable to find curriculum that is either missing or incomplete. On the other hand, it leads to an energetic interpretant for Ray is encouraged to adapt his teaching practice to whatever he can find aligning it to the State’s Learning Standards.
Ray a “graduate” teacher is positioned as a frustrated practitioner for he is unable to develop his practice because of an absence of resources. Ray’s use of pronoun grammar throughout this “account” indicates a distancing away from the task and from other teachers, both past and present, who have let him down. Despite this, he demonstrates a moral purpose by adapting material, ensuring that it meets the expectations of the VELS.
1/72 I think in some cases, yes it’s frustration... hang on this is my first year guys I’m doing VIT2 stuff and I’m also trying to do this, I’m correcting exam papers and doing tests… doing all the stuff that I’m being asked to do, but... to me the, the curriculum outline hasn’t changed... it’s still maths, you start off with revision from numbers from last year then you
A curriculum outline (object) is iconically related to teaching mathematics. The sign is mediative as it enters between and so connects two objects: a curriculum with corresponding resources required by teachers for effective teaching and learning practice. The effect of which is logical, i.e., one of frustration at working
Ray positions himself at the start of this episode in the first person, as the frustrated but committed teacher hero who is performing to the “role” and responsibility assigned to him as a teacher. Ray’s heroic cry (illocutionary effect) illustrates his degree of frustration at being
2 VIT – Victorian Institute of Teaching is a statutory authority to regulate the teaching profession established by an Act of the Victorian Parliament in 2001. Graduate teachers are required to undertake a structured induction program.
introduce directed numbers… and you do Cartesian planes, you do percentages, all that, that’s all the titles… so where are our great hands-on resources, go and find them? Some of them are missing, some of them aren’t there, you know, there’s just gaps in the materials that are there and I know that… during our curriculum… meetings that’s what we’re working on as well, you know, we’re working on all these… so from year 7 to year 10 there’s a continuum with everything meeting standards and progression points and all that sort of stuff, well that’s fantastic, wouldn’t [that] have been done?
at a school that doesn’t have a complete curriculum particularly as a support for first year out teachers.
positioned at a school, in a subject department with a fragmented curriculum that does not function well enough to support his teaching endeavour. Pronoun grammar use indicates a distancing away from his teaching responsibility. First person plural “we” refers to the body of teachers to whom Ray feels he belongs to in the reconstruction of curriculum material / teaching practice. Finally, Ray positions the listener “you know” as in agreement with his “teacher talk”.
Summary: Ray is made aware of the lack, of a well-structured curriculum and resources that point to what constitutes teaching at Grallina College. Ray is concerned that very little curriculum exists and struggles to come to understand the terms of meeting the moral requirement expected of his role as a teacher. Despite this, Ray hints to a constitutive order that supports his teaching practice.
Appendix 12
Transference Samantha is introduced as the helper who provides assistance to improve Grallina’s performance data. She is positioned as assisting a group of four year seven teachers of mathematics of which Ray is a member and also periodically runs after school maths meetings for the entire faculty. Theme “… working with Samantha… it’s given me some more confidence to stay on… track…”
Semiotic analysis Positioning analysis
1/60 ... it was third or fourth week… it was… first term, it was, “here’s your coach for maths”… and working with Samantha is great, you know, she sort of like, says “try this” or “how’d you go with that” and feedback with the class and all that sort of stuff, “this could be improved….” So I think and of course they run their… meetings on the Tuesday night and a Thursday night and that’s always relevant… or they bring in an expert to show you things and also resources…
The coach, socially constructed and representative of what constitutes good teaching and learning practice. The immediate hints to the dynamical object in that Samantha represents a tradition of teaching mathematics. The effect is that Ray notices the effect of the sign to its object and comes to accept what the coach brings to his practice (logical interpretant).
Ray positioned by the coach and the administrators as the one that requires assistance and the coach is the one that is able to provide it for she has epistemic authority in directing Ray to the “this” or the “that”. Ray through pronoun use positions the coach / administrators of the Grallina in the third person indexing lack of interpersonal relationship and or connection. In addition, Ray’s use of second person singular pronoun (“you”) may indicate a detachment or distancing from responsibility perhaps in being positioned by the coach (“they”, “their”) as requiring assistance. Finally, Ray positions the listener (“you know”) as in agreement with his “teacher talk”.
1/104 She will just ask, “how you’re going to approach it, what activities or resources are you going to use”, and then she’ll just accept what I’m going to do, she won’t change my mind or won’t force or… bend me... “don’t do that or”, and she’s never poo pooed anything that I’ve
Good teaching practice indexed to the coach (immediate object) who represents effective teaching. The effect of which is a logical interpretant. That is, a strengthening of Ray’s habit as represented by his appreciation for the hands-on learning
Coach positioned as the one that knows what good teaching and learning entails. Suggestions made by the coach point to a “hands on” approach rather than one that encourages the use of the prescribed student textbook.
suggested... but she’s always being there to suggest other things if you would like to take them on and they’ve mostly been activity-based and more engaging than what, “okay kids open up your textbook [to] page 324 let’s get into it”. So yeah, she’s been a complete font of, you know, hands-on activities or just activities other than the textbook to deliver the same focus for the lesson.
activities that appear to engage students more so than the textbook. This leads to another semiosis that of the textbook, indexed to ineffective learning. The interpretant is logical for this strengthens his Ray’s belief about teaching.
Rays use of third person plural indicates a distancing away from the coach. Ray perhaps feels repositioned as a failure based on status as a first year out teacher.
2/82 … and the object is to create the biggest number they can out of my random rolls [of the dice]…and it’s out of… Zed Osborne’s book about … maths games because that’s one of the... directions that Samantha’s… brought to Grallina is... you introduce your lesson, you start off with a game and hopefully that game can be relevant to the topic that you’re teaching but it doesn’t have to be, then you do information about the topic and then you let the kids go and do their lesson activities whether it’s textbook related or worksheets or whatever you’ve set up for them and then at the end of it, it’s a reflection of what they’ve learnt for that session and during the session Samantha’s just like walking around the room in this instance… she helped me out with a couple of... I got stuck for a few words and Samantha was there to bounce off… and then it was just around the room roaming conference as
The object (coach / coaching) mediates between two signs: Zed Osborne’s book (symbolic relationship to object) and teaching practice (indexical). Zed Osborne’s book as a social object bears a conventional relationship to teaching practice as a general category related to the activities presented in the “warm-up” component of the “lesson structure”3. The effect of which is energetic for Ray alters his practice to teach to the new “lesson structure” and does so with the acknowledgement of the coach.
Ray positioned as the novice teacher under the supervision of the coach. Ray’s use of first person singular “I” indicates that he is talking from the self as he describes his teaching.
3 Refer Appendix 1
Appendix 12
Samantha… was helping this student or looking at how that student was going and I was wanting her and I always want her to keep focusing on my level of conversation with the students… that’s the… constant concern for me is that I’m not talking over their heads…. Samantha just walks round with her experience and just tends to gauge the conversation, the... engagement of them, are they getting what I’m saying and then we at the end of that lesson it was a double… we sat down had a bit of a… debrief on... what the lesson was and Samantha was very… very happy with the way it was delivered and she didn’t actually have any negative criticisms, it was all very… constructive and she believes that… lesson went quite well…
Ray’s teaching practice bears an iconic relationship to that of a teacher who has the ability to connect with his / her students. The effect is energetic for Ray encourages Samantha to concentrate on this aspect of this practice.
Ray demonstrates a sense of ambivalence. On the one hand, he positions Samantha by referencing her in the third person positioning her away from him. On the other hand, Ray acknowledges Samantha through pronoun use that she has assisted him to develop confidence thereby developing his instructional capacity. Ray debriefs with the Samantha and positions himself in partnership with Samantha, pleased that Samantha does not criticize his practice. This reinforces the position of the coach. That is, the master – apprentice relationship. The storyline maintains Ray’s role specification is to work according to the institutional order as promoted by the coach.
3/34 ... she’s come along she’s observed what I’m doing in my classrooms and she just laid it out as a matter of fact you know, if she said something didn’t work she just said “oh, don’t think that worked”, and then we sit down and brainstorm; “yeah, that didn’t work, you could see the eyes glaze over in the students”.... For example, we decided to bring in the electronic whiteboard… it was fantastic because… especially the all-boys class, they were aching to get up on the board and indicate where a fraction was; turn that fraction into a percentage and we had
Coach as object indexed to improvement to teaching, mediates between the immediate object and the interpretant. In this instance, the object hints to the ontological dimension. The effect of which is an energetic interpretant for Ray experiences first hand that taking on suggestions made by the coach made improvements to his teaching, particularly to the “all-boys’” class. This class is indexed to disengaged students the effect of which shifted from an immediate
Moral repositioning of Ray by the coach into the role of teacher and of teaching mediated by objects (the lesson plan, laptop computers, whiteboard) the outcomes of which further strengthens the moral authority and moral capacity of the coach. Ray positions the researcher as understanding and in agreement to the “teacher talk” in which he shares his moment of heroic importance retrospectively comparing it to a lesson that didn’t work. Ray considers
volunteers coming out of every corner of the… classroom so they wanted to do it, yeah and sure when we then stopped that… when we stopped the whiteboard and got them to now reflect on their learning… they could actually articulate “oh I learnt, you know, that half is fifty percent and....” So the other one of the downside lessons was earlier on this year was the laptops, brought in the whole class set of laptops, got the kids going and we just sat back and felt that didn’t work because I think perhaps it was the first time I’d used the laptops in the classroom there was no control you know, it was my… inexperience… they were… doing stupid things…. But certainly going back to Samantha she… was just saying how it is and then you know, finally towards the end of this semester or this term… you know, we’d do our outline of, you know… the lessons… coming up and… she said while I can see that’s going to work just from my notes and my explanation… I… think nine times out of ten she came into the lesson and said “yeah that… worked”… we planned it was going to work so.
interpretant, i.e., an acceptance of the “all boys’” as not engaged to a strengthening of Ray’s practice as he experiences student engagement (logical interpretant). The interpretant leads to the final semiosis. The coach indexes improvement to practice (use of laptop computers). The effect of which is energetic for Ray changes his practice. The change is twofold, the strengthening of his relationship with the coach, as well as, adopting a reflective approach to evaluating his teaching.
himself a teacher that can make a lesson work, that perhaps he can “make a difference”. At times, Ray positions the coach away from himself, referring to the coach as “she”, in the third person. Perhaps not quite comfortable with her authority / gender. Despite this, Ray refers to the coach in the first person plural “we” indicating a closeness in working collaboratively in planning and reflecting on lessons.
Summary: This series of “accounts” indicate a strengthening bond between Ray and Samantha. The coaching relationship engages both Ray through reflective practice to try different approaches to his teaching of mathematics. This has a positive effect for it encourages confidence developing and strengthening Ray’s teacher identity in the process. Struggle The lack is overcome with Ray’s strengthening teacher identity.
Appendix 12
Theme “… just one of the tools that you can turn that reflection into…”
Semiotic analysis Positioning analysis
2/152 Well if the kids says “I can’t do this” and you know as the teacher that we did this same topic three weeks ago and they’ve written a reflection and their reflection is all about how easy this topic has been and “I can do this Sir” and then they come out, “oh, can’t do that” and you go back to their own reflection and say “three weeks ago you said you can do it, so why can’t you do it today?” As I said, just a prompting for the kids, cos kids will do their best to get out of doing anything… so yeah, that’s… just one of the tools that you can turn that reflection into but the main purpose I believe is to get the kids to create some ownership and recognition of what they’ve learnt, so.
Students in Ray’s class indexed to not wanting to learn, the effect of which is an energetic interpretant, i.e., he applies the reflection activity as a summative assessment tool encouraging students to engage with their learning. Student reflective activity (the sign) indexed to student learning. The effect is energetic, for Ray can see the benefits of encouraging students by means of the reflection as.
Ray positions himself within a storyline based on the principles expressed by the coach (the donor) to teach in a certain way, i.e., using the “structured lesson” approach. He justifies using the reflective activity (the magical agent) at the end of the lesson to address the lack as it repositions his students from “…get[ting] out of doing anything…” to motivating them to learn. Finally, Ray uses first person singular to position himself as talking from the authority of self. This shows affirmation of his teacher identity and repositioning as a result of taking on the reflective component of the structured lesson approach.
Summary: Ray confidently uses a technique (“Reflection”) provided by Samantha to encourage student learning. This demonstrates Ray’s identity transformation.
Return The difficulty of teaching to a traditional approach and delivering curriculum in a specified time frame appears to be overcome with Ray’s transformation. Theme “… the… trial that I implemented … was vastly different in the reaction in the class…”
Semiotic analysis Positioning analysis
3/18 … it certainly has changed and I think that’s been brought about by Samantha’s input... we also did some… maths CPT4 meetings towards the end of term three and … through term four but the … trial that I implemented with the maths activity and the “warm-up”… I think was vastly different in the reaction in the class than what I got at the beginning of the year where I was just going straight into the maths you know explanation of what we’re doing a few worked examples on the board and then… okay kids now it’s your turn [to] practice what we’ve just learnt and it’s been you know unfortunately maths textbooks but... from Samantha’s input... you know when I do the math, the maths “warm-up” game... that was… fantastic with chance and data because you can do probabilities of rolling dice numbers you know what’s a… probability of rolling a seven on a ten sided [dice] and all that sort of thing… and then over… five weeks they collected the data of the dice rolls and then they could you know, make some statements ... and then with another opportunity of
The new instructional approach (object) indexed to the improvement of Ray’s maths teaching. The effect is that Ray experiences a sense of achievement as an emerging teacher (energetic interpretant). Ray recognizes and internalizes the sign through the development of an assignment based teaching approach.
Ray locates himself as a successful teacher who can teach mathematics according to the expectations imposed by an institutional order i.e., having to cover the syllabus in the required time. Ray has come to appreciate the way that the “it” (teaching) should be done as expressed by the coach.
4 CPT – Curriculum Planning Team
Appendix 12
chance and data I put in an assignment… we weren’t sitting down doing exercises from the textbook... they were actually covering the content of what they needed to know and cover [it] in an assignment… I think the second half the second semester was much better than my first semester... and I did plan for next year to make continued changes as well and try and bring in... more assignment based work; if you can cover the course content in a general assignment that might cover three or four weeks instead of just you know let’s do it out of the textbook it might also continue with a little bit more interest from the kids.
The assignment bears an iconic relationship to the immediate object of effective teaching, the effect of which is energetic. Ray demonstrates this by planning forward using assignments. The assignment does not hint to the intransitive dimension for its use is connected to a previous semiosis of control; control over the curriculum and control over his students. That is, it is a response to the local specific exigencies and contingencies of the classroom.
Use of the “I” indexes Ray as agentive in his approach to the teaching of mathematics as expressed through the use of an assignment. The assignment approach to teaching perhaps indicates a means of controlling the delivery of mathematical content in the time required and of controlling his students. Ray achieves a transformation to his teacher identity, i.e., of a purposeful teacher who is now able to cope with the exigent and contingent realities of the class.
Summary: Ray’s identity transformation is evident in this “account” for he experiences success in the use of the Mathematics Lesson Structure, in particular the “warm-up” component. However, the success is attributable to a number of aspects. For one, the reaction from his students is positive for they appear to engage with the manipulable approach to teaching data, to another, one that assists Ray to get through the prescribed syllabus in the allocated time. Ray’s identity transformation saw Ray move away from a reliance on using the textbook demonstrating perhaps that his practice is framed by structural constraints. Constraints that don’t necessarily mean an improvement to student performance in mathematics.
Transformation Samantha will not work as the Regional Coach at Grallina in the following year. Replaced by Mandy who is the school-based coach for the following year. Ray speaks about how he intends to operate as a teacher without Samantha’s support. Theme “… I would find it hard to go back… I’m going to continue… forwards…”
Semiotic analysis Positioning analysis
3/84 ... I think the major impact’s going to be on access to the new ideas... I don’t think I’m going to go backwards in my teaching because Samantha[’s] not going to be here I’m going to continue… forward and as new ideas come through with our own numeracy coach now I’m going to be certainly willing to give [th]em a go and implement them into the classroom... and that’s certainly one of the things that I’ve, you know, learnt and trusted but just to give things a new go, you know, give it a go, if it doesn’t work, drop it, don’t do it again.... No, I don’t think I’m going to go backwards as far as I don’t think it’s going to have a detrimental effect to... our levels or our style of teaching… I think it’s just going to have a delay effect in the new ideas coming forth or a delay in consulting with the numeracy coach to try a new idea or a bit of a discussion because I myself will have to then make a time you know and that could be a random time you know because whereas currently or for this year it’s been period three on Monday is my interview time with Samantha that’s when we go and nut out and discuss what we’re
The interpretant in this instance is to “…give things a go…” to be innovative and operates as an inductive argument for it links the representamen to its object, that is, the linkage of ideas as presented by the school-based coach indexed to improvement in the teaching of mathematics. The effect of which is energetic for Ray indicates that he will continue on with the improvement of his practice, that is, to continue to “… give things a go…” The teacher that he has become under Samantha’s coaching is indexed to one that takes risks with his teaching. That is to try different approach and not rely on the old practices. The effect is energetic the new school-based coach won’t have a “detrimental effect” to his teacher identity.
Ray positions himself as successful; the committed teacher who knows that he needs to implement ideas (referred here as the “it”) on an ongoing basis and not “…go backward in [my] teaching….”, but rather to push forward. Ray positions himself as agentive through use of first person pronoun use and also in the way he positions himself closely with the maths department. Ray has internalized practice as evidenced through first person pronoun use. Ray engages the researcher in agreeing with his “teacher talk”.
Appendix 12
going to do with with the math’s lessons that she’s going to observe so and and unless next year it’s going to happen the same way where there’s with our own staff numeracy coach it’s going to be, you know, oh we’ll have to make a time… and unless you send somebody an e-mail with a time… calendar meeting thing attached to it ... it’s sometimes [that] just goes on forever… oh yeah, we must get together, oh yeah, we must get together, because people are just committed to being teachers I think, which is… a good thing thats what they’re here for.
New coach is indexed to lack of ideas. Ray’s teaching practice will be affected indicating a logical interpretant. In addition, the lack of meeting time to talk with another regarding his practice will also affect his practice. This also is a logical interpretant for it represents a habit change.
Ray does not position the school-based coach in the same way he positions Samantha. For one, the school-based coach won’t have access to the amount of ideas as presented by Samantha, and secondly, Ray feels that he won’t be afforded the same meeting time to talk to another about his teaching practice.
Summary: The coaching program transformed Ray’s practice developing his teacher identity in the process. Ray explains that his confidence as a teacher of mathematics won’t be affected by Samantha’s departure for he will continue to avail himself and apply new ideas to his teaching. However, whilst he feels comfortable with the newly appointed school-based coach, he does not believe that she is endowed with the same level of experience nor is he confident that they will meet to discuss improvement to his teaching practice.
Samantha’s response
“This is [a] surprisingly positive account and is encouraging for me. I feel that I
have had an impact on his outlook on teaching by reinforcing his positive
approaches. Great to have made a difference and that this teacher is determined to
continue improving and learning.”
Appendix 13
Liz Tayhlor, Grallina College1
Liz, a novice teacher in her second year of teaching, experienced difficulty working with a
coach at her previous school subsequently resigning to take up a teaching role at Grallina
College. At Grallina, Liz was initially apprehensive upon learning that she would be working
with a coach, despite this impression; she appreciated working with Samantha, developing
further her teacher identity. Liz consequently adopted the “Mathematics Lesson Structure” to
her practice engaging the coach more so in the final weeks of the 2009 school year to plan her
program for the following year.
1 Interview 1 – 7th Oct 2009. Interview 2 – 22nd Oct 2009. Interview 3 – 7th Dec 2009.
Liz’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
Young woman. Second year of teaching and not maths trained. Liz rejected a position at Grallina in the previous year (2008) because she wanted to work in a school that was not close to home. Liz experienced difficulty working with the coaching program at the school of choice and resigned. Later applied for a position and employed at Grallina.
A cheerful and happy person who is easily approachable and determined to achieve.
Belongs to the maths and science faculty. Gets along with most teachers and is viewed as a novice teaching member of staff.
Appendix 13
Initial situation
Liz, upon graduating secured a job at Flora College in 2008. She experienced difficulty as a result of working with an overly zealous coaching team and resigned toward the end of her first year. A position at Grallina College was advertised at the same time of her resignation. Liz applied and secured the position as teacher of junior mathematics and science. The first episode focuses on a brief background as to why Liz chose teaching as a vocation.
Theme
“… I was always thinking of being a teacher …”
Semiotic analysis Positioning analysis
1/2 … how did I become a teacher... I always wanted to be a vet[erinarian].... I always liked animals and I did a, I was going… [through the] backdoor into Veterinary Science, through doing a Science Degree, doing animal science and then, I really loved that course. So I got a job... at a veterinary clinic as a vet nurse and they were training me on-the-job, so I was doing that in my third year of university... and then, I, after two years of doing that, while I was studying, I hated it… I didn’t want to do [it] any more. So I decided I’d finished my degree in science and I was thinking of being a research scientist.... I did my Honours and then after that... my husband and I wanted to travel and so I was always thinking of being a teacher but [it] was always something I didn’t think I could do. So then my husband suggested it and I applied for the course and got in…. I did the course and I really loved it.... I did my course at William University… I did my rounds at... Jacobean the private school in
Career / vocation indexed to personhood the immediate object. The effect of which is energetic for Liz demonstrates intentionality in pursuing her interest in veterinary science as indicated by her university course and on-the-job training as a veterinary nurse.
The immediate object hints at the intransitive and it may be in this instance that Liz becomes aware of selecting the “right” vocation. Therefore the effect becomes the object of a further semiosis in that the new sign is an Honours degree indexed to science research.
Liz describes personhood, positioning herself in a moral landscape of tertiary study and with her husband. The journey comes to rest with teaching as a vocation.
Liz’s moral perspective is expressed in first person singular pronoun “I”, a window into her identity.
Behriana... second [teaching] round was at Elizabeth Grammar, which is an awesome school it was really amazing, I was put into another private school and then my third rounds was at Bullmer Secondary College.
The effect of selecting teaching indicates an energetic interpretant for Liz completed the training and is now working as a teacher.
Summary:
Throughout the episode signs are used as psychological tools to mediate behaviour. For example the sign of completing an Honours degree indexes success and entry into science research. Signs in this episode show Liz’s goal-oriented approach to personhood.
Appendix 13
Preparation
Liz finds that whilst she is emotionally supported in her teaching role at Grallina, there is a lack of material support.
Theme
“The support... emotionally was good but with resources it was very bad …”
Semiotic analysis Positioning analysis
1/56 Well I took over from... Joe Briggs… who was in a teaching position, he was a… Year Level, coordinator and he was going to AP Assistant Principal and I just followed him round and he sort of gave me all this material, like he just gave me some stuff he was doing currently with the class and then… the same thing with the other classes that I took over. One of the other teachers sat down with me who was teaching the same year level and went over what they were doing and [provided] some resources for me, but mostly I made up myself.... The support... emotionally was good but with resources it was very bad…. I was kind of dumped in it because... when I got here I was taking over for one term, I was taking over from a teacher that I was filling about three or four different places, like I was filling in [for] four or five different people and one person was in hospital and she couldn’t be contacted so I didn’t even know what I was suppose [to do] I didn’t even know the topic and nobody knew what she’d been teaching, so I didn’t get to speak to them. I
Newly appointed novice teacher indexed to a poor induction / mentoring program for new teaching appointments. The effect of which is logical for the “life-world” of teaching at Grallina makes evident to Liz what is to be expected from her, that is, of emotional support with a corresponding lack of support with respect to teaching resources.
Liz positions herself as an emerging teacher speaking from the authority of self as expressed through first person personal pronoun. In doing so, she positions others through third person singular and plural as perhaps not belonging to given stressful experience associated with her newly appointed role as teacher.
Liz frustrated at the lack of resources but takes on the challenge perhaps in response to the bad experience she had at her previous school.
didn’t know what they had done all term. I didn’t know what stage they were at or who they were like, so I just kind of had to just find that out myself and the other two teachers cos one went to a leadership position and one left the school... and on the first day… when I arrived I was told, oh you’ve got two days, like you’ll have two days to not teach and just to find… [your] way around and do all that stuff, introductory stuff. But then on the first day I arrived, I didn’t have a relief teacher so I just went into [a] six-on day... six-on day on the very first day I arrived.... I had a six-on day, but no, I was okay after... it was just the support of people, but resources wasn’t that great.
The interpretant becomes the object for a subsequent semiosis when Liz indexes lack of professional support afforded to teachers. The effect of which is energetic for the signing makes the lack evident to Liz that she must take responsibility for her own professional learning.
Liz demonstrates her emerging teacher identity demonstrated at the end of this account when she attends to the challenge faced on her first day as teacher at Grallina.
In a narratological sense after Propp (1969/1928), Liz is taken in by deception, put to the test and passed.
Summary:
Liz is inducted and prepared for her teaching role at Grallina. The induction program inadequately meets Liz’s expectations for whilst she is emotionally supported she finds a lack of material resources. Liz positions herself away from her colleagues and perhaps from her teaching role as a consequence of the lack being made evident to her. Despite this, she perseveres in the face of this difficult experience.
Appendix 13
Complication
The “lack” is made known to Liz.
Theme
“... getting disappointed that they didn’t do well ...”
Semiotic analysis Positioning analysis
1/118 Because maths is traditionally taught with the textbook and you do questions from the textbook and other teachers use to get through more work than me. Like I use to be always behind them, with the text, like as far as the curriculum from the textbook, I was always behind them because I [was] always doing all these enrichment activities in my class like extra activities and games and all that sort of thing…. So I was questioning... you know, I’m always behind and I’m, you know, I’m not getting through this content...
Approach to teaching mathematics incorporates both the use of the maths textbook with enrichment activities. The sign bears a symbolic relationship to the immediate object of the effective maths teacher. The interpretant is energetic for Liz teaches in this way. This becomes the object of a further semiosis, one where the interpretant is logical for it weakens her teaching habit / practice as Liz experiences difficulty keeping up with the other teachers in teaching to the set curriculum.
Liz positioned as novice teacher unable to keep up with the prescribed syllabus
Liz uses first person pronoun “I” speaking from the authority of the self. She positions herself as not belonging to her colleagues evident through use of third person plural “them”. The complication of unable to keep to task and follow the syllabus confounds her.
Liz engages the listener / researcher in agreeing with her “teacher talk”.
1/126 I think there was a lot of small things, like it was marking my exams and just getting disappointed that they didn’t do very well... like kids that should’ve done well didn’t do very well at the end of the year, and then a lot of professional development (PD) days, you know, at school and mostly PDs that I did. I did a lot of stuff on MindMatters2 with… the brain…. I remember this PD, professional development day that we had with a psychologist about how the brain works and everything we do we
Liz reflects on her previous years experience where exam results as the sign indexes the immediate object of success / fail. This hints to the dynamical for she is aware as a teacher the relationship good grades have to post secondary school pathways.
The interpretant is energetic. For Liz attends Professional development (PD) activities as a way of improving student
Liz realises a lack and goes in search of a solution to the problem. Donors offer Liz advice to assist her to solve the problems with student learning.
Liz positions herself as a moral agent, i.e., a teacher who transforms her practice in order to improve student learning and their results.
Liz talks from the authority of self and includes the listener / researcher as in
2 Australian Government initiative that promotes the mental health, social and emotional well-being of all within secondary school communities. http://www.mindmatters.edu.au
shouldn’t be doing because the things that you traditionally do just are shutting down the brain. So a lot of research on the brain and went to a couple of Lane Clark3 PDs… it’s a combination of PDs and thinking over the holidays, just thinking over the holiday about how I’m going to teach next year.
outcomes.
agreement with her moral stance.
Finally, Liz uses third person plural to distance herself from others who teach in the traditional way for this approach does little to promote student learning.
Summary:
The lack is made known to Liz in the form of poor student results. Liz is aware that to improve this area of concern she will need to gain support. Liz goes in search of assistance in order to attend to the lack and applies the magical agentry provided by the Donors (MindMatters psychologist, Lank Clark). Unfortunately, in doing so she lags behind her colleagues in the delivery of the school’s maths curriculum. Liz is mindful of the local specific exigencies of the classroom however demonstrates a commitment to thinking more deeply about how she may improve her teaching practice for the following year.
3 Lane Clark is the president of ‘Ideasys’ that provides educators with support in how to teach learners how to think utilizing approaches that are holistic and authentic. http://www.laneclark-ideasys.com
Appendix 13
Transference
Liz and her team of year seven teachers of junior mathematics are chosen by the principal to work with Samantha, the Regional Coach to improve the overall performance of mathematics at Grallina. The coaching program aims to assist Liz to realise how to overcome difficulties experienced.
Theme
“… she had a better way of explaining it than me.”
Semiotic analysis Positioning analysis
3/82 ... I always have her in the afternoon period five and six and the kids are off... half the time like… they come in after lunch. It’s a boys’ class so everything we do first is physical like it’s moving around, so we do [an] activity where we have to move the kids around and that sort of stuff. I didn’t think… the order was important, like I knew that I’d have to do something, change the activities to make something physical like so they can move from their seats but I would probably do that at the end because... closer to the bell, you know, we’ll just do... something that involves movement at the end of the class cos I would be too scared to do it at the beginning because I think there’s no control there if they’re all moving around once I come in from lunch, and then she knew that… was the time where they need to move and then they can sit down after that so I guess just to doing the order of activities that we’re doing is it’s like really important, which I didn’t quite often think of, like I knew that it was important to vary the
Improvement to teaching is indexed to the coach as the social object.
The coach offers Liz an
The coach is viewed as the donor in this episode who imparts her wisdom as an experienced teacher (referred to as the “that” in the episode).
Liz in turn realises the effect and transforms her approach to teaching her “all-boys” class (referred to as the “it”). Liz experiences success at the hands of the “all-boys” class who make it difficult for Liz to teach. Liz positions the students in her “all-boys” class away from herself referring to them in the third person personal pronoun “they”.
The coach is position by Liz as the one that knows whilst she, the novice does not. At times Liz works closely with and belongs to the coach as indicated in the use of first person plural “we”. At other times Liz positions herself away from the coach through third person singular “she”. Perhaps overwhelmed with the coaches experience.
activities and have activities that involve movement in a boys’ class but she knew that. If you do that straight away after lunch to get rid of the energy and all the aggression or whatever they had built up from lunch and then they just sit there and work afterwards so, and she had met the class, she just suggested that the first lesson so this is her experience.
opportunity to look more clearly at her teaching practice by challenging her view of teaching in order to tackle the lack that come from teaching an “all boys’” class.
The effect of which is energetic for Liz readjusts her practice and takes a risk with the way in which she manages and controls her class in line with Samantha’s suggestions.
On the other hand, Liz distances herself from the coach as expressed in the third person pronoun “she” and “her”, perhaps as someone she doesn’t feel comfortable working with.
Liz positions the researcher in agreeing to her “teacher talk”.
3/266 Yeah I think in the whole school because... the maths here has been very disorganized cos there’s no leader... we don’t have a math’s coordinator here and... she actually put in place these meetings special meetings for math’s people to meet and we shared. She… introduced the… lesson structure to the whole faculty of maths and we were able to share ideas and have time together cos we don’t have time here to meet and I think everyone I’ve spoken to has been… so grateful for the time we[’ve] had with her cos… she’d bring in all these examples of “warm-up” activities and they were probably the hardest thing to do in maths is the “warm-up” activities which is all the engaging hands-on activities that you have.
Coaching indexed to leadership of a subject department. The object hints to the ontological for without leadership there is disorganisation making change / innovation of practice difficult to effect.
The interpretant is energetic for Liz appreciates as does other teachers in the faculty the importance of meeting as a subject department to discuss and share pedagogical ideas that lead to mutual intelligibility in the improvement of teaching.
Liz talks from the authority of self to describe her position and the position of her colleagues within the local moral order. In doing so, Liz positions herself as belonging to a community of practice - of maths teachers that work at Grallina as expressed in first person plural “we”.
The coach as the donor after Propp (1928/1968) has brought with her a “magical agent” and powers to effect change in the local moral order. The lack is now realised amongst the staff as afforded by the “magical agent” that has been introduced to all by the coach.
Summary:
Samantha brings experience and a new approach to teaching that is well resourced. The practice of an experienced practitioner mediates the practice of a novice assisting Liz to transform her practice.
Appendix 13
Struggle
Even though Liz experienced a sense of empowerment in working with Samantha, barriers to improve and transform her practice are ever present, particularly when Samantha is not there to assist her.
Theme
“I would always question myself...”
Semiotic analysis Positioning analysis
1/110 ... Well Samantha’s been really positive, like she’s always been very positive and the things that I do… cos I do things a bit differently to the other maths teachers... I would always question myself, “oh why am I doing this?”, like I’m wasting time in doing, cos I have an all boys’ class and I have to teach it differently to the others cos they can’t sit still... they just have a lot of learning problems and they cannot sit still for 100 minutes of maths. So I have to change activities and have them doing stuff and do... brain gym activities and all those sorts of things... and then… she would just always give me positive feedback saying “oh you’re doing exactly what the region asked us to do”, you know, “you’re doing so much with your class”...
The coach is indexed to the improvement of teaching.
Liz brings a different teaching as the sigh that has an iconic relationship to the immediate object of the “all-boys’” class. The interpretant is immediate for she feels this is the only approach that has an effect on her students.
The coach symbolically representative of the DEECD (“region”). The interpretant is logical for Liz applies what the coach offers.
The coach as sign iconically related to the DEECD. The effect of which is logical.
Liz struggles to apply DEECD policy to her “all boys’” class for she feels sandwiched between the specific exigencies and contingencies of the classroom.
Liz, shamed struggles to come to terms with teaching and controlling her guilt and not able to teach her “all boys’” class made evident by Liz’s moral cry (“oh why am I doing this?”) for mercy, in the eyes of the “regional” representative.
Liz, through use of first person singular “I” displays her moral identity and agentive stance.
Liz positions the coach as distant (i.e., as representing the “regional” interest) and also positions her students away from her within this narrative of struggle.
2/80 So… I just… it didn’t work… I’m not great at it, like I still have lessons where… I just do work from the book in maths and I can’t think of anything and like I’ve had algebra
The “it” refers to pedagogy; connecting students to the topic, indexing good teaching practice.
Liz makes known the lack, a narrative of failure. Liz positions herself as a teacher speaking from the authority of self when she describes that she is struggles to connect
units were I can’t think of anything, there’s nothing that I can see that is important for them to know about algebra and this unit I can’t see how it relates to anything in life, like I, I just sit there and think about it and go “na, there’s nothing”. So it’s just going to be a unit on algebra, so…
The effect is logical for Liz recognizes her inability to connect pedagogical content knowledge to student learning.
students to algebra.
Liz positions her students as not belonging to her.
3/356 … they… the… complaints that I got were… “can’t we … do our work from the book?”, they just wanted to sit there by themselves and work from the... textbook that’s what they said… “we don’t wanted to play game[s], we don’t want to do this” so it is [a] big challenge because if your gonna start this lesson structure with older kids which you should… because they… start to lose knowledge when they get into the harder maths and you would need to reinforce it with the… activities. They [are] not interested in activities. I tried at least twenty times with my class, I finally got two or three games that they would like but I’d have to stick to those two or three games because by the time, you know, they just didn’t like it… they were very close minded with maths they just did not want to do anything other than the textbook... to the point where I had kids exited to the coordinator for arguing with me and refusing outright to do it. I had kids that refused.
Senior math’s students index learning as completing mathematical problems from textbook.
The effect is energetic as demonstrated through Liz’s encouragement.
The interpretant becomes the object for a subsequent semiosis where students are indexed to having a poor disposition to learning.
Liz’s struggles to implement the sanctioned lesson approach with her Year 10 maths class.
Liz defends her ability to teach. She positions herself inline with the sanctioned “lesson structure” as presented by the coach. However, she experiences difficulty in light of the contingent realities of the classroom.
Liz positions the “sanctioned lesson structure” as the “it” and as not belonging to her.
In addition, Liz positions her students away from her and not have a positive learning disposition.
The act of punishing students by sending them to the coordinator is a symbolic representation of where the problem lies.
Appendix 13
Summary:
Whilst Liz has welcomed the change brought by the Regional Coach, she struggles to implement the “sanctioned lesson structure” because of the local specific exigencies and contingencies of the classroom. That is, of having to get through the curriculum in the specified time and a lack of student disposition to their learning hinder Liz’s approach to implement the “sanctioned lesson structure”.
Transformation
Liz attempts to transform her practice as a consequence of realising that the coach will not work at Grallina in the following year.
Theme
“… one of those moments when we went ohhhh!”
Semiotic analysis Positioning analysis
3/158 Oh, you know, I’m stealing her from her desk cos I’ve got her to help me map out my, we’ve mapped out my first term with my new classes next year because I wanted help and setting up… the lesson structure we’ve been using. I wanted to start that off at the beginning of the year and have the kids… already like, train them up to… do these activities cos… sometimes you can’t do a lot of these activities cos the kids aren’t used to them cos they’re not used to such freedom in maths so…. I’ve… I stole her for three hours or four hours of the day and... she didn’t have anything on so I sat down with her and we mapped out the whole first term for year nine and ten maths for my classes, gone through and chosen activities for each lesson and she’s very good at... planning and she’s very good at cos she’s taught maths for a very long time and I haven’t. She knows what topics should be before... another proceeding topic like... for example, at this school every single year we’ve taught ... geometry before algebra we’d just do a whole term of geometry and then we do algebra in the next term and… she’s
Coach is indexed to good teaching practice. The effect of which is energetic for Liz shows an interest in teaching to the new “lesson structure” for the following year. The interpretant becomes the object for a further semiosis, the formulation of lesson plans based on the “structured lesson” approach.
Coach indexed to good teaching practice as a result of her experience and knowledge. The coach knows whilst Liz doesn’t. The interpretant is energetic for Liz engages Samantha to map out her teaching for the following year.
The coach is positioned as the one that knows how to teach mathematics.
In doing so, Liz positions herself as the novice and as belonging to the coach. Perhaps a desperate attempt, to shore up support from the coach to plan lessons for the following year.
Liz speaks with the authority of self through use of first person singular in articulating her position in working closely with the coach to plan her classes for the following year.
Liz distances herself from her students referencing their negative classroom behaviour.
Liz positions the coach as someone that she does not feel close to perhaps feels intimidated by her experience and mathematical knowledge.
Despite this distancing, Liz indexes coach through use of first person plural “we”, perhaps acknowledging the relationship formed as a result of working closely
Appendix 13
questioned that and said… “there’s no way that you can do geometry before you do algebra because you have to know how to solve equations to work out these, the shapes, the missing sides on the shapes”… [it] was… one of those moments when we went ohhhh! So that’s why… no kids could do those questions they’d all do really badly in geometry because they didn’t know they should do it second and do algebra first so she’s helped me reorganise all my topics which is just a document that we have here with everything in order so she’s helped me reorganise it and get everything in the right order to make it easier…
The coach indexed to teaching improvement hints to the dynamical object. That is, of a teaching sequence. The interpretant is energetic for Liz is now a believer in the epistemic and ontological authority of the coach.
with each other.
Summary:
Liz appreciated the coaching program for it supported her lack of experience as a novice teacher that encouraged her to challenge traditional approaches to teaching mathematics. Despite this, the exigencies and contingencies of the classroom proved too powerful, demonstrating that whilst the coaching program benefited Liz’s teaching, improvement to her practice was perhaps short lived.
Samantha’s response
“It surprised me that this teacher seemed to get so much out of our lessons together. It was nice
to hear that I had a positive impact. It also reinforced to me that the coaching needs to be a
partnership with both people working towards the same goal.”
Appendix 14
Jon Adams, Grallina College1
Jon Adams, a novice “graduate” teacher was awarded a Government sponsored Maths
Scholarship as encouragement to work in the government school system. The Mathematics
Scholarship awarded to Jon also ensured that he was automatically “on going” as a teacher in
the Government Education system rather than one who was employed on a yearly contract. Jon
did not have a University major in mathematics but rather in science. He entered Grallina
College qualified to teach both science and English.
Jon didn’t feel that his induction adequately prepared him for teaching at Grallina and he
expressed difficulty in settling into the role of teacher. Initially, Jon questioned his ability to be
a teacher given his concerns regarding classroom management and in having to get through the
prescribed curriculum in the time required particularly since the cohort of students studying
mathematics were not predisposed to learning. The coach was welcomed and provided Jon with
guidance and constructive feedback. Jon responded well to the coaching program further
encouraged by the structure of the sanctioned lesson approach. The coach mediated Jon’s
learning assisting him to grow in confidence as a teacher and to “take control of his class.”
1 Interview 1 – 7th Oct 2009. Interview 2 – 29th Oct 2009. Interview 3 – 19th Oct 2009.
Jon’s discursive identity formation after Gee (2000-2001) and Bullough (2005)
Nature perspective
Institutional perspective
Discourse perspective
Affinity perspective
A young male teacher. Unsure of his vocation in life.
Maths teachers are difficult to source and employ. Maths Scholarship offered by the DEECD as enticement, even to teachers who do not have a university major in mathematics. Jon is a teacher of junior mathematics.
A quiet, introspective person.
Jon experiences difficulty with classroom management and sources assistance from Teacher Aides who support students in his class.
Discourse identity of novice teacher experiencing difficulty in first year of teaching. That is, not experienced in responding to challenging cohort of students.
Member of the maths department and a teacher of junior mathematics.
Affinity identity – Novice teacher, new to teaching mathematics and requires support.
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Initial situation Jon, a first year out “graduate” teacher secures a government sponsored Maths Scholarship and appointed as permanent “on going”. Theme “… this is my first year at Grallina…”
Semiotic analysis Positioning analysis
1/12 I was lucky enough to… be put on a scholarship, so one of the Maths Scholarships they had…. I was automatically ongoing which… took… an amazing amount of pressure off, especially I would have been noticing it this time of year when you would have had been reapplying for the position looking for other positions.
Maths Scholarship symbolic convention used by the DEECD to recruit teachers of mathematics indexed to improvement to teaching mathematics in Victorian schools. The convention carries with it a financial incentive as well as ongoing status, the effect of which is logical for this strengthens Jon’s practice now that he has ongoing status.
The Maths Scholarship positions Jon in an education system that has a shortage of maths teachers. Jon is considered valuable in the moral order and therefore made permanent, i.e., a teacher that is not on contract and therefore not having to reapply for his position at the end of the academic year.
Summary: Jon is the recipient of a Maths Scholarship, offered to teachers as an incentive to stay on in a school / region that experiences difficulty attracting maths teachers. Jon is given an ongoing teaching position at Grallina College.
Preparation The rules and responsibilities of teaching initially overwhelm Jon. He grows in confidence with the support of a school-based coach / mentor. Theme “… I think the mentoring… was not great or very evident…”
Semiotic analysis Positioning analysis
Context: All students enrolling into Year seven at Grallina College sit a numeracy test to ascertain their level of mathematical understanding. The “Learning Acceleration Program” (LAP) targets those students who score low on the numeracy entrance test. The numeracy program at Grallina College consists of three levels: a LAP, a middle band and a Select Entry Acceleration Program (SEAL) for gifted students. The Aides that Jon refers to, are Secondary Teacher Assistants (STAs). STAs support teachers in their classrooms by attending to students who have a learning disability. 1/50 … part of the difficulty in
that for me was… like with the LAP classes here or with having Aides in classes, I’ve got Aides in… I had Aides in both of my classes last semester and I think I almost looked at them a little bit for that support cos there was another adult… in the room, where as, they’re used to working with teachers who go okay “I need you to do this”, and then that teacher… takes control of the class because they’re use to having control of the class. Where as, I came out of the university… and they almost stepped into that role of the… Mentoring Teacher, not that they … didn’t, I… felt like they were, I turned to them like I might turn to a… like a Supervising Teacher on rounds because there was an adult in the room. So I… that might have been to slightly my detriment in one sense, that I didn’t step into a room without someone, and say right,
Teacher as object indexed to one that is able to control and is in control of the class. Jon experiences difficulty teaching his LAP class. The interpretant is energetic for Jon seeks assistance from the Aides in his class. Which has an iconic relationship to the object. That is, of support that a mentor or Supervising teacher would afford a novice teacher. Jon indexes the Aides to supporting his need as a novice teacher. This hints to the dynamical object
Jon positioned as a novice teacher overwhelmed with the experience of teaching his LAP class. He experiences the contingent realities of the classroom. His dilemma sees him seek support from the Aides in his class, whom he sees as a Mentor or that of a Supervising Teacher. The illocutionary force shows Jon’s intention in producing the utterance. That is, one in need of assistance. He searches for the magical agentry that will assist him deal with the anxiety he is experiencing in maintaining control of his class. The Aides are the only ones in his class that can help Jon, for they come equipped with a history of taking control, just as a mother would know how to take control. Jon turns to them for support.
Appendix 14
what am I going to do, how am I going to handle this? I thought okay, maybe they know the situation or how it might work at Grallina College a little bit better than I do, so… [I] ask[ed] them for advice on what discipline, what behaviour all… those sort of areas.
for the Aides have a history of how teachers control their class at Grallina and this is the kind of support Jon is seeking.
1/54 I think… in the initial stages I think the mentoring… was not great or very evident…. I think, I thought as a mentor, a mentor might… on those three days that we’re here before school starts, that the mentor might look at things like… helping you get your head around, prepare for your first couple of days of class… like that, just run you through or show you where curriculum documents might be, like I went, through a whole last semester teaching science and just trying to scrounge bits and pieces from other people and then found out that there was a whole science curriculum available in part of a file on the… computer system here, so I think that… was… poorly done. A little bit later… Jason Smith… I am not sure if he was my mentor at the start because there’s a mentor in there and we have a coach as well…. Samantha is the numeracy coach, but we have a lot of teachers here, I think we’re almost split into bands of… teachers who may have only taught for one to three years… have a more experienced teacher who does coaching cycles with them. So individually and Jason will
Mentor indexed as someone who lends support to new teachers preparing them for the role of teacher. This is manifest in the correct use of the sign, i.e., novice (“graduate”) teachers require assistance. The effect is an immediate interpretant of recognition. Effective science teaching indexed to curriculum. A return to the original semiosis, i.e., Mentor as object symbolically related to improving practice of a novice teacher. This is a symbolic convention. A Mentor as a support that leads to the correct understanding of the sign.
Jon positioned in the storyline of novice teacher. Positioned in a storyline of helpless in his first moments at Grallina College. Jon expresses a moral cry from within for the support provided by a mentor. Jon indicates through first person pronoun (“I”) that he believes a Mentor is essential to a novice teacher. The use of the use of “you” refers to a generalised other, that is, all new teachers new to teaching should be afforded assistance in the form of a Mentor. Storyline of support, one perhaps related to nurturance found in a parent child relationship, i.e., Jon as the novice, “graduate” teacher, afforded an opportunity to develop with the support of a significant other.
come in… we’ll have a meeting to talk about… what I might like to do better… where I think improvements might be able to make or something along those areas and he’ll come in, watch what I do and then we’ll talk about what I do and maybe look for areas that I can improve that. So, I think as… professional development… that… coaching has been excellent and I’ve been lucky that I’ve had Jason cos he’s an unbelievable, unbelievably perceptive and really well trained teacher and quite easy to get along with, very professional. So from that point of view, professional development… [as] a coach, he’s… fantastic…
This is evident in Jon’s use of “I” and “we” and demonstrates that the school-based coach / Mentor was appreciated as a professional development activity for it assisted Jon to develop as a teacher.
2/36 No, I just, I set it, yeah, I… try and work out, I try and pick through... I use the text book to structure my lessons to an extend where I think that the textbook we’ve got at the moment builds on the skills of the students, so I’ll use that as a base and sort of work, try and work on different activities that complement that.... But yeah, I’ll pick out what I think might be particular questions or parts of that text chapter that are useful and then, yes structure my lessons and extra activities and sort of end of subject test on… what I’ve done basically. Yeah, so I’m not teaching to a test or anything like that... it’s a bit more sort of free, whether that’s a negative or a positive thing I don’t know.
Textbook, lesson plan and student activities as the signs all index teaching the teaching of mathematics. This hints to the dynamical for Jon becomes aware of the teaching paradigm alluded to by the researcher’s question. The effect of which is another semiosis in which “teaching to the text” indexes ineffectual teaching. The effect (logical interpretant) is an acceptance of the way in which mathematics should be taught.
Teaching as the storyline, involves use of historical artefacts. Use of first person singular pronoun indicates that Jon is in control, that is, he is speaking from the authority of the self and maths colleagues as expressed in first person plural (“we”) who have sanctioned this approach of teaching mathematics.
Appendix 14
Summary: Jon initially experiences difficulty in coming to terms with the demands of teaching in his first year at Grallina. A school-based mentor and the Regional Coach both assist Jon to plan and evaluate lessons thereby coming to appreciate the surface effect that coaching and mentoring afford in developing his confidence as a teacher at Grallina College. Finally, he also develops closeness to the prescribed maths textbook for it provides Jon with a road map in terms of how teachers of mathematics at Grallina teach maths. This artefact helps to establish and foster Jon’s teaching repertoire and his affinity identity emerges as a result.
Complication Jon’s qualification and contingent realities of the classroom complication his teacher practice. Theme “… I’m trained as a science English teacher…”
Semiotic analysis Positioning analysis
1/14 Technically no, I’m trained as a science English teacher and because they… couldn’t split me I guess into science English at the moment… they put me into science and the natural sort of pairing with that is maths. So I mean, it didn’t bother me. My maths skills aren’t bad and I guess, just that the strategies that teaching it could be improved and [this is where] I guess where Samantha (the Regional Coach) comes in a bit…
Symbolic conventions indicate the knowledge and skill Jon brings to the role of teacher. Conventions within the discipline of science index the teaching of mathematics. This is the immediate object and hints to the dynamical for Jon appears cautious for he realises there is more to teaching mathematics than what a science degree affords. The effect is logical for Jon acknowledges that he needs to seek assistance from the regionally appointed coach who is indexed to improvement to teaching practice.
Jon positions himself by using first person pronoun as a science and English teacher. Jon refers to the administrators as “they” (third person plural) as perhaps not quite making the correct decision in positioning Jon as a teacher of mathematics. The “it” that Jon refers to points to the fact that the administrators have positioned him as a maths teacher. Despite the positioning by administrators, Jon feels reasonably confident that whilst his maths skills are sound he acknowledges the role and responsibility of the coach in assisting him to develop his pedagogical approach to the teaching of mathematics. He therefore positions himself as a teacher in training once again with a coach as his mentor (A novice teacher storyline).
1/94 Yes, as far as like the socio-economics sort of side of things, yeah absolutely, I think, I… I don’t enjoy... like pigeonholing sort of an area like that but… you know, there is, I think a larger proportion of students around here that; say, where I grew up [from] that’s... aren’t taught the value of education or…
The relationship of the sign, that of socio-economic status to the immediate object, the students of Grallina College leads to a logical interpretant. That is, recognition of the relationship between the two, one that strengthens Jon’s perception of the students at Grallina as low
Jon positions himself away from the students at Grallina College who have a poor work ethic. According to Jon, students have a poor work ethic because of their socio-economic status and therefore not academically inclined (storyline).
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don’t have a great work ethic, as may be, what I’ve seen in other areas. So from that point of view, I think it’s necessary to have maybe that... a third-party in Samantha… come along and go okay maybe we can try this way... because her pure focus is on improving that and not just on, okay I’ve got [to] teach this bit of curriculum because it’s what it says in our Grallina guidelines or whatever... because she is there to do that…. We can go “okay I want to teach this” and then she goes “okay well this is one way that we might be able to do it, that might help improve student outcomes.” So yeah, I think that looking at the socio-economics... of Shire of Behriana is, I think... that’s part of why Samantha’s here.... Unfortunately it’s just got a bit of a pigeonholing, I mean not everyone’s like that, we’ve got fantastic kids here and even the ones who may be behind the “eight ball”, there are still a lot who try it pretty hard but there is a proportion of our students that... I think the value of education just isn’t there for them, they, I don’t think they can think long term very well because they don’t put... at the end of school, a job, or you know, have a plan… I mean not even I had a plan at Year seven, but I guess I, I knew that... getting through school well, and doing well at it would allow me better opportunities in the future, whatever that might be.
performing. This becomes the object of a further semiosis, one where the coach is indexed to improvement of maths teaching thereby improving student learning. The effect of which is also logical for it strengthens Jon’s perception of both the ability of his students and puts into question his ability to improve student outcomes. This becomes the object of a further semiosis where the coach indexes improvement to student outcomes. For the coach indexes how to improve maths teaching. This hints to the dynamical object, the world of mathematics that is relatively independent of Jon’s present thought. The effect is energetic i.e., that the kids at Grallina need assistance to improve. The socio-economic status of families of students has an iconic relationship to the object. In this case it is that of the metaphor of being “behind the eight ball”. The effect of which strengths Jon’s habit of belief about the students whom he teaches (Immediate interpretant).
Jon positions the researcher into agreeing (“you know”) with his “teacher talk”. This reaffirms his position as a teacher. Jon aligns himself to the coach who is committed to the improvement of the “that” (of the improvement to student performance). The coach is therefore positioned as the one that can make an improvement to student performance particularly given that Jon doesn’t requires assistance in order to deal with students at Grallina.
Summary: Jon recognises that he does not have the qualification to teach mathematics and also experiences difficulty teaching students who don’t have a positive learning disposition. The coach is a welcomed sign for she provides the assistance to improve Jon’s practice and emerging identity as a teacher of mathematics.
Appendix 14
Transference Samantha, the Regional Coach transforms Jon’s practice. Theme “… it was also the fact that we had, I had a period to talk to an experienced teacher…”
Semiotic analysis Positioning analysis
1/86 Basically we have our… meeting on a Tuesday morning and then we will… plan a class or we’ll talk about what I’m doing or what I plan to do [in] that class and then we’ll just look for ways that we can, ways that I… can improve the manner in which that’s taught or… breakdown the subject into smaller bites so that students can understand it more readily… and then we’ll go into the class together. It will either be a team teaching thing where Samantha might take part of it, [or] I might then, I’ll take part of it or maybe I’ll do the whole introduction that sort of thing. Samantha might be there as a, as another hand to go round to speak to students and... just help them out through whatever the work is they’re doing.
The coach is indexed to support in the improvement of teaching practice. This is evident in the discussion that takes place on Tuesday mornings (once every fortnight). The coach reinforces improvement to teaching practice. The relationship is between the sign and the object is iconic, for the coach models an approach to teaching. The effect is energetic for Jon is participating in the coaching program.
Jon accepts and belongs to the practice of improvement by indexing his close involvement with the coaching program through use of “we” and “I”. Despite Jon’s relationship with the coach he positions himself away from his student as evidenced in use of pronoun grammar (“them” and “they”) This distancing away is reflective of the difficulty he experiences teaching this cohort of students.
1/96 ... the research that Samantha has brought in, suggesting, that okay, you should be looking at having a quick “warm-up” and then your introduction should be 5 to 15 minutes or whatever it might be and then the bulk of the lesson should be students on task and then you… focus teaching or… going around to those students that need that extra help… and just allowing them to work on something…. Looking at
Samantha indexed to the improvement of teaching practice. Research indexes the known and proven, the “ought” for it has epistemic validity. To adhere to research is to follow normative and warrantable practice. Improvement to student learning indexes research
Jon positions himself in alignment with the Regional Coach to the improvement of student-learning outcomes (storyline). Despite this Jon distances himself away from his student (third person plural pronoun) and the Mathematics Lesson Structure (second person singular pronoun) of not belonging both.
the research at suggesting that that’s a good way of doing it seriously. So yes, from that point of view I think it’s… working slowly, I think it’s, it’s gotta be a two or three year thing to make sure that it’s well ingrained and that... we don’t fall back into older habits, so yeah, I think it’s… working… I think we’ve got to work at it for that couple of years before we see the real results in the students, so… I mean yeah I don’t think we gonna see any great changes in students, say this year from anyone’s teaching but… maybe next year and following that… it might.
/ the new Mathematics Lesson Structure. The alteration to Jon’s practice indicates an energetic interpretant for Jon is responding to the program’s implementation and believes that with a consistent long-term approach students will improve.
Jon perhaps feels unsure about whether the Mathematics Lesson structure will have an effect on student outcomes. He hypothesises that student learning may improve with a concerted effort by all of his colleagues in the maths department. Otherwise it will have little effect on the “we”, Jon includes himself with others who teach mathematics at Grallina.
1/104 Yeah, I believe so, yeah and I think, you know, that’s what she’s, she’s doing and you know they’re not always, you know, all the bells and whistles sort of stuff but... it’s just looking at some activities in a light that, in a different light, like making a something as simple as a “fraction wall”2 but noting down how different students are breaking up their strips of paper into their fractions and who’s measuring, who’s guessing, who’s using what techniques to do it. As forms of assessment or giving them an open-ended activity like we were talking like the other day... we’re looking at angles now so... draw a… robot and label or... show the angles in the robot and it’s
The coach as object mediates between the transitive and the intransitive dimension of improvement as presented by pedagogical approaches that she demonstrates to Jon. Jon acknowledges (energetic interpretant) of an alternative response to a teaching practice as demonstrated by the coach.
The coach is positioned as the one who knows how to teach and what to look for in student learning to effect improve teaching practice. In this episode, the coach uses a pedagogical approach and attends to closely to student engagement in the activity. This practice assists Jon to realise the positive effect it has on his student learning. Jon joins confidently with the coach, positions himself closer to her, as demonstrated through use of first person plural “we”. Perhaps as her understudy, in order to
2 http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/number/n32508p.htm accessed 12
April 2012.
Appendix 14
sort of like okay you haven’t told them how many angles you want... so it’s, it’s often simple but it’s just her ability to put those ideas forward.
explore the intransitive dimension. Despite this, Jon refers to his students as “them”, away from himself.
2/42 ... I think because, I was probably talking to Samantha a bit and thinking about exams a little as well and I was saying to Samantha, “oh, you know, I’m not going to get through all this textbook…” [and she said] “don’t worry about [the] textbook just try and cover your VELS (Victorian Essential Learning Standards) and... work on whether the kids can do what they’re supposed to do” and then I thought yeah, well from that point of view it’s interesting because the textbook probably over covers areas of VELS and doesn’t touch other parts very well at all... and things like problem-solving strategies and thinking strategies they’re expected to almost have to solve the questions in the textbook but are not explicitly taught them. So, I think if we used... a more general approach to maths using more, sort of worded questions where students explore a question possibilities, sort of, frame that question in different ways like whether they need to draw a diagram to show that the question, what the question means to them or show it in a numerical format, then they’re probably going to acquire skills that will benefit them if they did go on to say high-level maths,
Good teaching practice indexed to the coach (immediate object), the effect is energetic for Jon connects with the VELS. The VELS as a sigh has an iconic relationship to teaching mathematics for it hints to the dynamical object, one that existed up until now as relatively independent of Jon’s present thought, i.e., intransitive. This becomes an energetic interpretant for Jon who now acknowledges broader pedagogical approaches such as problem solving and represents a strengthening of Jon’s teaching practice.
Jon positions the Regional Coach as the one that knows how to solve the dilemma of having to get through the syllabus in the time required. The coach’s advice to Jon is to redirect his practice away from textbook delivery of the content and focus on delivering the learning outcomes as defined by the VELS for this will assist him to solve the problem. In doing so the coach transforms Jon’s identity as a teacher of mathematics, for Jon is beginning to think more broadly about the delivery of maths and the impact it may have on students in their later years of school. Jon positions himself closely with the coach but still at a distance from his students as evident through use of pronoun grammar.
say Year nine or ten they might start more textbook-based maths but then usually seven and eight and nine to build the thinking skills and strategies that are going to benefit them in not only maths but the other subjects as a whole.
2/52 ... No, actually I... Samantha... we suggested the activity, or we sort of came up with that when we were working together and then I said, oh, I might do that in this class because it fitted in nicely with a single that I had, so I administered the activity just in a single session... took up the work and then myself and Samantha just got together over, sort of 10, 15 minutes and just talked through what it looked like students were doing... what students definitely had a good grasp on measuring angles recognizing what type of angle it was, labeling angles correctly and what common problems were with students who couldn’t, some might have been not knowing where to place a protractor properly, not putting the number of degrees in an angle in the correct spot that you could actually know what angle they were talking about without guessing, that sort of thing.
The coach indexed to improvement to teaching practice. The effect of which was a logical interpretant for it strengthened Jon’s understanding of formative assessment as a means of understanding where students were at with their learning. In doing so Jon developed an understanding of the degree to which students applied mathematical understanding to complete a problem thus framing future lessons to address student misconceptions.
Jon positions himself as belonging to the coach, as expressed by the “we”. For example, Jon implemented the lesson (“it”) as demonstrated through the use of “I” and “my”. As a result his identity is strengthening as a teacher practitioner, gaining confidence coming closer to his students in the process.
3/116 … and it wasn’t always the fact that she’d gone out and researched it extensively or anything like that…. I think it was also the fact that we had, I had a period to talk to an experienced teacher as well, you know I could probably sit down
Coach indexed to improvement to teaching and of student learning; hints at the dynamical object of an “experienced teacher”, one that references the world of past experiences. The effect is energetic for Jon
The coach is positioned as an “experienced teacher”, as a significant other, a counsellor that afforded Jon the opportunity to learn. Jon positions the researcher as agreeing
Appendix 14
with… Mandy or someone else like that and… speak to her about okay what I could do here and maybe I’d get some similar... responses and similar... suggestions but I think part of it was the fact that you’ve got an hour a fortnight even if it doesn’t seem a lot to talk to an experienced teacher about how to teach… a certain area / aspect of a topic as much as she was a, you know, obviously a designated coach, but it was an experienced teacher that you’ve got this specified time to work with so
(the novice) recognises the value in spending time with an experienced member of staff. Time as a resource is referenced and indexed to improvement. Time to talk to another more “experienced teacher” about improvement to practice. The interpretant is logical for Jon recognises how practice may be improved. Mandy, a colleague and school-based coach is referenced iconically in a relationship of similarity with that of an “experienced teacher”.
with his teacher talk, that conversing with an experienced teacher afforded him the opportunity to develop his teacher identity. The storyline is one of a novice teacher who has benefitted from the coaching relationship and perhaps a moral cry from within given that the Regional Coach has come to the end of her tenure at Grallina.
Summary: At the commencement of this narrative aspect of Jon’s “accounts”, he continues to harbour doubts about teaching junior mathematics; all the whilst enjoying his experience working with Samantha. Jon experienced first hand how an “experienced teacher” was able to deal with the local specific exigencies and contingencies of the classroom. For example, the way in which curriculum may be delivered differently in order to cover the VELS in the limited time required, rather that teaching prescriptively from the text, and secondly, how student understanding may be evaluated in order to inform his teaching practice. Both of which became evident through discourse with Samantha as the significant other. By the end, Jon begins to feel more at ease with his students forming a closer relationship. His identity formation thus strengthened as a result of being afforded an opportunity to work with an “experienced teacher”.
Struggle Whilst Jon realised the opportunities working with the coach, his pedagogical repertoire in teaching mathematics is limited. Theme “… so I mean it opens up a pretty big can of worms in the end of it…”
Semiotic analysis Positioning analysis
Context: The coach demonstrated an activity from the Mathematics Developmental Continuum where students construct a fraction wall. 1/118 … it appeared to be good...
I think it be a form of diagnostic assessment for the… beginning of a unit... so yeah, for its simplicity and yeah, it is a basic activity, but if you’ve got students in there who can’t do it, then I guess you got to reassess… what else you’re going to teach them. So I mean it opens up a pretty big can of worms in the end of it but, yeah I think it would be something that I would use later on down the track.
A student activity (fraction wall) indexed to student learning. Completing the activity becomes the new social object of assessment. The fraction wall activity as a diagnostic tool is indexed to student understanding. The effect is logical for it strengthens Jon’s practice. The metaphor “…it opens up a big can of worms….” bears an iconic relationship between the sign and the immediate object, the effect is one of uncertainty. Of not knowing how to follow this activity if students don’t know how to complete it.
The “it” refers to the activity the coach introduced and how it can be used as a form of assessment, i.e., indicating which students are capable of doing what (storyline). Jon positions himself as the novice who is under the guidance of the coach who has taught him how assessment may strengthen his practice and how it may apply to the improvement of student learning. Jon’s use of first person pronouns (“I”) indicates his understanding of how the “it” may be used to gauge how students learn and in what he may do to encourage and engage this learning further. He is still unsure of his ability positioning his students away and of not belonging to him.
2/76 … these activities… they’re quite short... but they do tell you things about what the student knows…. I think they’re fairly beneficial. I mean maybe looking up things like the maths continuum… maybe that’s… I’ve looked at the science continuum a fair bit and tried to use that where I can and I daresay the maths
The maths activities introduced by the coach indexed to student learning and understanding achieved through a formative assessment process. The effect of which is an immediate interpretant for Jon expresses an interest but also an uncertainty in
Jon positions the coach as the knower and in doing so positions himself as a novice / patient in the teaching of mathematics. Jon appreciates the learning that open-ended activities affords and knows where they come from. Despite this, he does not use the maths
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continuum has a similar aspect. There’s great teaching ideas there.... For me it’s just… being able to put all the ideas or some of the ideas that say one of the continuums has into the curriculum that I’m teaching and still have a good flow to what I’m expected to teach while teaching it…
teaching in this way. The interpretant becomes the object for a subsequent semiosis. Whilst Jon expresses and energetic interpretant with using the Science Continuum, he expresses uncertainty in using the Maths Continuum in teaching to the syllabus provided by the Maths department.
on-line activities because of his science background and as a response to the lack. The lack of mathematical pedagogical content knowledge has Jon focus primarily on the job of getting through the maths syllabus in a specified time. This expectation ensures that he may work toward strengthening his affinity identity particularly given that his institutional identity (awarding of Maths scholarship) has positioned him with the ability to do so.
Summary: The importance of an experienced teacher as a significant other is made evident as a form of professional development, particularly in assisting novice teachers make valuable connections to practice. Despite this, the coaching exercise was negated, having little effect on Jon’s emerging practice. The lack is brought into sharp relief, and shows the effect of not having a university qualification in mathematics. For without it, a novice teacher will struggle to make connections between pedagogical content knowledge and the effective imparting of knowledge as it pertains to the domain of mathematics.
Return Jon demonstrates a growing awareness of the umwelten as a teacher of mathematics realising on the one hand its potential and on the other, its limits without the support of the coach. Theme “… I think I’ll definitely keep going and trying to… get consistent with that throughout my lessons…”
Semiotic analysis Positioning analysis
3/28 ... I’d say an awareness of... possibly at the moment the best accepted practices in teaching maths... and that’s… bringing those… practices into my own teaching... splitting up lessons into... specific areas such as your “warm-up” your brief introduction to what the students are going to be doing and then whatever their main activity is and then the… reflection on that.... That’s something that I think I’ll definitely keep doing and trying to... get consistent with that throughout my lessons. The… thing with Samantha not being here is how... I guess how polished I can become at that... I mean as a… maths staff we’re pretty good staff and work together fairly well so I’m sure it will develop somewhat still but Samantha had that ability to well [she] had that position where she would do the, I guess the legwork as far as research… and be aware of certain techniques that might be going on anywhere in the world at a certain time... and then bring them to us and suggest that look this… appears to be working here there’s a lot of people who… say this is a very good way to do things let’s give it a try and see how we
Jon indexes the coach as the object that represents “the best accepted practices” to teaching mathematics. The effect of which is a logical interpretant as it strengthens Jon’s resolve to improve his practice. The interpretant becomes a new object of semiosis, in that the new “lesson structure” has an iconic relationship to the object of good teaching practice. The effect is energetic for Jon wants to persevere and “…get consistent…” with the new “lesson structure” once the coach has left Grallina. This episode also references the culture of learning within the maths faculty indexed to improvement. The effect for Jon is one of uncertainty for Jon uses a metaphor (“legwork”) to iconically relate the coach to improvement hinting that a teacher lacks coaching / significant other as a way of improving practice. Perhaps Jon here is indexing the lack of experience in the maths department as Grallina.
The coach is positioned as the person who brings new techniques / approaches to the teaching of mathematics in order to improve the storyline of teaching of mathematics at Grallina. The act / action of restructuring the maths lesson demonstrates Jon’s agency in wanting to maintain a practice that the coach has introduced. Jon aligns himself to the (“we”), that is, the body of teachers that represents the maths staff at Grallina College. The coach positioned with the ability and the time to source new resources that she would articulate to others in order to improve practice. Jon feels, as expressed through first person possessive adjective (“our”) as belonging to his colleagues at Grallina, that without the positioning of the coach their “bank of knowledge isn’t going to be expanded” therefore dampening improvement at how “polished” the maths department can become.
Appendix 14
go with it so I think that from that point of view that... our current bank of knowledge isn’t gonna be expanded or... refined so that’s sort of a good working model of what the original was that she brought to us.
3/36 ... I like problem-solving because of the type of skills I think that students need to do it and then the thinking that goes on especially if they’re not just solving them, as a you know, if they’re a good student then they can probably solve it without writing anything down, that sort of thing, but to have... to push problem-solving further, getting students to do things like okay show it numerically or show it diagrammatically so that they’re actually... aware of what they are solving and giving those students who aren’t as capable possibly tools or a view of the problem that they do understand a little better. So from that point of view, I think it’s something I like to use a lot more and I think another thing that Samantha brought was the fact that yeah we have a textbook and we have a lot of subjects and things we’re supposed to cover from that textbook... but she started to push and suggest that we look at what the VELS ask us… and then use any time that you’ve got, you know for other worthwhile activities that might cover other areas of the VELS that are important but not necessarily... set out in the topics as such…
This “account” shows how Jon indexes the coach. Problem solving indexed to teaching mathematical skills; an immediate object linked to Jon’s perception of what is required and the necessary procedure students should apply to solve respective problems. The effect of which is immediate, that is, Jon shows an interest in the pedagogical ideas that Samantha has presented. Samantha also introduced the VELS. The VELS iconically related to the improvement of teaching. The effect of which is also an immediate interpretant. For Jon recognises how the VELS offers another perspective to how mathematics may be taught.
The storyline of Jon as teacher positioning students (“they”) as benefiting from completing problem-solving tasks (“it”) as presented to Jon by the coach. Samantha positioned by an institutional order at Grallina to encourage Jon and the maths department to whom he belongs (“we”) to teach differently using the VELS (“that”). Jon positions Samantha in third person singular “she” as not belonging to her and to what she has on offer. Perhaps too hard to implement siding with and in agreement with his colleagues in the subject department.
Summary: In this “account”, Jon shows his institutional identity and his affinity identity. Jon’s allegiance drifts between the two, from the exigencies and contingencies of the classroom to positioning himself in an aspect of least resistance. Whilst this affords him the most protection and comfort he positions his students away and as not belonging to him. Despite the coaching effort, Jon returns to the normative world of teaching at Grallina.
Appendix 14
Transformation Jon shows that his practice has transformed to one that is more engaging as a consequence of working with the coach. Theme “… it’s a more engaged sort of environment…”
Semiotic analysis Positioning analysis
2/14 … I would say… I’ll demonstrate then you do it, okay, so I’d… be at the board and I’d demonstrate something then expect them to know how to do it and work from that... and you know I’d still probably do that sometimes but it’s changed a lot more to, you know, getting students to help demonstrate, try to get them involved whether it’s them doing it as I do it whereas... somehow finding an activity where they can build on their skills as they go or... whether they come up and show the class how they did it and we can talk to what they did… in a perfect classroom, you know, that would be all very intriguing discussion. It doesn’t always go perfectly but it’s a more engaged sort of environment anyway.
Jon as social object indexed to a traditional approach to teaching mathematics. The energetic interpretant becomes the object for a subsequent semiosis one that hints to the ontological dimension of a possible world of possibility. This is demonstrated when Jon invites his students to the board to engage them with their learning. This effect to the object is logical for whilst Jon strengthens a practice he feels that it does not engage students sufficiently enough.
Jon positions himself in the role of teacher teaching to a traditional method of solving a mathematical problem (“it”) on the board. Jon positions the body of students (“they”) away from him. He invites a student to the board (front of the class) to demonstrate, where the approach is an attempt to form a closer connect with other students in the class as demonstrated through the first person plural pronoun “we”. Jon positions the researcher as agreeing to and understanding the difficulty of teaching.
2/48 ... We’ve done, what have we done? We’ve played a game, where using Maths 300 software and the interactive whiteboard…. I grouped the tables into teams and it be an estimation game…. [Students were] given… a diagram of a angle and each student from the table would come up and get a different angle to guess what it was and then I worked out for each table the average error so whether they were 2
Jon indexes a game (social object) to effective teaching (sign). The object hints to the intransitive dimension of a world of possibility and as such remains an influence upon semiosis for Jon experiences a positive effect engaging students with the “warm-up” activates. The interpretant is logical strengthening his practice.
Jon positions himself alongside the coach to develop his emerging practice (storyline). Jon belongs to the coach in this episode as evidenced through use of first person plural (“we” and “us”). This indicates an acceptance of a change in practice away from the traditional approach of teaching mathematics. The act / action in this episode is the use of games to develop skills in
degrees out, whether they were 15 degrees out... and use that as the table scores so we use those just two game[s], and it was, you know, as simple as it was. It was pretty good because every student was looking all the time at what the other tables [were] getting, thinking “Oh, how far are they away from... from what I think the angle is?”, so every student was actually doing each angle without probably knowing it, because they were thinking oh, they’re looking at making that 217 degrees or if I think that’s more 200, so that would be good for us because they’re further away error wise. So that was one where [we] use all the students.... Another open ended one that we worked on with Samantha was they got to draw any, any sort of shape or object they wanted... I suggested things like robots, cars, that sort of stuff, and I think I gave them a base criteria, okay it’s gotta have one reflex angle, two acute angles and an obtuse angle, you can have any… amount of angles after that, but it has to have at least that... and from there it’s sort of allowed us to, we took up everything that was drawn and it showed us a really interesting range of what skills of maybe we need to work on when they were measuring the angles, when they were naming the angles... where they placed the 60 degrees if there was a 60 degrees angle whether it was on the inside and it
protractor use and the recognition of the various angles referred to as the “it”. The “it” also assisted Jon to formatively assess students in order to inform his practice.
Appendix 14
looked, and it was depicting that angle in particular or whether it was just sort of out in the middle of nowhere... yeah, so that activity gave us a… look at what we might need to work on a bit more.
3/88 That was like that ... well I guess a lot of my lessons now… have a “warm-up” activity it might be... one that seems to engage them… a lot is, if I’ll give them a number and I’ll say okay this is the answer to… a question you give me the question and I rate the questions from you know awesome to boring and you know they start getting… pretty competitive about what they come up with so you know even my not necessarily low and intellectual ability but low in participating... students... came up with a combination of bus fares that would equal to that sort of number if it was a dollar amount that sort of thing so that would be an example of you know and… I end up getting you know 90% of the students willingly participating in that compared to I’d know well that one in particular there are other others that we [are] doing, they have good participation but that one seems good so far. So I do that, and then, say recently, if we’re revising fractions I’ll work through the specific skills we might need to... change an improper fraction to a mixed number... and then try and keep that reasonably short... put a couple of examples on the
The maths game Jon uses is indexed to effective learning. The object in question is the “warm-up” activity that hints to a dynamical object that is, the engagement of students with their learning (Jon imagining student inner conversations in more detail). The effect of which is energetic for Jon believes it to be the solution to engaging his students with mathematics.
Pronoun grammar used in this passage indicates Jon’s agency (“I” and “we”) in the use of a “warm-up” activity. Positioned as the teacher acting to a moral order as articulated by the coach. The act of teaching to the structured arrangement shows that Jon is enacting the storyline of improvement to practice as presented in his more confident teacher identity.
board... then like I said go around and check... students that I generally… know [who] will need maybe some extra help... just encourage other students who might be doing it well but you know just like for the sake of giving them some attention and acknowledging that they’re doing their work and then at the end of it work on a reflection so it might be okay “... can you give me a certain way that you’re gonna revise for this on the exam or... what are two things that you found difficult in the class today” and I’ll say “you know, it doesn’t have to be your maths work exactly, it could be something else in the class” and you know, you might get some come up saying that... it was a bit noisy for me to concentrate or it was... you know, there was this aspect of the maths that was tough so just being aware of their environment and of… how they’re working in that environment and… from my understanding, that’s… the model that you know is suggested as being, it’s fairly productive and... yeah, it’s… a teaching model
Summary: Jon who still experiences difficulty demonstrates an identity transformation evident largely due to working with the Regional Coach. This transformation was due to the approach taken by Samantha in coaching Jon to move away from the traditional textbook approach to teaching mathematics. In doing so, Jon experienced a closer relationship to teaching his students.
Appendix 14
Samantha’s response
“It surprised me that this teacher was so thoughtful about a number of aspects of
his teaching, considering the limited time we had together.
This teacher’s willingness to continue improving and learning in encouraging.”
Minerva Access is the Institutional Repository of The University of Melbourne
Author/s:
DIMAGGIO, SOL
Title:
The positioning of the coach and the transformative agency of teachers: The problem of
constituting joint meaning in an “underperforming” secondary mathematics department
Date:
2013
Citation:
DiMaggio, S. (2013). The positioning of the coach and the transformative agency of teachers:
the problem of constituting joint meaning in an “underperforming” secondary mathematics
department. Doctorate, Melbourne Graduate School of Education, The University of
Melbourne.
Persistent Link:
http://hdl.handle.net/11343/38480
File Description:
The positioning of the coach and the transformative agency of teachers: the problem of
constituting joint meaning in an “underperforming” secondary mathematics department
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