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Early Years Teachers’ Attitudes
Towards Mathematics
Kylie Sweeting
BEd (Early Childhood)
Centre for Learning Innovation
Faculty of Education
Queensland University of Technology
This thesis is submitted in fulfilment of the requirements for the degree of Masters of
Education.
May 2011
i
Keywords
teacher attitude, early years, mathematics, practising teachers, case study
ii
Abstract
Worldwide, there is considerable attention to providing a supportive
mathematics learning environment for young children because attitude formation and
achievement in these early years of schooling have a lifelong impact. Key influences
on young children during these early years are their teachers. Practising early years
teachers‟ attitudes towards mathematics influence the teaching methods they employ,
which in turn, affects young students‟ attitudes towards mathematics, and ultimately,
their achievement. However, little is known about practising early years teachers‟
attitudes to mathematics or how these attitudes form, which is the focus of this study.
The research questions were:
1. What attitudes do practising early years teachers hold towards mathematics?
2. How did the teachers‟ mathematics attitudes form?
This study adopted an explanatory case study design (Yin, 2003) to
investigate practising early years teachers‟ attitudes towards mathematics and the
formation of these attitudes. The research took place in a Brisbane southside school
situated in a middle socio-economic area. The site was chosen due to its accessibility
to the researcher. The participant group consisted of 20 early years teachers. They
each completed the Attitude Towards Mathematics Inventory (ATMI) (Schackow,
2005), which is a 40 item instrument that measures attitudes across the four
dimensions of attitude, namely value, enjoyment, self-confidence and motivation. The
teachers‟ total ATMI scores were classified according to five quintiles: strongly
negative, negative, neutral, positive and strongly positive. The results of the survey
revealed that these teachers‟ attitudes ranged across only three categories with one
teacher classified as strongly positive, twelve teachers classified as positive and
seven teachers classified as neutral. No teachers were identified as having negative or
strongly negative attitudes. Subsequent to the surveys, six teachers with a breadth of
attitudes were selected from the original cohort to participate in open-ended
interviews to investigate the formation of their attitudes. The interview data were
analysed according to the four dimensions of attitudes (value, enjoyment, self-
confidence, motivation) and three stages of education (primary, secondary, tertiary).
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Highlighted in the findings is the critical impact of schooling experiences on
the formation of student attitudes towards mathematics. Findings suggest that
primary school experiences are a critical influence on the attitudes of adults who
become early years teachers. These findings also indicate the vital role tertiary
institutions play in altering the attitudes of preservice teachers who have had
negative schooling experiences. Experiences that teachers indicated contributed to
the formation of positive attitudes in their own education were games, group work,
hands-on activities, positive feedback and perceived relevance. In contrast, negative
experiences that teachers stated influenced their attitudes were insufficient help,
rushed teaching, negative feedback and a lack of relevance of the content. These
findings together with the literature on teachers‟ attitudes and mathematics education
were synthesized in a model titled a Cycle of Early Years Teachers’ Attitudes
Towards Mathematics. This model explains positive and negative influences on
attitudes towards mathematics and how the attitudes of adults are passed on to
children, who then as adults themselves, repeat the cycle by passing on attitudes to a
new generation. The model can provide guidance for practising teachers and for
preservice and inservice education about ways to foster positive influences to attitude
formation in mathematics and inhibit negative influences.
Two avenues for future research arise from the findings of this study both
relating to attitudes and secondary school experiences. The first question relates to
the resilience of attitudes, in particular, how an individual can maintain positive
attitudes towards mathematics developed in primary school, despite secondary
school experiences that typically have a negative influence on attitude. The second
question relates to the relationship between attitudes and achievement, specifically,
why secondary students achieve good grades in mathematics despite a lack of
enjoyment, which is one of the dimensions of attitude.
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Table of Contents
Keywords ...................................................................................................................... i
Abstract ........................................................................................................................ ii
Table of Contents ........................................................................................................ iv
List of Tables .............................................................................................................. vii
List of Figures ........................................................................................................... viii
List of Appendices ...................................................................................................... ix
Statement of Original Authorship ................................................................................ x
Acknowledgements ..................................................................................................... xi
1 Introduction .......................................................................................................... 1
1.1 Preamble ........................................................................................................ 1
1.2 Chapter Overview .......................................................................................... 1
1.3 Purpose of the Study ...................................................................................... 1
1.4 Significance ................................................................................................... 2
1.5 Thesis Overview ............................................................................................ 5
1.6 Chapter Summary .......................................................................................... 5
2 Literature Review ................................................................................................. 7
2.1 Introduction ................................................................................................... 7
2.2 Attitudes......................................................................................................... 7
2.3 Teacher Attitudes ......................................................................................... 12
2.4 Student Attitudes ......................................................................................... 18
2.4.1 Attitudes and early years mathematics internationally ........................ 21
2.4.2 Attitudes and early years mathematics nationally ................................ 23
2.4.3 Attitudes and early years mathematics in Queensland ......................... 24
2.5 Preservice Teachers‟ Attitudes to Mathematics .......................................... 25
2.5.1 The effects of education experiences on attitude formation ................ 25
2.5.2 Addressing preservice teacher attitudes towards mathematics ............ 27
2.6 Preservice Teacher Attitudes Towards Science ........................................... 30
2.7 The Cycle of Teacher Attitudes ................................................................... 31
2.8 Measuring Teachers‟ Attitudes .................................................................... 35
2.9 Conclusion ................................................................................................... 37
3 Research Design and Methodology.................................................................... 39
3.1 Chapter Overview ........................................................................................ 39
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3.2 Research Design .......................................................................................... 39
3.3 Research Methods ....................................................................................... 41
3.3.1 Research setting and researcher ........................................................... 41
3.3.2 Participants ........................................................................................... 42
3.3.3 Data collection ..................................................................................... 43
3.3.3.1 The attitude survey........................................................................ 43
3.3.3.2 Interviews...................................................................................... 45
3.3.4 Data analysis ........................................................................................ 47
3.3.4.1 Analysis of the Attitude Towards Mathematics Inventory ........... 47
3.3.4.2 Analysis of interview data ............................................................ 48
3.4 Quality and Rigour of the Study .................................................................. 49
3.4.1 Reliability ............................................................................................. 49
3.4.2 Trustworthiness .................................................................................... 49
3.4.3 Ethical considerations .......................................................................... 50
3.5 Chapter Summary ........................................................................................ 50
4 Results ................................................................................................................ 53
4.1 Chapter Overview ........................................................................................ 53
4.2 Survey Results ............................................................................................. 53
4.2.1 Overall survey results ........................................................................... 54
4.2.2 Subscale scores..................................................................................... 57
4.3 Interviews: Themes Representing Teacher Attitudes Towards Mathematics
60
4.4 Past Experiences of Teachers with Positive Attitudes ................................ 62
4.4.1 Primary school experiences.................................................................. 63
4.4.2 Secondary school experiences.............................................................. 66
4.4.3 Tertiary experiences ............................................................................. 67
4.4.4 Summary .............................................................................................. 69
4.5 Survey and Interview Results for Teachers with Positive Attitudes ........... 69
4.6 Understanding Teachers with Positive Attitudes ........................................ 72
4.7 Past Experiences of Teachers with Neutral Attitudes ................................. 73
4.7.1 Primary school experiences.................................................................. 74
4.7.2 Secondary school experiences.............................................................. 78
4.7.3 Tertiary experiences ............................................................................. 81
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4.7.4 Summary .............................................................................................. 85
4.8 Survey and Interview Results for Teachers with Neutral Attitudes ............ 86
4.9 Understanding Teachers with Neutral Attitudes ......................................... 89
4.10 Comparison of Teachers with Positive and Neutral Attitudes ................. 91
4.11 Impact of Past Experiences on Teaching ................................................. 93
5 Conclusion ........................................................................................................ 101
5.1 Chapter Overview ...................................................................................... 101
5.2 Summary of Findings ................................................................................ 101
5.2.1 Practising early years teachers‟ attitudes towards mathematics ......... 101
5.2.2 The formation of early years teachers‟ attitudes towards mathematics
103
5.3 Limitations of the Study ............................................................................ 107
5.4 Implications of the Study ........................................................................... 109
5.4.1 Implications for future research ......................................................... 109
5.4.2 Implications for preservice teacher education .................................... 109
5.4.3 Implications for professional development ........................................ 110
5.5 Chapter Summary ...................................................................................... 110
References ................................................................................................................ 113
Appendices ............................................................................................................... 125
Appendix A: Attitude towards mathematics inventory (Schackow, 2005) ...... 125
Appendix B: Interview stimulus questions ...................................................... 130
Appendix C: Information and consent forms for teachers and principals ........ 131
Appendix D: Interview transcripts ................................................................... 137
vii
List of Tables
Table 3.1. Lower Creek teachers‟ tertiary training.....................................................43
Table 4.1. Scoring ranges on the ATMI.....................................................................54
Table 4.2. Results from the ATMI.............................................................................56
Table 4.3. Subscale results from the ATMI...............................................................58
Table 4.4. Teachers‟ memories and stage of schooling.............................................62
viii
List of Figures
Figure 2.1. Theory of Reasoned Action (Ajzen & Fishbein, 1975)............................10
Figure 2.2. Preliminary Cycle of Teacher Attitudes towards Mathematics................34
Figure 3.1. Phases of explanatory case study design..................................................41
Figure 4.1. Teachers‟ ATMI subscale and total scores..............................................59
Figure 5.1. Cycle of Early Years Teachers‟ Attitudes towards Mathematics...........106
ix
List of Appendices
Appendix A. Attitude towards mathematics inventory (Schackow, 2005)..............125
Appendix B. Interview stimulus questions...............................................................130
Appendix C. Information and consent forms for teachers and principals................131
Appendix D. Interview transcripts...........................................................................137
x
Statement of Original Authorship
The work contained in the thesis has not been previously submitted to meet
requirements for an award at this or any other higher education institute. To the best
of my knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
Signature: ______________________________
Date: __________________________________
xi
Acknowledgements
This thesis was undertaken with the assistance of a number of people. I would like to
acknowledge the work and support of the following:
Professor Carmel Diezmann, for her constant encouragement and unparalleled
guidance and wisdom;
Dr Ann Heirdsfield, for her patience and assistance with the technical aspects of
writing;
Dr Jill Fox, for her unwavering support and willingness to offer whatever assistance I
needed;
Kent Sweeting, my husband, for enduring this journey with me. His understanding
and support always kept me going; and
Eloise Sweeting, my daughter, anything can be achieved once you set your mind to it.
1
1 Introduction
1.1 Preamble
The benefit of having a positive attitude towards mathematics is well documented in
the student attitude literature (e.g., Brown, McNamara, Hanley, & Jones, 1999) and
the preservice teacher literature (e.g., Trujillo & Hadfield, 1999). Because an
individual‟s attitude influences not only how they see the world around them but also
how situations, circumstances, and the actions of others are interpreted by individuals
(Fritz, 2008), attitudes are important in teaching and learning. However, there is
scant research on practising teachers‟ attitudes towards mathematics. Practising
teachers‟ attitudes are of particular importance because their attitudes can influence
their teaching methods (Wilkins, 2002) and, in turn, teaching methods can influence
student attitudes (Duatepe-Paksu & Ubuz, 2009; Stipek, Salmon, Givvin, & Kazemi,
1998). Thus, teachers have a critical impact on the formation of their students‟
attitudes towards mathematics (Philippou & Christou, 1998; Quinn, 1997; Trujillo &
Hadfield, 1999). Due to the importance of the early childhood years in mathematics
learning, this study investigates practising early years teachers‟ attitudes towards
mathematics, the formation of these attitudes, and the experiences that contribute to
the formation of these attitudes.
1.2 Chapter Overview
There are four further sections in this chapter. First, the purpose of the study is
outlined including the two aims of the study (Section 1.3). Following this, the
significance of this study is identified highlighting the importance of research within
the affective domain and linking the importance of attitude in national and
international expectations for mathematics learning (Section 1.4). Next, an overview
of the thesis is provided (Section 1.5). Finally, this chapter concludes with a
summary (Section 1.6).
1.3 Purpose of the Study
The purpose of this study was to investigate the attitudes of practising early years
teachers towards mathematics and the formation of these attitudes. This study
examines attitudes towards mathematics. However, for teachers, their attitude
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towards mathematics extends to their teaching of mathematics. The research
questions guiding this study were:
1. What attitudes do early childhood teachers hold towards mathematics and
2. How were these attitudes formed?
Investigating these questions will achieve the following aims:
1. To identify the attitudes of a group of early years teachers using the Attitude
towards mathematics inventory (Schackow, 2005) and
2. To investigate how a selected group of teachers, with varying attitudes,
perceive their attitudes were formed.
Teachers‟ attitudes were investigated through an explanatory case study
(Yin, 2003). Data was collected from a survey completed by 20 practising teachers
and follow up interviews with six teachers. Early childhood teachers are an important
cohort to investigate due to the role that early learning plays in laying the
foundations for future success in mathematics and in the formation of lifelong
attitudes (Chapter 2). The design and methods are described further in Chapter 3.
1.4 Significance
Investigating teacher attitudes and how attitudes are formed is important for four
reasons. First, young children‟s interest in mathematics begins well before they enter
formal schooling. Studies have revealed that children develop an enjoyment of
mathematics and an understanding of some informal mathematical concepts prior to
school (Baroody, Lai, & Mix, 2006; Baroody & Wilkins, 1999; Ginsburg, Cannon,
Eisenband, & Pappas, 2002; Sarama & Clements, 2008). It is the role of the teacher
to build on children‟s informal knowledge and maintain the interest and enjoyment
of mathematics that they bring with them from home (Sarama & Clements, 2008).
The ways in which they maintain the student‟s interest and enjoyment may influence
the attitude that is developed towards the subject. Additionally, developing children‟s
mathematical skills in the early years lays the foundation for mathematics learning in
their future (Entwisle & Hayduk, 1998; Ginsburg & Baroody, 1990; Varol & Farran,
2006). Therefore, identifying the factors that can contribute to positive and negative
attitude development will ensure that children are given the opportunity to engage in
mathematics in a positive way.
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Second, mathematical achievement has been identified as a critical
component to lives of children and adults living in the 21st century successfully
(Kilpatrick, Swafford, & Findell, 2001). Students encounter mathematics problems
and investigations while attending school. In addition, students are presented with
daily experiences that require mathematical knowledge and skill, such as, shopping
at the supermarket, telling the time and trying to fit toys into a container. As children
move through formal schooling and beyond, the importance of mathematics remains
as Kilpatrick et al. (2001) state “For people to participate fully in society, they must
know basic mathematics ... Innumeracy deprives them not only of opportunity but
also of competence in everyday tasks” (p. 1). Additionally, mathematics is of
particular importance for children living in the 21st century due to technological
advancements (Clements, 2004; Department of Education, Employment and
Workplace Relations (DEEWR, 2008; Kolstad & Hughes, 1994; National Council of
Teachers of Mathematics (NCTM), 2009; Queensland Studies Authority (QSA),
2007; Riley, 1998). As society evolves technologically, so do the mathematical
demands expected in the workforce (Furner, Yahya, & Duffy, 2005; Riley, 2008;
Telese, 1997). The importance of mathematics in the lives of children has been
recognised both nationally and internationally by both Government documents and
policies produced by influential mathematics organisations (DEEWR, 2008, NCTM,
2000; National Association for the Education of Young Children (NAEYC), 2008)
(see Section 2.4). The term „young children‟ refers to children between the ages of
four and eight years old.
Most recently, the Queensland Government highlighted the significance of
early mathematics foundations by developing curriculum to support young children‟s
early mathematical foundations (QSA, 2006). These documents highlight the critical
nature of early mathematical development in children due to the fundamental role
that mathematics plays in students‟ day-to-day lives as well as the role that
mathematics plays in a child‟s future. Because children require a school environment
in which positive attitudes towards mathematics are fostered and nurtured, there is a
need to identify the types of attitudes that teachers bring with them in schools and
how these attitudes formed. Within the teaching profession, teachers of young
children are referred to as early years teachers. The initial years of schooling provide
two main stepping stones for young children with regards to mathematics learning.
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The first relates to providing opportunities for children to develop the foundational
mathematical understandings which are built upon in subsequent years. It is critical
for young children to learn and consolidate a variety of different mathematical
concepts including patterning and number operations. Without these foundational
understandings, children will struggle to comprehend more complex concepts such as
algebra and geometry (Clements & Sarama, 2009; NCTM, 2000).
Third, when studying factors that influence children‟s mathematics learning,
it is recognised that the affective domain, including attitude, plays a central role in
the way that students learn. This is because learning is influenced by emotional
responses (McLeod, 1992). Emotional responses include joy, as a positive response,
and frustration, as a negative response (McLeod, 1992). The affective domain
impacts on student interactions with mathematics providing a context for learning
(McLeod, 1992; McLeod & McLeod, 2002; Ruffell, Mason, & Allen, 1998). Hence,
when students‟ affective responses to mathematics are positive, their interactions are
positive. Conversely, when students‟ affective responses to mathematics are negative,
their interactions are negative (Gomez-Chacon, 2000; McLeod, 1992).
Fourth, this research has particular significance due to the limited number of
studies available investigating the attitudes of practising early years teachers (see
Section 2.3). In contrast, research on preservice teachers‟ attitudes has been the focus
of many research agendas (Bobis & Cusworth, 1994; Brown et al., 1999; Meyer,
1980; Trujillo & Hadfield, 1999). The information gained from preservice studies
has provided insights into effective preservice teacher education. However, there is a
lack of research on the attitudes of existing teachers practising in the field. The
purpose of this study, therefore, is to investigate practising teacher attitudes to
mathematics and how their attitudes formed.
In summary, the critical nature of attitude research has stemmed from an
understanding that schooling experiences greatly influence the development of
attitudes in students. Further, attitudes and the affective domain impact significantly
on children‟s learning of mathematics. Moreover, national and international
documents (e.g., DEEWR, 2008; NAEYC, 2008) have recognised the importance of
mathematical competency in young children, advocating for quality mathematics
programs as students‟ learning and attitudes are impacted by teachers‟ attitudes.
Considering the importance of mathematics in early childhood, the influence of
5
attitudes on mathematical achievement and teachers‟ role in attitude formation, a
study of practising early years teachers‟ attitudes towards mathematics is warranted.
This study is of significance because there is a paucity of research investigating
practising teachers‟ attitudes towards mathematics and their attitude formation.
1.5 Thesis Overview
This document has five chapters. This chapter provides an introduction to the
research topic and its significance. Chapter 2 provides a review and discussion of
literature on attitudes and mathematics. Chapter 3 describes the case study design. In
addition, participant selection, data collection and data analysis methods are
described. Chapter 4 presents the results obtained through a survey and interviews
and a discussion of the findings. Chapter 5 presents the conclusion, the limitations of
the study, suggestions for future research and the implications for teacher education.
1.6 Chapter Summary
The purpose of this study was to investigate the attitudes of practising early years
teachers towards mathematics and the formation of these attitudes. In this chapter,
the research aims and questions of the study have been identified. The significance of
the study has been discussed highlighting both national and international
commitment to the provision of quality mathematics education. In addition, it has
explained that teachers‟ attitudes towards mathematics are important because they
are linked to the teaching methods used within the classroom, which impact on
students‟ attitudes and their achievement. Further discussions about the literature
that underpins the research focus are presented in Chapter 2.
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2 Literature Review
2.1 Introduction
The purpose of this chapter is to review the literature on attitudes, mathematics
education, and their interrelationship in order to develop an understanding of
previous research that contributes to an understanding of practising teachers‟
attitudes to mathematics. Further, the importance of investigating teachers working
in the early years will be established through studies identifying this cohort as having
differing attitudes to teachers in higher grades.
This chapter has six further parts. The first part of this chapter defines the
term attitude and outlines the theoretical framework underpinning this project
(Section 2.2). The second part outlines previous research conducted in the field of
teacher attitudes (Section 2.3) and student attitudes (Section 2.4). The third part
describes preservice teacher attitudes in relation to mathematics (Section 2.5) and
science (Section 2.6). The fourth part presents a cycle of teacher attitudes based on
the literature (Section 2.7). The fifth part examines how attitudes can be measured
(Section 2.8). The final part contains the chapter summary (Section 2.9).
2.2 Attitudes
The term „attitude‟ has many definitions and is a word commonly used in our daily
lives (Albarracin, Zanna, Johnson, & Kumkale, 2005). In recent times, Eagly and
Chaiken (1993) have defined attitude as, “a psychological tendency that is expressed
by evaluating a particular entity with some degree of favour or disfavour” (p. 155).
To date, literature has revealed the complex nature of defining the term „attitude‟
(McLeod & McLeod, 2002; Thompson, 1992; White, Way, Perry, & Southwell,
2005/2006). Early in the 20th
Century, Allport (1935) defined attitudes as “a mental
and neural state of readiness, organized through experience, exerting a directive or
dynamic influence upon the individual‟s response to all objects and situations with
which it is related” (p. 810). This definition implies that an attitude is a response to
something and is formed through life experiences. His definition identifies the vital
role that experiences play in the formation of attitudes specifically noting
experiences as an integral part to attitude function. Thus, Allport‟s recognition of
experiences in attitude formation makes his definition central to this study. The
8
literature pertaining to attitude formation also has revealed the important role that
education experiences play in attitude formation (Section 2.6).
The development of attitudes is closely linked to a person‟s beliefs. Ajzen
(1989) proposes that attitudes are “…not merely related to beliefs, they are actually a
function of beliefs” (p. 247). Hence, attitudes cannot be discussed in isolation from
beliefs but rather, can be better understood when the relationship between the two is
clear. Although attitudes are a function of beliefs, the two terms are defined
differently. Ajzen (1989) stated that, “…attitude refer(s) to a person‟s favourable or
unfavourable evaluation of the object, whereas, beliefs represent the information a
person has about the object. Specifically, a belief links an object to some attribute”
( p. 12) (emphasis in original). Attitudes are a function of beliefs, meaning that
beliefs about an attribute of an object contribute to the attitude held towards that
object (Ajzen, 1989). Therefore, according to Ajzen (1989), beliefs about
mathematics may directly affect the attitude formed towards mathematics. For
example, if a student believes that mathematics is „hard‟, their attitude is more likely
to be negative as a result of this belief. In contrast, if a student believes that
mathematics is „fun‟, their attitude is more likely to be positive as a result of that
belief.
As individuals accumulate beliefs about mathematics, they form an attitude
toward it. Attitudes may be favourable or unfavourable. Fishbein and Ajzen (1975)
stated “we learn to like (or have favourable attitudes toward) objects we associate
with good things, and we acquire unfavourable feelings toward objects we associate
with bad things” (p. 217). Therefore, attitudes towards mathematics are a function of
beliefs that we hold about the attributes of mathematics and an evaluation of those
attributes. For example, a student may believe that learning long division is hard
(belief about a mathematics attribute). If the student does not consider himself to be
particularly good at mathematics, he or she may then develop a negative attitude
towards long division (evaluation of an attribute). In addition to beliefs influencing
attitudes, a person‟s beliefs and attitudes towards mathematics can also influence the
way they behave towards the subject. The relationship between beliefs, attitude and
behaviour can be understood through Ajzen and Fishbein‟s (1975) Theory of
Reasoned Action (see Figure 2.1). For example, students with positive attitudes and
who believe that participating in mathematics experiences will develop their skills,
9
may engage in all mathematics experiences. In contrast, students with negative
attitudes and who believe that participating in mathematics experiences has no value,
may avoid engaging in mathematics experiences.
10
Figure 2.1. Theory of Reasoned Action (Ajzen & Fishbein, 1975, p. 16)
Beliefs about
consequences of
behaviour X
Normative beliefs
about behaviour X
Attitude toward
behaviour X
Subjective norm
concerning behaviour X
Behaviour X
Intention to perform
behaviour X
Influence
Feedback
11
The Theory of Reasoned Action (Ajzen & Fishbein, 1975) represents beliefs
as being the fundamental building blocks of attitude. The first phase of this theory
begins with a person being presented with the decision of whether or not to perform a
behaviour, for instance, engaging in a mathematics lesson. The decision is influenced
by personal beliefs regarding the consequences of engaging in the mathematics
lesson (e.g., I will fail even if I try) or normative beliefs. Normative beliefs refer to
an individual‟s perception of the behaviour and are influenced by the judgment of
significant others (e.g., parents, friends, teachers) (e.g., Do I value trying hard in
mathematics?).
The second phase of the model involves the activation of a person‟s attitude
towards the behaviour (e.g., I like engaging in mathematics) and subjective norms
(social acceptance of engaging in mathematics) (e.g., Will my peers laugh at me if I
engage in the lesson?). This then leads to a person‟s intention to perform the
behaviour and finally to the enacting or rejecting of the behaviour.
Teachers‟ beliefs about mathematics may affect their teaching. A negative
attitude may affect teachers‟ mathematical pedagogy in a different way to a positive
attitude. For example, a teacher with a negative attitude may not allocate the required
hours to mathematics in their timetable as a means of avoiding the teaching of it.
Furthermore, we might expect that teachers‟ attitudes towards mathematics can be
influenced by their previous experiences with mathematics. Hence, identifying how
these teachers‟ attitudes formed will provide a greater understanding of the factors
influencing attitude development in students. This knowledge will provide greater
understanding of how teachers‟ attitudes affect their teaching.
Attitudes can greatly affect how people, including teachers, view and interact
with mathematics. Further, attitudes towards mathematics are formed through
experiences (Allport, 1935) with many experiences encountered during different
stages of education. Whilst attitudes begin to form during early childhood, they can
persist throughout formal schooling into adulthood. Attitudes and their formation are
particularly pertinent to those students who become teachers. Ajzen and Fishbein‟s
(1975) Theory of Reasoned Action posits that attitudes towards mathematics are the
result of direct experiences with the subject and beliefs attached to those experiences.
Hence, investigating how the attitudes of practising teachers formed will assist in the
identification of experiences that have contributed to the development of their
12
attitudes. In view of the significance of attitudes within the education context, it is
important to consider teacher attitudes to mathematics and how these attitudes were
formed. For teachers, attitudes towards mathematics may influence the teaching
methods they adopt in the classroom; therefore, teachers‟ attitudes may have a direct
affect on the development of their student‟s attitudes (Uusimaki, 2004; Wilkins,
2002). For students, attitudes towards mathematics can influence achievement and
engagement in, as well as, enjoyment of mathematics (Chamberlain, 2010; McLeod,
1992). Considering the impact that teachers and teaching has on students and their
learning, understanding the role that teacher attitudes play within educational
contexts is vital. To date, little research has been conducted on practising early
childhood teachers‟ attitudes towards mathematics and the formation of these
attitudes.
2.3 Teacher Attitudes
Teachers are responsible for providing their students with quality educational
experiences, both cognitive and affective, in the mathematical domain: “… high
quality, challenging and accessible mathematics education for 3-6 year-old children
is a vital foundation for future mathematics learning” (NAEYC, 2002, p. 1).
Mathematical foundations are built upon a natural curiosity that children possess for
mathematics, and a surprising amount of knowledge that can naturally develop in
children before they enter formal schooling (Balfanz, 1999; Baroody, Lai, & Mix,
2006; Baroody & Wilkins, 1999; Ginsburg, Cannon, Eisenband, & Pappas, 2002;
NCTM, 2000). Teachers are considered to play a critical role in contributing to
children‟s informal mathematics skills and knowledge developed before entering
formal school settings (Sarama & Clements, 2008). Thus, it is necessary that young
children experience quality teaching at school.
Extensive searches of library catalogues, shelf investigations, and database
searches of ERIC, Proquest, ProQuest Dissertations and Theses, Psychinfo and the
Australasian Digital Theses database revealed scant literature involving the
investigation of practising early years teachers‟ attitudes. Many articles imply the
significant impact of teacher attitudes on teaching and learning, within their
introductions and conclusions (e.g., Brown, McNamara, Hanley, & Jones, 1999;
Philippou & Christou, 1998; Quinn, 1997; Trujillo & Hadfield, 1999). However,
13
only one of the studies investigated the formation of teacher attitudes, thus
highlighting a critical gap in the literature. The other projects, however, do not
provide evidence to support these claims especially in their use of preservice teachers
as participants. A small number of studies were found regarding practising teacher
attitudes within the classroom context.
There have been scant studies conducted in the field of mathematics attitudes
using practising teachers as the participant group. Two areas of research have been
identified in the literature, the differing attitudes of early years teachers compared to
teachers in higher grades and the effects of teacher attitudes towards mathematics on
the teaching methods they employ in the classroom.
The first research area pertaining to teachers‟ mathematics attitudes relate to
differences found between the attitudes of early years teachers compared to those of
teachers in higher grades or other teaching fields. King (2006) investigated practising
elementary teachers‟ attitudes towards mathematics and their feelings about how
prepared they were to teach mathematics. Three hundred and forty-nine Kindergarten
to Year 6 teachers from three New York school districts completed the Scale for
measuring attitudes towards mathematics or science (Aiken, 2000). The survey
included an additional thirteen statements about their preparedness to teach
mathematics. The survey used a five point Likert scale (strongly negative, negative,
neutral, positive, strongly positive) to indicate the teachers‟ attitudes towards
mathematics. High scores indicated a positive attitude towards mathematics. The
survey was used to identify teachers‟ mathematics attitudes in relation to four sub-
scales of enjoyment, motivation, importance and preparedness to teach.
Results from King‟s (2006) study showed that as a group the teachers
enjoyed mathematics, felt it was important and were not fearful of it. These results
indicated a high percentage of statements were answered in the positive range. The
survey subscales regarding the teachers‟ preparedness to teach and their motivation
to learn more scored lower than the subscales relating to enjoyment and importance
but were still not low enough to indicate negative attitudes. When comparing the
results of the early years teachers to the upper primary teachers, King reported that a
greater fear of mathematics was identified amongst the early years teachers. For
teachers, fearing mathematics is also known as mathematics anxiety and is linked to
negative attitudes (Kolstad & Hughes, 1994). Mathematics anxiety is considered to
14
play a role in the development of student and teacher attitudes towards mathematics
(Uusimaki, 2004). King‟s (2006) study provides evidence of the importance of
investigating early years teachers‟ attitudes towards mathematics in order to identify
areas where teachers feel more negative towards the subject. It must be noted,
however, that some of the statements used to collect the data were not trialled but
were simply examined by ten elementary teachers in districts other than those used in
the study. These ten elementary teachers were required to present feedback on the
appropriateness of the questions for the study. Without trialling the instrument and
analysing the psychometrics associated with it, validity can be questioned. Thus, in
this Master‟s study, an instrument with established validity was used to investigate
teacher attitudes (Section 3.3.3.1).
Differences were identified between the attitudes of early years teachers
compared to the attitudes of various other educators within the school in a study
conducted by Kolstad and Hughes (1994). Similar to King (2006), a survey was also
used to gather data relating to the mathematics attitudes of the teachers. They
administered the Mathematics Attitude Test Revised (Dutton & Adams, 1961) to 157
participants teaching in Kindergarten to Year 4, middle school and special education.
Principals, other administrators and individuals working on teacher certification were
also included in the participant group. Kolstad and Hughes (1994) reported that of
the 157 participants, 38.2% had strongly positive attitudes towards mathematics, 34.4%
had neutral attitudes towards mathematics, and 27.4% had strongly negative attitudes
towards mathematics. This shows that the majority of participants had either strongly
positive or neutral attitudes towards mathematics. Importantly, when results were
separated according to the participants‟ teaching area, the Kindergarten to Year 4
group recorded the highest percentage of strongly negative attitudes, being 34.0%,
compared to 25.0% for special education teachers and 10.0% for middle school
teachers. This finding indicated that, as a cohort, the Kindergarten to Year 4 teachers
from this school had more negative attitudes compared to educators in other areas of
the school. Similar to the study conducted by King (2006), Kolstad and Hughes‟
(1994) results suggest that investigating the attitudes of early years teachers is
worthwhile due to the more negative attitudes held by this cohort compared to
teachers of older children.
15
In addition, early years teachers were found to have more negative attitudes
towards mathematics compared to the attitudes of teachers in higher grades, in a
study conducted by Wilkins (2002). A group of 407 American elementary teachers
from the same district completed surveys that gathered data relating to mathematical
content knowledge, attitude towards mathematics, beliefs about effective
mathematics instruction, instructional practices and background information. Wilkins
(2002) reported that there was a significant difference between the attitudes of
Kindergarten to Year 2 teachers compared to Year 3 to 5 teachers with the teachers
of lower grades having less positive attitudes to mathematics than teachers in the
higher grades. This finding is consistent with King (2006) and Kolstad and Hughes‟
(1994) studies, further strengthening the argument that early years teachers are a
worthwhile participant group to investigate. Inadequate information was provided in
this study about the instrumentation. The attitude survey was unnamed as were the
two instruments which used Likert scales to measure attitude towards mathematics
and beliefs about the importance of particular teaching methods for effective
mathematics instruction. Therefore, the results must be considered with some caution
as validity and reliability cannot be assured.
In contrast to the above three studies, Thiel (2010) found that the
Kindergarten teachers participating in his study had mostly positive attitudes towards
mathematics. The question of whether Kindergarten teachers feel open or reluctant
towards mathematics was investigated through a ten statement questionnaire created
by the author. This was administered to 110 German Kindergarten teachers. Being
more open to mathematics indicated a positive attitude and a willingness to engage in
mathematics as opposed to being reluctant which indicated a negative attitude
towards mathematics and a reluctance to engage in mathematics. Overall, the
teachers were found to be more open than reluctant towards mathematics indicating
the cohort had positive attitudes towards mathematics. These results compared to
King (2006), Kolstad and Hughes (1994), and Wilkins (2002) offer an indication that
the attitudes amongst early year teachers can vary. It must be noted, however, that
the method of data collection used in this study was also questionable. The
instrument‟s internal consistency reliability was .71 with a reliability of only .58.
Results, therefore, must be considered with caution as items that propose to measure
the same construct may not. Instrumentation with greater consistency and reliability
16
may produce different results. Investigating the attitudes of these teachers further
would provide greater understanding of early years teachers‟ attitudes towards
mathematics. Hence, the focus of this study will be to investigate early years teachers‟
attitudes and the formation of attitudes towards mathematics in order to build a more
in-depth knowledge.
The second area identified in the literature relates to the effects of teacher
attitudes towards mathematics on their teaching and teaching methods. Along with
identifying more negative attitudes amongst the early years teachers participating in
the study, Wilkins (2002) also found that positive attitudes had a significant effect on
teaching methods chosen by teachers. Wilkins‟ (2002) results suggest that teachers
with positive attitudes were more likely to believe in the effectiveness of reform-
oriented instruction and use it in their classroom as opposed to teachers with high
content knowledge who were less likely to believe in the effectiveness of reform-
oriented instruction. Hence, positive attitude rather than content knowledge is
associated with the use of effective teaching strategies. This finding highlights the
importance of research within the affective domain, in particular attitude research.
Interestingly, an analysis of the results from the Wilkins‟ (2002) survey which
identified content knowledge and beliefs about effective instruction, showed that
teachers tended to teach as they were taught themselves, thereby, showing the
intergenerational impact of teaching approaches. Similar results have been found in
other studies (Ball, Lubienski, & Mewborn, 2001; Brown, McNamara, Hanley, &
Jones, 1999; Middleton, 1992), highlighting the impact of teachers and teaching
methods on students. This occurrence can be cyclical because some students will
later become teachers with already formed attitudes.
Although mathematics attitudes were identified as playing a role in the types
of teaching methods employed by teachers in Wilkins‟ (2002) study, Lacefield (1999)
reported a weak relationship between teacher attitudes towards mathematics
instruction and the implementation of teaching methods. While this study
investigated teacher attitude towards mathematics, it differs from Wilkins (2002) in
that it was the teachers‟ attitude towards mathematics instruction, rather than general
attitude towards mathematics, that was investigated. In Lacefield‟s (1999) study, 90
American Kindergarten to Year 4 teachers completed two surveys using Likert scales.
The first unnamed survey administered consisted of statements regarding attitude
17
towards the teaching of mathematics. It was based on a survey by Nisbet (1991) as
well as the Fennema Sherman Mathematics Attitude Scale (Fennema & Sherman,
1976) and teachers responded to each statement on a five-point Likert scale (strongly
agree, agree, undecided, disagree, strongly disagree). A high score would suggest a
positive attitude towards teaching mathematics and a low score the converse.
Lacefield‟s (1999) survey consisted of a list of teaching methods which the teachers
had to record the frequency with which they used each method (daily, frequently,
occasionally, seldom, never). The traditional approaches listed in this survey
included teacher-focused lectures, teacher-focused demonstration on the chalkboard,
teacher-focused demonstration on overhead projector, teacher-led question and
answer session with students and skills practice with flash cards. Contemporary
teaching methods included real-life problem solving, hands-on activities and the use
of manipulatives.
The results of Lacefield‟s (1999) study suggested a very weak and
inconsistent correlation between attitudes towards mathematics and the frequency
with which teachers planned and implemented particular teaching methods. Lacefield
suggested that inconsistencies in the relationship between a teacher‟s attitude
towards teaching mathematics and how they taught implied that elementary teachers‟
attitudes towards mathematics instruction might not always determine the teaching
method they implemented. Additionally, the teaching methods chosen by teachers do
not always match their attitudes towards mathematics instruction. It must be noted,
however, that similar to the study conducted by Thiel (2010), the instrumentation
used did not have strong internal consistency reliability and that instruments having
stronger levels might produce different results. This study highlights the importance
of collecting multiple sets of data in order to provide a full picture of the topic being
investigated. The second questionnaire conducted by Lacefield (1999) strengthened
the results by elaborating on the data collected from the first questionnaire. Further
investigation revealed participant‟s attitudes towards teaching mathematics differed
from what they actually implemented. Thus, further investigation identified the
discrepancies between articulated and implemented classroom practice. For this
reason, this Master‟s study employed the use of open-ended interviews to elaborate
on survey results, hence, providing a more comprehensive view of teacher attitudes
and attitude formation.
18
In conclusion, the literature review has identified a lack of research
investigating the attitudes of practising teachers. Along with identifying teachers‟
attitudes towards mathematics amongst different cohorts of teachers, the other area
covered in the associated literature relates to the effects of teacher mathematics
attitudes on their teaching and teaching methods employed.
The literature review provided guidance on four points for a study of
practising teachers‟ attitudes towards mathematics. First, early childhood teachers are
a population of interest because various studies report they have more negative
attitudes to mathematics than teachers in higher grades (Kolstad & Hughes, 1994;
Wilkins, 2002). Second, the instrumentation used in the investigation should be
highly credible and clearly identified in all reporting due to a concern with the
instrumentation in other studies of teacher attitudes (King, 2005; Wilkins, 2002).
Third, the use of two forms of data collection, namely a survey and interviews
provide a greater depth to the results. Finally, there is a paucity of studies on the
attitudes of practising teachers with no studies identified on how these attitudes form.
Whilst investigating teacher attitudes towards mathematics is vital, identifying
factors which contribute to attitude formation, is equally important.
2.4 Student Attitudes
Student attitudes play a central role in mathematics learning and achievement
(McLeod, 1992). A student‟s attitude towards mathematics can have a positive or
negative effect on their learning. This means that a student‟s attitude could be the
critical factor behind his or her success or failure within the subject. Students may
develop either positive or negative attitudes towards mathematics during their
education experiences. Positive attitudes form the basis for optimism. Optimism is
the assignment of favourable interpretations to actions and events (Gillham, Shatté,
Reivich, & Seligman, 2001). For students, optimism can present itself as persistence.
If failure is encountered, an optimistic student is more likely to be able to rationalise
the event. Instead of becoming depressed and helpless, the student, if optimistic, is
more likely to demonstrate resilience and try again. Optimistic children do not
generalise bad experiences across to other related areas, but see the bad experiences
as limited to the particular case (Seligman, 1998). Through persistence, optimistic
children are more likely to remain engaged in learning episodes and this engagement
19
will assist in achievement (Wigfield, 1994). In contrast, negative attitudes can
enhance maths-anxiety (Trujillo & Hadfield, 1999). Feelings of anxiety can lead to
panic, helplessness, fear, sweaty palms, nervous stomach, and loss of ability to
concentrate. Any one of these physical effects may contribute to poor student
outcomes and achievement in mathematics.
Student attitudes have been linked to achievement (e.g., Ma, 1997). However,
the nature of the relationship between attitudes and achievement continues to be
debated. A review of current literature identifies two conflicting thoughts
surrounding the link between positive student attitudes and student achievement.
Studies using participants from western countries report a link between positive
attitudes and achievement (Iben, 1991; Ma, 1997; Ma & Kishor, 1997; Tocci &
Engelhard, 1991). However, where studies were conducted in Asia or where Asian
students were selected as participants, the results indicated that positive attitudes
were not always present in students with high achievement scores (Leung, 2002;
Stevenson, Chen, & Lee, 1993). While student achievement does not always
correlate with a positive attitude, Wilson (2008) recommends that fostering positive
attitudes can have long-term effects. Wilson argues that positive attitudes will assist
in producing numerate members of society through engagement with mathematics at
school. Others agree that it is particularly important to foster positive attitudes in
mathematics because positive attitudes will allow students to engage in mathematics
productively, instead of eliciting feelings of anxiety during mathematics time
(Cornell, 1999; Ruffell, Mason, & Allen, 1998; Wilson, 2008). Investigating attitude
formation, therefore, will provide valuable knowledge as to the factors contributing
to the development of both positive and negative attitudes. This understanding of
teachers‟ attitude formation is important due to the influences that teaching methods
have on student attitudes.
Student attitudes are influenced by the teaching methods their teachers
employ in the classroom (Duatepe-Paksu & Ubuz, 2009; Stipek, Salmon, Givvin, &
Kazemi, 1998). A teaching method can be characterised as a set of principles,
procedures or strategies which teachers implement to achieve desired learning in
students. Teachers choose teaching methods according to a theory of learning and the
nature of the subject matter needed to be taught (Westwood, 2008). Findings of two
20
studies support the notion that teachers and teaching methods contribute to student
attitude formation.
The benefits of particular teaching methods on student attitudes and
achievement have also been reported by Duatepe-Paksu and Ubuz (2009). The
mathematics instruction they investigated was drama-based. This type of instruction
is an integration of mental and physical activity in which children were taught
through imagining real-life experiences (Erdogan & Baran, 2009). In Duatepe-Paksu
and Ubuz‟s (2009) study, 102 seventh-grade students from a public school in Turkey
were engaged in either a drama-based instruction or non drama-based instruction.
Two classes experienced drama-based instruction and a third class was the control
group. Five tests and an interview were conducted at various times throughout the
study. Prior to exposure to either forms of instruction, the students completed the
Van Hiele Geometric Thinking Levels Test (Van Hiele, 1986), the Geometric Attitude
Scale (Duatepe & Ubuz, 2007) and the Mathematics Attitude Scale (Askar, 1986). At
the end of the instructional period, the students completed these tests again along
with the Angles and Polygons Achievement Test and the Circle and Cylinder
Achievement Test (Duatepe-Paksu & Ubuz, 2009). Interviews were conducted with
thirteen of the participants who also received the drama-based instruction at the end
of the instruction period. The results showed that the drama-based instruction had a
significant effect on students‟ achievement compared to results from the control
group. Also, students‟ attitudes towards geometry and mathematics in general
significantly improved through the use of drama-based instruction.
Positive student emotions were fostered through a particular teaching
method in a study conducted by Stipek et al. (1998). Although attitudes were not the
direct focus of Stipek et al.‟s (1998) research, teachers were identified as playing a
role in their students‟ affective responses to learning fractions. As mentioned earlier,
the affective domain encompasses attitude and the emotional responses that influence
learning (McLeod, 1992). Hence, these results strengthen the claim that teachers and
teaching methods may influence affective variables related to student learning.
Twenty-four fourth, fifth and sixth grade teachers participated in the study
together with their students. The classes were divided into three groups, two groups
with teachers committed to implementing reform-based mathematics instructional
practices and a program named „Seeing Fractions‟. Reform-based mathematics
21
instruction recognises the importance of encouraging the development of a range of
processes, such as problem solving, reasoning and proof, communication, and
reflection (Bobis & Anderson, 2006). Group One, who were committed to
implementing reform-based instruction, received intensive reform-oriented
intervention throughout the year to assist in their implementation of the program and
practices. Group Two also committed to teaching reform-based mathematics, simply
implemented the reform-based mathematics instructional practices without guidance.
Group Three, not committed to implementing reform-based mathematics, used
traditional teaching methods and textbooks. Teaching data were collected through
videotapes, field notes and a questionnaire. Student data were collected through pre
and post questionnaires, videotapes and pre and post fractions tests. The results
indicated that students who received the reform-oriented mathematics teaching
practices (Group One) had positive emotions towards mathematics learning as well
as showing an improvement with their fractions knowledge. In contrast, students
from the class whose teachers used traditional teaching methods (Group Three)
showed more negative and fewer positive emotions than children in reform-oriented
classes (Groups One and Two). This study contributes to the argument that teaching
methods can significantly affect students‟ emotional responses towards mathematics.
In conclusion, recent research findings indicate that attitudes and the affective
domain play a vital role in the learning and achievement in mathematics for students
which can lead to positive interactions and experiences in the subject. These
interactions and experiences lay the foundations for attitudes towards mathematics
that may be carried by individuals through their education and into teaching careers.
Hence, by investigating how teacher attitudes are formed, experiences that lead to
positive and negative attitudes can be identified. This information can inform future
professional development for teachers. In addition to previous research identifying
the impact of attitudes on students‟ learning and achievement, current curriculum
documents outline the importance of mathematics in the early years. The following
sections outline influential documents on an international level (Section 2.4.1),
national level (Section 2.4.2) and state level (Section 2.4.3).
2.4.1 Attitudes and early years mathematics internationally
Internationally the importance of early years mathematics to children‟s future life
options has been recognised. Influential documents that espouse the importance of
22
early mathematical experiences and learning are Principles and standards for school
mathematics (NCTM, 2000) and a collaborative document Early childhood
mathematics: Promoting good beginnings (NAEYC, 2008; NCTM, 2000). Although
these documents originated in the USA, they influence mathematics education in
Australia.
The Principles and standards for school mathematics (NCTM, 2000)
establishes guidelines for mathematics teaching and learning and consider broad
issues such as equity, assessment and technology. In relation to children‟s attitudes to
mathematics, they suggest that solid mathematical foundations developed during the
early years of schooling are essential for all children. Further, this document
acknowledges that beliefs about mathematics and attitudes towards mathematics
form during these early years. Potentially the attitudes students develop towards
mathematics in the early years impact upon the way that they will interact with the
subject for many years to come. Hence, it is vital to investigate how teachers
influence students‟ attitude formation specific to mathematics. The first step in this
process is to understand early years teachers‟ attitudes to mathematics and how their
attitudes formed.
Similarly, the position statement on early childhood mathematics titled Early
childhood mathematics: Promoting good beginnings (NAEYC & NCTM, 2002) also
endorses the viewpoint that mathematics education for 3- to 6- year-olds should
provide a foundation for future mathematics learning and must be high quality,
challenging and accessible. The position statement discusses the inclusion of the pre-
kindergarten year into the Principles and standards for school mathematics (NCTM,
2000). They argue that the reason behind the inclusion was the increasing evidence
of the importance of early years‟ experiences on mathematics learning and children‟s
attitude to mathematics. Further, positive teacher attitudes are advocated due to the
impact that attitudes have on teaching preparation and effective teaching as stated by
NAEYC and NCTM, 2002:
23
Essential as this knowledge is, it can be brought to life only when teachers
themselves have positive attitudes about mathematics. Lack of appropriate
preparation may cause both preservice and experienced teachers to fail to see
mathematics as a priority for young children and to lack confidence in their
ability to teach mathematics effectively. Thus, both preservice education and
continuing professional development experiences need to place greater
emphasis on encouraging teachers‟ own enjoyment and confidence, building
positive mathematical attitudes and dispositions. (p. 14)
The recognition of the effect of both teachers‟ and students‟ attitudes to mathematics
justifies research with a focus on teacher attitude formation.
2.4.2 Attitudes and early years mathematics nationally
At a national level, the Australian federal Government educational agenda is
focussed on the quality of our education system. In 2008, the then Prime Minister,
Kevin Rudd and the then Deputy Prime Minister, Julia Gillard launched the
document Quality education: The case for an education revolution in our schools
(Department of Education, Employment and Workplace Relations (DEEWR), 2008).
Within this document, it is stated that economic and individual potential for all
Australians is developed through schooling. The document suggests, “The basic
numeracy skills developed in school provide the necessary foundation for developing
higher order skills that contribute to a more productive workforce” (DEWEER, 2008,
p. 15). Currently, a national curriculum is being developed by the Australian
Curriculum, Assessment and Reporting Authority (ACARA) (2009). The national
curriculum will include specific content detailing what teachers will be expected to
teach and what students will be expected to learn. Achievement standards will also
be articulated in the curriculum coupled with annotated student work samples and
reporting frameworks (ACARA), 2009).
The early years of schooling are a critical period for the development of
important foundations for mathematical learning. This viewpoint is also expressed by
the Australian Association of Mathematics Teachers (AAMT) (2006). This
association provides support for teachers regarding the teaching and learning of
mathematics. It recognises that many preservice teachers will need support to “build
positive views of mathematics and themselves as users and doers of mathematics”
24
(2006, p. 3). This could be because of the large number of preservice teachers
entering university with negative views and attitudes towards mathematics
(Philippou & Christou, 1998). Therefore, the attitudes of practising early years
teachers are important.
2.4.3 Attitudes and early years mathematics in Queensland
At a state level, two documents created by the Queensland Studies Authority (QSA)
(2006) influence early childhood mathematics. These are the Early Years Curriculum
Guidelines (EYCG) (QSA, 2006) and the Essential Learnings (QSA, 2007). The
EYCG focuses on a framework for teachers to follow in order to achieve desired
learning outcomes for students in the preparatory year of schooling. „Early
mathematical understandings‟ is included as an early learning area within the EYCG
(2006) with a focus on early mathematics skills. These skills lead into Essential
Learnings (QSA, 2007) for mathematics. The inclusion of mathematics in the EYCG
(QSA, 2006) is consistent with the research on the importance of early years
mathematics for later success in school (Wilson, 2008).
The Essential Learnings (QSA, 2007) provides teachers with directions as to
content that is required to be taught. It covers key learning areas for children in
school and includes mathematics. It also documents the expected learning outcomes
for students by the end of Year Three. Supporting documents like the Scope and
sequence guide (QSA, 2008) have been developed to explicitly identify outcomes at
each year from prep onwards, highlighting the importance of mathematics learning
from the first year of formal schooling.
Thus, in Queensland, nationally and internationally, policy and curriculum
documents highlight the importance of mathematics for children in the early years.
Within these documents, the influence of mathematics on children‟s future
mathematics learning is emphasised. Likewise the relationship between children‟s
mathematical competencies and the economic growth of our communities is
highlighted. Whilst research on practising teachers‟ attitudes to mathematics is scant,
considerable research attention has been given to preservice teachers in an attempt to
identify major contributing factors to the formation of their attitudes towards
mathematics.
25
2.5 Preservice Teachers’ Attitudes to Mathematics
Preservice teachers‟ attitudes towards mathematics have been investigated in
numerous studies (Bobis & Cusworth, 1994; Brown et al., 1999; Meyer, 1980;
Trujillo & Hadfield, 1999). These studies identified the effects of education
experiences on attitude formation (Section 2.5.1) and investigated the effectiveness
of preservice teacher education on attitudes towards mathematics (Section 2.5.2).
2.5.1 The effects of education experiences on attitude formation
Considerable research attention has been directed towards preservice teachers in an
attempt to identify major contributing factors to the formation of their attitudes
towards mathematics (Brown et al., 1999; Meyer, 1980; Trujillo & Hadfield, 1999).
Results from these studies have revealed one reoccurring theme, that is, past
educational experiences have a major effect on the formation of attitudes towards
mathematics. Results from three studies over the past three decades report findings
that support this viewpoint.
Teachers‟ past educational experiences were found to be the major
contributing factor to the development of their attitudes towards mathematics in a
study conducted by Meyer (1980). An attitude questionnaire consisting of two open-
ended questions was administered to 120 preservice teachers. The purpose of the
study was to investigate the types of attitudes existing amongst the teachers as well
as the factors they believe contributed to the formation of their attitudes. The
questions How do you feel about mathematics in general? and What do you think
accounts for your particular feelings towards mathematics? were asked with
respondents recording short answers in response. Meyer reported that there was no
significant difference in the number of teachers who liked mathematics (positive
attitude) to those who disliked mathematics (negative attitude). Interestingly, when
comparing the answers to the second question between the preservice teachers who
had positive attitudes to those who had negative attitudes, the factor which most
teachers from both groups reported influenced the formation of their attitude was the
teachers they had had at school. This finding indicated that for this participant group,
teachers influenced the formation of both negative and positive attitudes. Two
interesting findings were reported in this study. First, that teachers have a clear
impact on attitude formation in students and experiences with teachers in schooling
26
are carried through to adulthood. Second, there were similarities between the answers
provided by the preservice teachers with positive and negative attitudes with each
group reporting the influence of teachers on their attitudes. However, the sole use of
a questionnaire, a single method of data collection, did not allow for elaboration on
answers such as when the attitudes formed or what specific experiences with teachers
contributed to their attitude formation.
Similar findings were reported in a study by Brown, McNamara, Hanley, and
Jones (1999). Sixteen of the 20 preservice teachers interviewed reported having
negative experiences at school. The teachers believed that these experiences were
major contributing factors to the formation of their attitudes. Three semi-structured
interviews were used to track how preservice teachers conceptualised mathematics
and its teaching as they progressed through an initial training course. The first
interview obtained information regarding the preservice teachers‟ history with
mathematics, beliefs about mathematics, their college and school experiences and
perceptions of their future tasks as mathematics teachers. The second interview was
coupled with a lesson observation and was used to identify the participants‟
understanding of mathematics. The third interview required participants to discuss
their perceptions of any changes that had occurred over the year-long study in
relation to their mathematical knowledge and attitudes. It was through the first
interview that teachers and education experiences were noted as contributing to the
formation of their attitudes. The preservice teachers recalled specific encounters with
mathematics along with feelings attached to those experiences. Hence, investigating
the formation of teacher attitudes through qualitative methods of data collection is
necessary in identifying the types of experiences which influence attitude formation.
Brown et al.‟s (1999) implementation of this qualitative approach enabled the
tracking of participants‟ understanding of mathematics and its relationship to
teaching. This project shows the value of qualitative data within this topic area,
hence qualitative data collection is pivotal in this research project.
Educational experiences were found to be a major contributing factor to
preservice teachers‟ negative attitudes towards mathematics in a study conducted by
Trujillo and Hadfield (1999). In contrast to the single methods of data collection used
by Meyer (1980) and Brown et al. (1999), Trujillo and Hadfield (1999) used a multi-
method design incorporating surveys and interviews to investigate factors
27
contributing to preservice teachers‟ maths-anxiety. First, they administered an
attitudinal questionnaire named the Revised Mathematics Anxiety Rating Scale
(RMARS) (Plake & Parker, 1982) to 50 American preservice primary teachers. The
results from this questionnaire were used to identify five participants to interview.
The selected participants were those showing the highest levels of anxiety from the
survey results. Each of Trujillo and Hadfield‟s (1999) participants identified past
education experiences as a contributing factor to their mathematics anxiety and
negative attitudes towards the teaching and learning of mathematics. The personal
accounts recorded during the interviews revealed negative experiences relating to
teaching methods, where teachers were seen to rush through content, teach in a rigid,
traditional manner and were insecure in their content knowledge. This study revealed
the value of using qualitative and quantitative methods for data collection. A greater
understanding of variables affecting attitude formation was gained from a
combination of the survey, which revealed levels of mathematics anxiety, and the
interviews which provided an elaboration on the role of past education experiences
on the development of negative attitudes towards mathematics. This study adopts a
similar mix of data collection methods to obtain a comprehensive view of teachers‟
mathematical attitudes and their perspectives on how they were developed (see
Section 3.2).
2.5.2 Addressing preservice teacher attitudes towards
mathematics
To date, a number of studies have focussed on addressing preservice teacher attitudes
towards mathematics (Philippou & Christou, 1998; Putney & Cass, 1998; Robinson
& Adkins, 2002; Schackow, 2005). Evidence suggests that there are a significant
number of preservice teachers entering tertiary education with negative attitudes
towards mathematics. This is a concern because of the cycle of negativity which
seems to pass from teacher to student (Uusimaki, 2004). It should not be interpreted
that commencing teachers purposefully transfer negative attitudes towards
mathematics to their students. They might be unaware of the impact their attitudes
have on their students. However, there is a need to break this cycle to avoid future
students developing negative attitudes. Issues addressed in studies investigating the
effectiveness of preservice teacher education include improving attitudes towards
28
mathematics (Philippou & Christou, 1998; Putney & Cass, 1998; Robinson &
Adkins, 2002; Schackow, 2005) and improving mathematical understandings (Amato,
2004).
Preservice education can contribute positively to attitude development in
mathematics. Philippou and Christou (1998) reported that the mathematics attitudes
of 128 Cyprian preservice teachers showed significant improvement during tertiary
education. The preservice teachers completed a three-year mathematics methods
course based on the history of mathematics, the history of the development of
mathematics concepts and was complimented by the use of hands-on experiences
throughout. The majority of preservice teachers used in this study entered their
tertiary studies with a negative attitude. The mathematics attitudes of a large number
of these teachers were found to have been impacted upon positively through the
history lessons and hands-on activities.
Similarly, Putney and Cass (1998) found that teachers who engaged in a
variety of hands-on mathematics activities and reflection of these activities had
positive changes to their attitudes towards mathematics. Survey results and journal
entries were used with 150 American preservice teachers to monitor changes in their
attitudes. The positive changes occurred following engagement in a variety of hands-
on mathematics activities and reflection of these activities. These activities were
modelled to preservice teachers as they were expected to teach them within their own
classrooms. The same method of teaching mathematics content was used by
Schackow (2005). She administered a revised Attitude towards mathematics
inventory to 33 American preservice teachers at the beginning and end of a hands-on
constructivist mathematics methods course. She found that as a whole, participants
showed significant positive changes in their attitude. Another positive finding was
reported by Robinson and Adkins (2002) in a survey study of 35 preservice teachers
They found that the use of experience-based activities including a hands-on and
manipulative focus, impacted positively on the negative attitudes of the preservice
teachers. Interestingly, in the section of the study which asked participants to identify
how they believe their attitude formed, 54.0% of the group recorded previous
experiences with teachers as the major contributing factor.
The studies discussed above have shown that negative attitudes towards
mathematics amongst preservice teachers are widespread. Importantly, they also
29
showed the benefits and effectiveness of mathematics methods courses in changing
these attitudes. Without intervention, many of these teachers would have entered the
workforce with negative attitudes. These negative attitudes may have affected their
teaching and ultimately influenced their students‟ attitudes.
However, not all preservice teachers‟ attitudes towards mathematics
improved during their preservice education. Additionally, if improvement occurred,
it differed between cohorts. Quinn (1997) reported on varying results found through
the implementation of a mathematics methods course with American preservice
teachers enrolled in either an elementary course or a secondary course. These courses
used manipulatives, technology and co-operative learning to teach mathematics
content. At the conclusion of the courses, the 29 preservice elementary teachers were
found to have significantly improved attitudes towards mathematics as well as
improved content knowledge. While the 18 preservice secondary teachers had
increases in both their attitudes towards mathematics and their content knowledge,
these increases were not significant. Thus, studies of teacher attitudes need to focus
on specific cohorts of teachers because the results are not consistent across cohorts.
A plausible reason for the difference between these two groups is that the secondary
teachers began the course with higher scores regarding mathematics content
knowledge, and therefore, had less content knowledge to learn.
More recently, Charalambous, Panaoura and Philippou (2009) surveyed and
interviewed 94 preservice teachers from Cyprus in order to identify the effects of a
mathematics subject based on building the teachers‟ historical understandings of
mathematics. The preservice teachers who participated in this study were enrolled in
an elementary teaching course. In contrast to the work by Philippou and Christou
(1998) and Quinn (1997), the university subject did not include the use of any
activities or reflection. As a result, the participants were found to have increased
negative attitudes towards mathematics, citing the lack of hands-on activities, time to
experiment and less focus on subject matter as reasons for the decrease. Hence,
tertiary subjects which do not include the use of hands-on, exploratory methods of
teaching, appear to affect preservice teacher attitudes negatively.
The mathematical understandings of preservice teachers were improved in a
study conducted by Amato (2004); however, no significant change was reported in
relation to the teachers‟ liking of mathematics. Amato (2004) used four data
30
collection instruments to monitor the effects of the course including a diary, pre and
post questionnaires, middle and end of semester interviews and pre and post
mathematics content tests. The research was conducted over two semesters and the
participants for each semester were 20 and 45 respectively. With regard to improving
mathematical understandings, the participants reported that the use of children‟s
activities during the course was valuable. However, improvements in teachers‟ liking
of mathematics had mixed results. Many preservice teachers reported no change to
their attitudes. It is unclear whether the teachers reporting no change began with
positive or negative attitudes. These findings suggest that for these preservice
teachers, the mathematics methods courses they undertook incorporating methods
they are expected to use in the classroom, were effective in improving their
mathematical understandings. These courses did not, however, significantly improve
their attitudes towards mathematics.
Studies addressing the improvement of preservice teachers‟ attitudes towards
mathematics found the method of teaching used to educate preservice teachers was
worth noting. Teaching strategies which are considered to facilitate positive attitudes
in students are being adopted in many mathematics methods courses in order to
model these effective strategies (Amato, 2004; Putney & Cass, 1998) and are
producing positive attitudes with preservice teachers. A prevailing teaching method
throughout many of the studies reported as having a positive effect in mathematics
methods courses is that of using a hands-on approach to teaching the content (Amato,
2004; Philippou & Christou, 1998; Putney & Cass, 1998; Quinn, 1997; Schackow,
2005). The field of mathematics research has not been alone in reporting the impact
of educational experiences on attitude formation and the effectiveness of preservice
teacher education. Previous studies investigating preservice teacher attitudes towards
science have reported similar findings.
2.6 Preservice Teacher Attitudes Towards Science
Not only have attitudes been investigated in the field of mathematics but much
research has also been conducted surrounding attitudes and attitude formation in the
field of science also. As with mathematics, science methods courses have been
implemented in an attempt to change preservice teacher attitudes before they enter
the classroom. Four studies which investigated the effects of science methods
31
courses were that of Kelly (2000), McDevitt, Heikkinen, Alcorn, Ambrosio, and
Gardner (1993), Palmer (2002) and Pedersen and McCurdy (1992). Similarities
between these and studies investigating the effects of mathematics methods courses
(e.g., Putney & Cass, 1998; Robinson & Adkins, 2002) include the use of surveys to
identify any changes to preservice teachers‟ attitudes.
Studies conducted by Kelly (2000), McDevitt et al. (1993), Palmer (2002)
and Pedersen and McCurdy (1992) reported a positive change in participants‟
attitudes towards science at conclusion of the university course. This finding is
similar to results found in studies investigating mathematics methods courses.
Further, as found in the mathematics attitude studies of Amato (2004), Philippou and
Christou (1998), Putney and Cass (1998), Quinn (1997), and Schackow (2005), a
study conducted by Stefanich and Kelsey (1989) showed the benefits of
implementing a science methods course which employed a practical, hands-on
approach. Students in this course showed more positive attitudes to science as
opposed to students in courses with lecture formats.
Similar to research conducted on attitudes towards mathematics, studies of
preservice elementary teachers reveal that negative attitudes towards science develop
as a result of their own educational experiences (Jasalavich, 1992; Mullholland &
Wallace, 1996; Talsma, 1996). Hence, both attitudes towards mathematics and
science are developed through experiences at school. The similarities between the
results reported in the literature relating to teacher attitudes towards mathematics and
teacher attitudes towards science are overwhelming. This similarity highlights the
critical role of attitudes within the teaching and learning context. Further, findings
from attitude research suggest that the attitudes which teachers develop through
education experiences may cycle back into the classroom via students who go on to
become teachers.
2.7 The Cycle of Teacher Attitudes
Within the context of schooling, the perspective that attitudes are formed through
experiences is of great importance because the attitudes that individuals form when
they are young can persist throughout formal schooling and into adulthood (Eagly &
Chaiken, 1993). Thus, for a teacher, the formation of attitudes is cyclic (Uusimaki,
2004). Their own attitudes were shaped by their educational experiences, including
32
their early years of schooling, their subsequent school education, and in adulthood,
through their teacher education and careers. In turn, their attitudes then shape their
students‟ attitudes and the cycle continues.
The discussion of studies focussing on teacher (Section 2.3) and preservice
teacher (Section 2.6) attitudes show a cycle linking teacher attitudes, teacher
behaviour and student attitudes and achievement (see Figure 2.2). What is known is
that teacher attitudes impact on teaching methods employed by teachers in the
classroom (Uusimaki, 2004; Wilkins, 2002) which in turn results in positive or
negative student attitudes. These attitudes have flow-on effects either positively
through persistence and engagement (Wigfield, 1994) or negatively through maths-
anxiety (Trujillo & Hadfield, 1999). Ultimately, some school students become
teachers with negative attitudes towards mathematics.
It is also known that different cohorts of teachers have different attitudes
towards mathematics (King, 2005; Kolstad & Hughes, 1994). To understand early
childhood teachers‟ attitudes to mathematics, there is a need to focus on early years
teachers as a cohort. Both their current attitudes and the formation of these attitudes
needs to be explored to establish what attitudes they hold and what influenced the
formation of these attitudes. In studies of preservice teachers, the identification of the
influences on the formation of their attitudes was used to inform preservice
instruction with improved outcomes for particular types of courses (e.g., Philippou &
Christou, 1998; Putney & Cass, 1998; Quinn, 1997; Schackow, 2005). Similarly, it is
expected that once the factors influencing practising teachers‟ attitudes towards
mathematics are identified, strategic support could be provided for teachers with
negative attitudes to break the cycle of negativity.
Figure 2.2 visually represents the preliminary cycle of teacher attitudes
derived from the literature. This cycle shows how student attitudes influence
attitudes in adulthood which for teachers then impact on their students. Teacher
attitudes impact upon their teaching behaviours and teaching methods (Uusimaki,
2004; Wilkins, 2002). This in turn impacts upon their students‟ attitudes. If positive
attitudes are fostered, the student is more likely to develop persistence and remain
engaged with the subject. This can then lead to high achievement. This positive
attitude may remain with the student, who goes on to become a teacher, and carry
through into their career. Conversely, if a student develops a negative attitude, they
33
may experience maths-anxiety, which can lead to low achievement. At this point,
without intervention, it is the attitude that this student exits school with that they
may potentially carry through with them into their own classroom. This final
scenario is of greatest concern because teachers influence numerous children over
their careers. However, research into teacher attitudes can inform preservice teacher
education and professional development for practising teachers. Further, identifying
the attitudes of practising teachers will provide them with vital information
regarding the impact of their attitudes and the experiences they provide for their
students. According to Trujillo and Hadfield (1999), a critical first step towards a
positive attitude is for an individual to reflect on the origins of their own negative
experiences. They state, “An in-depth look at one‟s own negative prior experiences
can often help to set a more positive direction for future encounters” (p. 223). Hence,
the identification of negative attitudes and the sources of these attitudes are essential.
However, identifying attitudes is not an easy task.
34
Figure 2.2. Preliminary Cycle of Teacher Attitudes Towards Mathematics
35
2.8 Measuring Teachers’ Attitudes
To understand a person‟s attitude, first the attitude must be identified. The most
effective way to achieve this is through the use of an attitude measurement
instrument. Attitudes cannot be directly observed and therefore inferences must be
made using answers given by respondents. The most common way to obtain attitude
responses is through surveys or questionnaires. Generally, data collected in attitude
measurement does not include personal responses but involve statements which have
a numerical value attached to them (Schwarz, 2008). These are referred to as self-
report methods (Albarracin, Johnson, & Zanna, 2005). Researchers commonly adopt
three main self-reporting methods. These are Thurstone‟s equal-appearing intervals
method, Likert‟s method of summated ratings and Osgood, Succi and Tannenbaum‟s
semantic differential (Albarracin, Johnson, & Zanna, 2005). A researcher may
choose to employ an already established measurement instrument or to create their
own. The following outlines the specifics of each method, concluding with the
identification of an attitude measurement instrument for this Master‟s study and the
reasons for choosing it.
Attitude measurement instruments adopting Thurstone‟s method (Eagly &
Chaiken, 1993) are composed of statements relating to a particular issue or topic.
Each statement has a numerical value attached to it. Participants then choose
whether they will only identify the statements they feel unfavourable towards or the
statements they feel favourable towards. Each participant‟s attitude is identified by
calculating the mean of numerical values attached to the statements they have
responded to.
In comparison to Thurstone‟s method, Likert‟s method (Eagly & Chaiken,
1993) requires participants to rate their degree of agreement or disagreement to each
statement included in the instrument, on a number continuum rather than just
identifying statements they agree with. Each statement has set amount of response
levels or numbers attached to it (e.g., strongly positive, positive, neutral, negative,
strongly negative) and the respondent must choose one for each item. In some cases,
item scores are analysed separately. Alternatively, item scores can be grouped and
therefore the scale can be referred to as a summative scale.
36
Where Thurstone and Likert‟s methods rely on participants responding to
statements, Osgood, Succi and Tannenbaum‟s semantic differential (Eagly &
Chaiken, 1993) presents the participant with a pair of opposite adjectives like hot
and cold. Similar to Likert‟s method however, participants must indicate their
evaluation of the statement along a rating scale. The difference with this method is
that it is anchored by the adjectives rather than numbers.
An important factor in instrument choice for a study is to decide whether to
use an established instrument or to create a new one. Advantages for creating your
own instrument include the fact that it will be tailored to meet the exact needs of
your project. The main disadvantage for creating a new instrument is how labour
intensive instrument creation is and the amount of time needed to run pilot tests to
check for reliability and validity. For the purposes of this Master‟s project, an
already established instrument was chosen to identify the attitudes of teachers, the
Attitude Towards Mathematics Inventory (Schackow, 2005) (see Section 3.3.3.1). It
uses a Likert scale to measure participants‟ attitude and has already been used in
mathematics attitude research.
The ATMI (Schackow, 2005) investigates four underlying dimensions of
attitudes: value, enjoyment, self-confidence and motivation. These dimensions of
attitude have been investigated by other researchers in the last two decades. For
example, Goldin (2002) includes values as a sub-domain of affect: “Values, ethics,
and morals (deeply held preferences, possibly characterized as “personal truths”,
stable, highly affective as well as cognitive, may also be highly structured)” (p. 61).
Enjoyment of an activity or experience, such as mathematics, is associated
with a feeling of satisfaction and therefore a willingness to participate and if
necessary persistence in the development of a skill (King, 2006). Self confidence in
math has also been linked to attitudes, with high math confidence correlating with
low math anxiety (Kloosterman, 1988). Kloosterman asserts that self-confidence and
achievement have a particularly strong relationship in comparison to other affective
variables that influence attitudes and therefore learning. To be successful, students
must find instruction motivating. Therefore, motivation appears to be an important
dimension of attitude (Schiefele & Csikszentmihalyi, 1995). The importance that
students place on subject matter or their interest in what they learn is a force that
drives intrinsic motivation (Schiefele & Csikszentmihalyi, 1995). The four
37
dimensions of attitudes (value, enjoyment, self-confidence and motivation)
underpinning the ATMI (Schackow, 2005) are well documented in the literature
surrounding attitudes and their core components.
2.9 Conclusion
This chapter has highlighted the salient role that educational experiences and
teachers play in the formation of attitudes in young children. The critical role of
attitudes and the affective domain within the context of learning and teaching
mathematics has been identified and the scant and varied nature of research on
practising teachers within this field has been revealed. Further, the importance of
studying early years teachers as a cohort has been indicated. Additionally, a cycle of
teacher attitudes was proposed in which teachers‟ own educational experiences
influence their attitudes and they in turn influence the attitudes of their students.
Thus, a study of practising early years teachers‟ attitudes towards mathematics and
the formation of these attitudes is justified due to the lack of evidence-based
literature on this topic.
38
39
3 Research Design and Methodology
3.1 Chapter Overview
The purpose of this study was to investigate the attitudes of practising early years
teachers towards mathematics and establish how these attitudes were formed.
Specifically, this study investigates the following research questions:
1. What attitudes do practising early years teachers hold towards
mathematics?
2. How did the teachers‟ mathematics attitudes form?
This chapter presents the research design and method used for investigating
the attitudes of practising early years teachers towards mathematics and has four
further sections. The first section presents the research design (Section 3.2). The
second section outlines the research methods chosen for this study including the
research setting, participants, data collection and data analysis (Section 3.3). The
third section addresses the quality and rigour of the study including reliability,
trustworthiness and ethical considerations (Section 3.4). The final section
summarises the chapter (Section 3.5).
3.2 Research Design
Teachers‟ attitudes towards mathematics are a complex social phenomenon that have
been formed and influenced by their educational experiences and achievement.
Hence, this study adopted an explanatory case study design (Yin, 2003) to
investigate practising teachers‟ attitudes towards mathematics and the formation of
these attitudes. Yin (2003) defines explanatory case study as a method used when
„how‟ questions are being posed. Yin (2003) also states that explanatory case studies
can be used “when the investigator has little control over events, and when the focus
is on a contemporary phenomenon within some real-life context” (p. 1). This study
adopted a single-case design as a means of investigating mathematics attitudes and
their formation in practising early years teachers in one school. Hence, this cohort
represents a typical case (Yin, 2009). According to Yin (2003), “The case study is
used in many situations to contribute to our knowledge of individual, group,
40
organizational, social, political, and related phenomena” (p. 1). Merriam (1998)
identifies an advantage of explanatory case studies being the benefits of its reliance
on multiple sources of evidence when drawing conclusions. This method produces a
more holistic account of the phenomenon by illuminating meaning and offering
knowledge. The purpose of this study was to discover early years teachers‟ attitudes
to mathematics and what influenced the formation of their attitudes. Therefore, this
design is appropriate for this study.
This study was conducted in three sequential phases (see Figure 3.1). In
Phase 1, early years teachers were surveyed to establish their attitudes towards
mathematics. The two purposes of this phase were to identify early years teachers‟
range of attitudes to mathematics and to establish a cohort of teachers whose
attitudes could be investigated in depth. Phase 2 consisted of interviewing a smaller
cohort of early years teachers representing a range of attitudes to mathematics
(determined in Phase 1 from survey data) to establish how their attitudes formed.
Phase 3 was the data analysis in which the two sets of data (survey and interview)
were used to respond to the research questions (Section 3.1). The use of multiple
methods of data collection strengthens the study‟s credibility (see Section 3.3.4).
Consistent with explanatory case study design, the outcomes of this study are
presented as a model of a cycle of teacher attitudes (Figure 5.1). A preliminary
model was developed from the literature (Figure 2.2) and elaborated using the results
of this study. Thus, while statistical generalisation would be inappropriate in this
case study due to the convenience sampling described shortly (Section 3.3.2),
analytic generalisability is appropriate (Yin, 1994).
41
Figure 3.1. Phases of the explanatory case study design.
3.3 Research Methods
In this section, four aspects of the research methods are discussed. First, the research
setting is described (Section 3.3.1). Next, participant selection is explained (Section
3.3.2). Data collection methods are then presented (Section 3.3.3). Finally, data
analysis methods employed for the purposes of this study are outlined (Section 3.3.4).
3.3.1 Research setting and researcher
This research took place at Lower Creek School (Pseudonym), a Brisbane southside
public school, approximated 25 km from central Brisbane. The co-educational, state
school was situated in a middle socio-economic area. At the time of the data
collection there were approximately 2000 children enrolled in the school, with
approximately 400 children in the Junior School (Prep to Year 3). Lower Creek
school administration is highly committed to providing its staff with ongoing
professional development. For example, on staff at the school there are facilitators
for three early years mathematics initiatives (First Steps in Number, First Steps in
Measurement, Jump into Number). All early years teachers have attended regular
workshops for each professional development program over the past five years.
PHASE 1 PHASE 3 PHASE 2
Survey instrument
ATMI (Schackow,
2005)
Open-ended
interview Data analysis
Survey
Comparative
analysis
Interview
Pattern
coding
Early years
teachers n=20
Early years
teachers n=6
42
This research setting was chosen for two reasons. First, the setting was a large,
state run school with 22 early years teachers who could be participants. Second, this
site was chosen due to ease of access. Rapport had already been established with the
research cohort, therefore, convenience sampling was used.
The researcher had a professional relationship with staff at Lower Creek
School. She has been a staff member for six years, undertaking roles within the early
years including P-3 mathematics facilitator. This role entailed providing professional
development and support for teachers within the P-3 years. A collegial relationship
existed between the researcher and participants.
3.3.2 Participants
Twenty teachers completed surveys. The participants consisted of 20 early
years teachers employed at Lower Creek School who had agreed to participate from
a total pool of 22 early years teachers. The teachers each completed the Attitude
towards mathematics inventory (Schackow, 2005), providing data identifying the
types of attitudes existing amongst the group (Figure 3.1, Phase 1). Table 3.1 shows
the participants and the teacher education that they received at university. To
investigate the formation of their attitudes towards mathematics, this group of 20
teachers was then narrowed to six teachers who participated in open-ended
interviews (Figure 3.1, Phase 2). The selection of these six teachers is described in
the reporting of the survey results (see Section 4.2.1). Each of the six teachers had
graduated within the last ten years. The interview participants were chosen to ensure
that a diverse range of mathematical attitudes as possible were represented in the data.
However, due to convenience sampling, statistical generalisability would be
inappropriate because these participants might not be representative of the broad
population (Yin, 1994).
43
Table 3.1
Lower Creek teachers’ tertiary training
Teacher Early childhood trained Primary trained
Teacher 1
Teacher 2 (Mary)
Teacher 3 (Bianca)
Teacher 4
Teacher 5
Teacher 6
Teacher 7
Teacher 8
Teacher 9
Teacher 10
Teacher 11
Teacher 12
Teacher 13
Teacher 14
Teacher 15
Teacher 16 (Linda)
Teacher 17 (Yvonne)
Teacher 18 (Lily)
Teacher 19 (Sandra)
Teacher 20
3.3.3 Data collection
Within this explanatory case study design, data were collected in two phases. Phase 1
involved quantitative data collection through the administration of the Attitude
towards mathematics inventory (ATMI) (Schackow, 2005) to 20 early years teachers
(Section 3.3.3.1). Subsequently, Phase 2 involved open-ended interviews with six
teachers with diverse attitudes to mathematics (See Section 3.3.3.2).
3.3.3.1 The attitude survey
In Phase 1, the ATMI (Schackow, 2005) was administered to the participants as a
means of identifying their individual attitudes towards mathematics (see Appendix
44
A). Attitudes cannot be directly observed, though responses or indicators can be used
to infer their existence (Eagly & Chaiken, 1993). Surveys are commonly used in this
instance because they provide participants with statements to consider (Tashakkori &
Teddlie, 1998). The survey results were used to describe trends amongst the
population involved in the study, provide individual opinions on the topic of the
survey (Creswell, 2008; De Vaus, 2002) and to identify a group for Phase 2 of the
research.
This instrument was originally developed by Tapia (1996) for measuring
students‟ attitudes towards mathematics. Shackow‟s (2005) adaptation of the ATMI
provided an appropriate instrument for measuring teachers‟ attitudes towards
mathematics. It contained forty Likert type statements. For each statement, there
were five levels of agreement: strongly agree, agree, neutral, disagree, and strongly
disagree. Each level was assigned a score of one to five, generating a score out of
five for each statement. Out of the 40 statements, 29 used anchors of 1: strongly
disagree, 2: disagree, 3: neutral, 4: agree, and 5: strongly agree. The other 11
statements were reversed items using anchors of 1: strongly agree, 2: agree, 3:
neutral, 4: disagree and 5: strongly disagree. The score is a sum of the ratings, thus,
total scores could range from 40 to 200 (Schackow, 2005).
During its initial testing (Tapia, 1996), subscales were identified within the
inventory through factor analysis. The 40 questions were divided into four subscales:
value, enjoyment, self-confidence and motivation. These subscales were considered
to be underlying dimensions of students‟ attitude towards mathematics. Each
subscale contained a different number of questions. Questions 1 – 10 related to value,
questions 11 – 20 related to enjoyment, questions 21 – 35 related to self-confidence
and questions 36 – 40 related to motivation. Tapia (1996) and Tapia and Marsh (2002)
tested this instrument for internal consistency and construct validity. An alpha
coefficient of .95 was achieved. Schackow (2005) revised Tapia‟s (1996) inventory
for use with preservice teachers rather than students. When Schackow (2005)
administered the ATMI, an alpha coefficient of .98 was found. Alpha coefficients for
each of the four subscales were not reported in Schackow‟s (2005) adaptation of the
instrument for use with pre-service teachers. However, results from the instrument‟s
original development and use with high school and tertiary populations suggest that
the subscales have sound internal consistency. In an undergraduate population, Tapia
45
and Marsh (2000) calculated the Cronbach alpha coefficients as .93 for value, .88 for
enjoyment, .96 for self-confidence and .87 for motivation.
These figures provide evidence of this instrument‟s reliability and therefore
suitability for use in this study. Based on these results, this instrument was employed
in this study. Participants were asked to indicate their degree of agreement with each
statement using a five point Likert scale, from strongly disagree to strongly agree.
The ATMI (Schackow, 2005) survey provided a general picture of the types
of attitudes held by the participants in this study and was used to select participants
for interview. The process of using data for secondary analysis is common to
explanatory case study design (Yin, 2003). Thus, the survey data served a primary
purpose to select participants and a secondary purpose to provide baseline data for
the interviews with the selected participants.
3.3.3.2 Interviews
In Phase 2, open-ended interviews were conducted as a means of elaborating on
responses given through the ATMI (Schackow, 2005). Further, the interviews
assisted in the identification of factors contributing to each teacher‟s attitude
formation. These qualitative interviews were characterised by the conversational
manner in which they were conducted (Rubin & Rubin, 2005). According to Rubin
and Rubin (2005), the interviewing process should have three organisational
components to ensure depth, detail, and vivid answers. These components are: (a) the
main questions, (b) the follow-up questions, and (c) the probes.
The main questions were created from the research topic (Rubin & Rubin, 2005).
The wording of these questions contained terms used in the research questions. The
following open-ended questions were available to guide the conversation with each
participant:
Your results from the ATMI (Tapia, 1996) suggest that you have a
strongly positive/neutral attitude towards mathematics. Can you tell me
more about your attitude to mathematics?
Can you tell me about how or when this attitude formed?
Can you recall specific incidences which might have contributed to the
formation of your attitude towards mathematics?
46
How does your attitude towards mathematics affect your teaching of
mathematics?
Whilst these questions were used as a guide, they were altered or omitted depending
on the progress of the interview (Moustakas, 1994). However, leading questions
were avoided because they would have influenced the responses and the direction in
which the conversation went (Seidman, 2006).
Follow-up questions related directly to what the participant had stated during
the conversation. Answers to follow-up questions provided depth and detail as they
encouraged elaboration and nuance (Rubin & Rubin, 2005). Some of these questions
related back to specific responses given in the ATMI (Shackow, 2005). If a
participant, for instance, answered a follow-up question, with a contradicting
response, additional follow-up questions were used to clarify and expand the
participant‟s response. For example,
Your attitude was identified as positive yet you have recounted
experiences in a negative manner which contradicts your survey
responses. Can you explain the difference between your survey response
and your interview response?
The probes were used to extend the conversation, ensuring that enough
detail and clarification was obtained throughout the conversation. Probes were used
to seek in-depth responses when participants may have responded without detail or
with a general statement. For example,
I noticed that you mentioned particular teaching methods in your
preservice course as contributing to the formation of your attitude
towards mathematics. Can you elaborate further?
Seidman (2006) argues that individual interviews should not be rushed in
order to gather an adequate amount of information from each participant. In
accordance with this, the length of the interview was determined largely by the
participants‟ responses, but on average lasted approximately fifteen minutes. The
interviews were audio recorded and later transcribed.
47
3.3.4 Data analysis
The following sections outline the procedures used in the analysis of the ATMI
(Schackow, 2005) and the interview data. The first section discusses the scoring
protocols used in the analysis of the survey data (Section 3.3.4.1). The second section
outlines how themes were identified within the interview data (Section 3.3.4.2).
3.3.4.1 Analysis of the Attitude Towards Mathematics Inventory
The question of What attitudes do early years teachers hold towards mathematics?
was explored through the ATMI (Schackow, 2005). This survey contains four
attitudinal components: value, enjoyment, self-confidence and motivation (see
3.3.3.1). Consistent with the scoring protocol for this instrument, scores were
calculated for each of the 20 participants on each of these components as well as an
overall attitude score which combined all four components. To allow summation of
attitude components, total scores were calculated. This set of scores informed the
question of What attitudes do early years teachers hold towards mathematics? Five
levels of attitude were created for this Master‟s project using the scores for ease of
attitude identification. These levels were strongly positive, positive, neutral, negative
and strongly negative.
Comparative analysis (Ragin, 1994) was conducted using the survey data. In
this way, similarities and differences were identified within the results. A table (see
Table 4.3) and bar graph (see Figure 4.1) were used to present the findings and
provide a visual interpretation for ease of data comparison. The data were analysed
in three ways: total scores, subscale scores and attitude group (positive and neutral)
scores. First, the teachers‟ total scores were calculated. In doing so, the teachers were
assigned their attitude level of strongly positive, positive, neutral, negative or
strongly negative. These data were primarily used in the selection of the six teachers
to interview. Second, the survey results from the six teachers identified to participate
in the interviews were analysed in terms of the four subscales: value, enjoyment, self-
confidence and motivation. The subscales are considered to be the underlying
dimensions of attitude (Tapia, 1996). The data provided critical information used in
the analysis of the interviews by identifying the influence of each dimension of
attitude (subscales) in the formation of the teachers‟ attitudes. Third, the total scores
and subscale scores from the positive group were compared to those of the neutral
48
group. These scores were used in conjunction with interview comments made by
teachers, during the analysis of process (see Chapter 4) to provide possible
explanations. They also allowed for trends to be identified amongst the teachers.
3.3.4.2 Analysis of interview data
The question of How did these attitudes form? was investigated through an analysis
of six representative teachers‟ responses to the open-ended interviews. Data on the
attitudes teachers hold were used to triangulate the survey data. Credibility was
improved through the use of triangulation, whereby two sets of data, being the ATMI
(Schackow, 2005) and the interviews, were used to answer the research questions
(Creswell, 2008). These data provided an insight into how teachers perceived their
attitudes towards mathematics formed. The analysis of the interviews followed Yin‟s
(2003) explanation building format, where the data collected was used to create a
theory about attitude formation in early years teachers. In this way, experiences
leading to each participant‟s attitude formation were explained.
In order to identify themes from the interview data, the process of pattern
coding was adopted. Pattern coding identifies themes within the data. This process
pulls together large amounts of data into more workable sets (Miles & Huberman,
1994). Within the data, pattern coding (Miles & Huberman, 1994) identified three
stages of education influencing the teachers‟ attitude formation being experiences
recalled from primary school, secondary school and tertiary studies. The identified
themes acted as a way to collate a lot of material into smaller and more meaningful
units to analyse (Miles & Huberman, 1994). Within these stages of education,
teachers‟ comments were further explored using the four dimensions of attitude:
value, enjoyment, self-confidence and motivation. Further, within the dimensions of
attitude, comments made by teachers containing similar content were grouped.
Analysing the teachers‟ comments according to these dimensions provided a clear
picture of the importance of each dimension during the three stages of education
identified by the teachers as well as the importance of each dimension for the
differing attitudes. Survey data were referred to where comments matched ATMI
(Schackow, 2005) scores or where disparity was evident between scores and
interview responses.
49
3.4 Quality and Rigour of the Study
The quality and rigour of the study was addressed in three ways. First, through the
reliability of the survey (Section 3.4.1); second by the trustworthiness of the data
collection methods (Section 3.4.2); and third by the ethical conduct of the study
(Section 3.4.3).
3.4.1 Reliability
The reliability of a survey or its ability to produce similar scores across multiple
administrations is an important consideration when selecting a survey (Burns, 2000).
Reliability of the results may have been compromised due to particular wording used
in the statements (De Vaus, 2002). For example, if the participant did not understand
a statement or interpreted it differently from the researcher‟s purpose then the results
might not reflect the participant‟s true attitude. However, using a well-established
survey with high internal validity addressed the issues of reliability. The previous
uses of ATMI (Schackow, 2005; Tapia, 1996; Tapia & Marsh, 2002) have shown
that measures of internal consistency were high, indicating high reliability.
3.4.2 Trustworthiness
Throughout the research process, issues of trustworthiness (credibility,
confirmability and generalisations) were observed. Credibility, in terms of the open-
ended interviews involved establishing that the results were credible or believable
from the participant‟s perspective. To ensure credibility, participants were invited to
read through the transcripts of their interview to ensure that a true and accurate
account was reported (Burns, 2000).
Confirmability was assured through the use of a peer reviewer (i.e.,
supervisor) to independently analyse and interpret some of the data. Any
discrepancies between the researcher‟s and the peer reviewer‟s coding was resolved
through discussion. Adopting this strategy ensured that interpretations and
conclusions were questioned (Burns, 2000).
Statistical generalisations or transferability for the study was inappropriate
due to the method of participant selection because convenience sampling does not
provide a group of individuals representative of the population (Creswell, 2008).
Therefore, results cannot be transferred to the general population (see Section 5.3).
50
3.4.3 Ethical considerations
Ethics approval was sought and approved for this study from Queensland University
of Technology and the study was conducted in accordance with the National
Statement on Ethical Conduct in Human Research (2007) (Approval # 0900001179).
This was a low risk research project as there was only one identified risk being
discomfort during or following the interviewing process as participants were asked to
discuss their attitude towards mathematics. Some teachers may have felt that by
identifying themselves as having a negative attitude their professionalism would be
compromised. All participants completed surveys (see Appendix A) and took part in
interviews voluntarily. Issues concerning the participants‟ right to withdraw from
further participation at any time were discussed with them prior to commencement.
All teachers and the school principal and junior school principal were provided with
information about the study and informed consent was obtained from each
participant (Rubin & Rubin, 2005). Participants were provided a consent form
regarding the banking of their data for possible future projects. Consent for the
teachers‟ participation was also obtained from the junior school principal who was
the teachers‟ supervisor. A copy of the information pack and the consent form for the
teachers and the principals is provided in Appendix C. Ethical considerations for this
study include anonymity for the teachers and school. This was addressed by using
pseudonyms in all reporting (Burns, 2000).
3.5 Chapter Summary
This study adopted an explanatory case study design (Yin, 2003) in order to identify
teacher attitudes to mathematics and the formation of these attitudes. The design
consisted of two sequential phases of data collection. Quantitative data were
collected in Phase 1 and qualitative data were collected in Phase 2, as per
explanatory case study design. Phase 3 consisted of data analysis in which both the
quantitative and qualitative data were analysed separately and also compared.
Participants were selected through convenience sampling. They all taught at Lower
Creek School, a Brisbane southside school, from a middle socio-economic area
approximately 25 km from central Brisbane. Data from participants were collected
through the ATMI (Schackow, 2005) and open-ended interviews. The ATMI
(Schackow, 2005) identified each teacher‟s attitude towards mathematics. From
51
these data, six teachers with varying attitudes were invited to participate in the
interview process. The interview identified consistencies and inconsistencies
between the survey results about the attitudes that teachers hold and investigated
how the teachers‟ attitudes formed.
52
53
4 Results
4.1 Chapter Overview
This study investigated early years teachers‟ attitudes towards mathematics and how
these attitudes were formed. Data were collected through an attitude survey
(Schackow, 2005) (Appendix A) and open-ended interviews (Appendix D). Twenty
early years teachers completed the Attitude towards mathematics inventory (ATMI)
(Schackow, 2005) to identify their attitudes towards mathematics. Six teachers
representing a range of attitudes were then selected to participate in open-ended
interviews (see Section 3.3.2).
This chapter has five parts. The first part of this chapter presents the survey
results and identifies the six teachers who were interviewed (Section 4.2). The
second part presents the data collected from the open-ended interviews conducted
with the teachers along with the themes identified within the data (Section 4.3). The
third part focuses on teachers with positive attitudes and presents the experiences that
these teachers attribute to the development of their attitudes towards mathematics
(Section 4.4), a comparison of the survey and interview data (Section 4.5), and how
the results of this study relate to the existing literature (Section 4.6). The fourth part
focuses on teachers with neutral attitudes and presents the experiences that these
teachers attribute to the development of their attitudes towards mathematics (Section
4.7), a comparison of the survey and interview data (Section 4.8), and how the results
of this study relate to the existing literature (Section 4.9). The fifth part compares the
findings of the positive teachers and neutral teachers (Section 4.10) and the long-
term impact of schooling experiences on the teachers interviewed (Section 4.11).
4.2 Survey Results
Phase One of this study used a survey instrument to investigate the research question,
What attitudes do practising early years teachers hold towards mathematics? The
ATMI (Schackow, 2005) is a 40 item instrument that measures attitude through the
four subscales of value, enjoyment, self-confidence and motivation (Section 3.3.3.1).
Results from the ATMI (Schackow, 2005) were used to identify the types of attitudes
existing amongst the 20 teachers participating in this study (Section 4.2.1). The
teachers‟ scores were then used to identify six focus participants, representing a
54
range of attitudes, who would be interviewed in order to investigate how their
attitudes formed (Section 4.2.2).
4.2.1 Overall survey results
The ATMI (Schackow, 2005) was completed by 20 teachers employed at Lower
Creek School. This inventory was administered and a total score was calculated for
each teacher based on their responses to the 40 statements. Teachers responded to
each of the 40 statements by indicating their level of agreement with each statement.
Schackow‟s (2005) scoring scheme was implemented (see Section 3.3.3.1). Just as
Schackow (2005) calculated summative scores, scores were calculated for each
interview participant. The teachers‟ total scores on the ATMI (Schackow, 2005) were
used to infer how positive their attitudes were towards mathematics.
For the purpose of this Master‟s study, teachers‟ attitudes were categorised
into five levels for ease of attitude identification: strongly negative, negative, neutral,
positive and strongly positive (see Table 4.1). These categories were assigned by
identifying the possible range of each participant‟s score by five. A range of 160 was
identified with the lowest possible score of 40 (rating of 1 on each of 40 statements)
and the highest possible score of 200 (rating of 5 on each of 40 statements). Divided
the range of scores as evenly as possible by the five levels, each category
cumulatively increased by 31 points:
Table 4.1
Scoring Ranges on the ATMI
Scoring Range Attitude
40-72 Strongly negative
73-104 Negative
105-136 Neutral
136-168 Positive
169-200 Strongly positive
The attitude scores of each of the 20 teachers surveyed can be found in Table 4.2.
The six focus teachers for interview are also identified on this table. Their selection
is discussed shortly. After the 20 teachers‟ survey responses were scored, only three
categories of teacher attitude were identified. These were strongly positive, positive
55
and neutral, with no teachers identified as having negative or strongly negative
results (Table 4.2). No teachers were found to have negative or strongly negative
attitudes towards mathematics. This is in contrast to the findings of Kolstad and
Hughes (1994) who reported that 34% of Kindergarten to Year 4 teachers held
strongly negative attitudes towards mathematics. This discrepancy between Kolstad
and Hughes‟ (1994) findings and the outcomes of this study suggests that further
investigation of this topic is warranted. A possible reason for the absence of negative
and strongly negative attitudes found amongst the participants of this study, may
relate to the fact that the surveys were not anonymous. Further, the teachers may
have been hesitant to divulge their true feelings due to their collegial relationship
with the researcher.
56
Table 4.2
Results from the ATMI (Schackow, 2005)
Teacher Total Score Out of
200
Total Score % Attitude Category
Teacher 1 170 85.0 Strongly positive
Teacher 2 (Mary) 167 83.5 Positive
Teacher 3 (Bianca) 161 80.5 Positive
Teacher 4 158 79.0 Positive
Teacher 5 156 78.0 Positive
Teacher 6 156 78.0 Positive
Teacher 7 156 78.0 Positive
Teacher 8 154 77.0 Positive
Teacher 9 153 76.5 Positive
Teacher 10 151 75.5 Positive
Teacher 11 149 74.5 Positive
Teacher 12 146 73.0 Positive
Teacher 13 144 72.0 Positive
Teacher 14 125 62.5 Neutral
Teacher 15 124 62.0 Neutral
Teacher 16 (Linda) 119 59.5 Neutral
Teacher 17 (Yvonne) 118 59.0 Neutral
Teacher 18 (Lily) 117 58.5 Neutral
Teacher 19 (Sandra) 114 57.0 Neutral
Teacher 20 110 55.0 Neutral
A key purpose of the survey was to select six teachers for indepth interviews.
The purpose of the interviews was to identify how they perceive their attitudes
formed (Section 4.3). The original intent was to identify a representative group of
teachers with a range of attitudes in order to interview two teachers with positive
attitudes, two teachers with neutral attitudes and two teachers with strongly negatives
attitudes towards mathematics. However, the results from the 20 surveys revealed the
absence of a single teacher with a negative or strongly negative attitude (see Table
4.2). Further, the strongly positive teacher (Teacher 1) and the two teachers scoring
highest in the neutral range (Teacher 14, Teacher 15) declined to be involved in the
interview process. Therefore, to reflect maximum variation in attitudes, the two
57
teachers with the closest scores to the strongly positive range (Bianca, Mary) were
selected for interview. The interview group containing neutral teachers was
represented by Linda and Yvonne as they were the top two teachers with neutral
attitudes who agreed to participate in the interview process. Lily and Sandra were
included in the absence of teachers with negative or strongly negative attitudes. The
reason for including the two additional neutral teachers was that they would seem
more likely to give some insight into negative views as opposed to adding either
strongly positive or positive teachers in the interview cohort. Unfortunately, the
neutral teacher (Teacher 20) with the lowest attitude score was unavailable for
interview. Thus, using the positive and neutral teachers it was hoped to obtain insight
into the broadest range possible of teacher attitudes within this cohort.
4.2.2 Subscale scores
The ATMI (Schackow, 2005) has four subscales: value, enjoyment, self-confidence
and motivation. These subscales are considered to be underlying dimensions of
attitudes towards mathematics (Schackow, 2005; Tapia, 1996). For example, the
following statement is found within the category of enjoyment: I have usually
enjoyed studying mathematics in school (see Appendix A). Subscale scores were
calculated for the six selected teachers and are presented in Table 4.3. Due to
different numbers of items per subscale, both total scores and percentages are
presented.
58
Table 4.3
Subscale Results from the ATMI (Schackow, 2005)
TO
TA
L S
CO
RE
/20
0
TO
TA
L S
CO
RE
%
Val
ue/
50
Val
ue
%
En
joym
ent/
50
En
joym
ent
%
Sel
f-co
nfi
den
ce/7
5
Sel
f-co
nfi
den
ce %
Mo
tiv
atio
n/2
5
Mo
tiv
atio
n %
Positive
teachers Mary 167 83.5 45 90.0 42 84.0 61 81.3 19 76.0
Bianca 161 80.5 45 90.0 36 72.0 64 85.3 16 64.0
Neutral
teachers Linda 119 59.5 41 82.0 28 56.0 32 42.7 18 72.0
Yvonne 118 59.0 40 80.0 24 48.0 43 57.3 11 44.0
Lily 117 58.5 42 84.0 21 42.0 42 56.0 12 48.0
Sandra 114 57.0 40 80.0 22 44.0 34 45.3 18 72.0
The teachers‟ subscales scores on the ATMI (Schackow, 2005) provide some
indication of the contribution of value, enjoyment, self-confidence and motivation
towards their mathematics attitude. The six teachers‟ subscale percentages are
presented in Figure 4.1 for comparative purposes. The results for value, enjoyment,
self-confidence and motivation were later compared with their interview responses
relating to these dimensions of attitude (Section 4.5, 4.8).
59
Figure 4.1. Teachers‟ ATMI total and subscale scores.
Value statements refer to mathematics being worthwhile and necessary
(Hannula, 2002). Valuing mathematics also relates to a desire to develop
mathematics skills as well as valuing the role mathematics plays in our everyday and
professional lives. The percentage scores relating to the value statements in the
inventory are similar across all teachers with a range of 80.0% to 90.0% (Figure 4.1,
Table 4.3), suggesting that, although their overall attitudes vary, all six teachers
valued mathematics.
Enjoyment statements refer to feeling satisfaction when solving problems and
enjoying challenges (King, 2006; Ma, 1997; Thorndike-Christ, 1991). They also
relate to the feeling of happiness experienced as well as the level of interest held for
the subject. The enjoyment scores varied greatly between the positive teachers Mary
and Bianca (average 78.0%) and the neutral teachers Lily, Linda, Sandra and Yvonne
(average 47.5%). In contrast, the scores relating to value showed little variation (90.0%
average for positive c.f. 81.5% average for neutral). The enjoyment scores suggest
that the teachers with positive attitudes enjoyed mathematics where the teachers with
neutral attitudes enjoyed it less.
Self-confidence statements relate to expectations about doing well, solving
problems without difficulty and how easily new concepts are learnt (Goolsby, 1988;
Kloosterman, 1988; Linn & Hyde, 1989; Randhawa, Beamer, & Lundberg, 1993).
The negative self-confidence statements refer to feelings including dread, dislike,
0
10
20
30
40
50
60
70
80
90
100
Total % Value % Enjoyment % Self-confidence %
Motivation %
Pe
rce
nta
ge
Total and Subscale Scores
Mary
Bianca
Linda
Yvonne
Lily
Sandra
60
nervousness, being uncomfortable and confusion. The four neutral teachers all scored
lowly (average 50.3%) compared with the positive teachers (average 83.3%). Similar
to the dimension of enjoyment, this finding suggests that self-confidence also plays
an important role in the teachers‟ overall attitude. The teachers with high self-
confidence have positive attitudes where the teachers with low self-confidence have
neutral attitudes towards mathematics.
Motivation statements refer to the desire to learn more complex mathematics,
the appeal of challenges faced in mathematical problems and willingness to teach
mathematics (Schiefele & Csikszentmihalyi, 1995; Singh, Granville, & Dika, 2002;
Thorndike-Christ, 1991). The scores obtained by the teachers on this subscale
showed a different trend to the other subscales. The positive teachers (Bianca –
64.0%, Mary – 76.0%) along with two of the neutral teachers (Linda – 72.0%,
Sandra – 72.0%) had similar scores to each other. On the other hand, the other two
neutral teachers‟ (Lily, Yvonne) scores were much lower (48.0% and 44.0%). This is
in contrast to enjoyment and self-confidence where the positive teachers‟ scores were
similar to each other and the neutral teachers‟ scores were similar to each other. The
mix of both positive teachers and neutral teachers receiving high scores in motivation
suggests that high motivation does not appear to distinguish between the two groups.
In conclusion, all six teachers valued mathematics and the role that
mathematics plays in their everyday and professional lives. The dimension of
motivation was not easily distinguished between the two groups of teachers. What
did distinguish the two groups were their levels of enjoyment and self-confidence.
Scores for enjoyment and self-confidence were considerably higher for the positive
teachers than those for the neutral teachers.
4.3 Interviews: Themes Representing Teacher Attitudes
Towards Mathematics
Phase Two of this study used interviews to answer the research question, How did
the teachers’ mathematics attitudes form? Open-ended interviews were conducted
with the six focus participants as a means of elaborating on responses given through
the ATMI (Schackow, 2005) (see Section 3.3.3.2). The first interview question
focused on the teachers‟ overall attitude towards mathematics: Your results from the
ATMI (Schackow, 2005) suggest that you have a positive/neutral attitude towards
61
mathematics. Can you tell me more about your attitude to mathematics? (see
Appendix B). The following questions varied according to the direction of the
interview and the follow-up or probing required to elaborate on previous answers.
The interview questions were designed to encourage teachers to discuss how their
attitudes formed. In describing their attitudes, teachers discussed their memories in
relation to stages of education: primary school, secondary school and tertiary
education. These memories also related to the four dimensions of attitude; value,
enjoyment, self-confidence and motivation (e.g., Hannula, 2002; King, 2006;
Kloosterman, 1988; Schackow, 2005; Schiefele & Csikszentmihalyi, 1995; Tapia,
1996). The questions did not address stages of education or the dimensions of
attitude unless in a follow-up question. Therefore, the interview data were presented
according to when the individuals recalled their memories and according to which
dimension of attitude they discussed. Primary school experiences included any
memories the teachers recalled during Years 1 to 7. Secondary school experiences
included memories recalled during Years 8 to 12. Tertiary experiences related to any
recollections from the teachers‟ university education.
The stage of education when teachers recalled memories varied (Table 4.4).
The positive teachers, Mary and Bianca, shared memories from primary and
secondary school. Bianca also discussed experiences during her tertiary studies. Two
of the teachers with neutral attitudes towards mathematics, Yvonne and Lily, recalled
memories from their primary, secondary and tertiary studies. Sandra, another neutral
teacher, only recalled memories from primary school and tertiary years, and Linda
only discussed her secondary school and tertiary study years. Thus, stages of
education recalled do not appear to be related to whether the teacher had a neutral
attitude or positive attitude towards mathematics.
62
Table 4.4
Teachers’ memories and stage of education
Attitude towards
mathematics
Teacher Stage of education
Primary
school
Secondary
school
Tertiary
study
Positive Mary
Bianca
Neutral Yvonne
Sandra
Lily
Linda
In the following sections, the responses of positive teachers (Section 4.4)
and neutral teachers (Section 4.7) are presented. In each of these sections, responses
given by the teachers are presented according to the stage of education, that is
primary school experiences, secondary school experiences and tertiary experiences,
and then according to value, enjoyment, self-confidence and motivation (e.g.,
Hannula, 2002; King, 2006; Kloosterman, 1988; Schackow, 2005; Schiefele &
Csikszentmihalyi, 1995; Tapia, 1996).
4.4 Past Experiences of Teachers with Positive Attitudes
Both Mary and Bianca recalled past experiences from their primary school years
(Section 4.4.1) and their secondary school years (Section 4.4.2). Bianca also
discussed her experiences during her tertiary studies (Section 4.4.3).
63
4.4.1 Primary school experiences
Mary and Bianca recalled primary school memories that influenced their attitudes
towards mathematics. Their memories related to enjoyment and self-confidence.
Mary also recalled a memory relating to motivation.
Enjoyment
Enjoyable experiences featured in Mary and Bianca‟s interview comments about
games, group work and hands-on activities.
Games were memorable experiences for both Mary and Bianca.
Mary: I do remember doing fun maths games ... lots of maths games
not just sit and learn, rote learning.
Bianca: We got to do different games and the parents came in to help. It
was once a week I think. We got to rotate through the different
games.
Mary also commented on a game she used to play in upper primary school. She
associated being good at this game with a feeling of enjoyment.
Mary: ... we used to do „Mad Minutes‟ which was where we used to
whatever we were up to, addition or subtraction, and we would
time ourselves every week. I was very good at that. So, of
course I liked doing that.
Thus, games appear to have promoted enjoyment and in turn the development of
positive attitudes in these teachers.
Group work was noted by both Mary and Bianca as being an enjoyable
experience for them.
Mary: I don‟t really remember Year 1, but I do remember Year 2 and
3 doing group activities ... I do remember with Mrs. Hannah,
she used to do a lot of group work.
Bianca: I guess my attitude to maths formed when I was in primary
school. It started off, I remember, we had maths groups and
things like that and I always enjoyed them … I remember in
Grade 2 we had maths groups and I was in the Kangaroos maths
group.
64
Hence, group work appears to have had a positive effect and contributed to their
feelings of enjoyment towards mathematics during their primary school years.
Hands-on activities were also reported to be enjoyable by Bianca. She
recalled enjoying the use of hands-on activities to learn mathematical concepts.
Bianca: We got to do lots of hands-on activities … We also got to do
cooking and I really enjoyed the cooking in maths, the counting
and the measuring and all that …
Hands-on activities, therefore, provided Bianca with an enjoyable way to learn
mathematics. These activities allowed her to manipulate objects in a real-life context.
Interestingly, not only did Bianca enjoy games, group work and hands-on
activities, she also associated positive memories with completing tests
Bianca: I also enjoyed when we would do maths tests and things like
that.
The variety of enjoyable experiences recalled by Mary and Bianca suggests that there
are many opportunities to foster enjoyment in mathematics lessons.
Self-Confidence
Self-confidence was developed in both Mary and Bianca through particular positive
experiences with mathematics. Positive experiences included achieving good grades,
playing games and teacher feedback.
Bianca remembered feeling confident in mathematics in primary school.
This self-confidence was validated by her success.
Bianca: I think I felt quite confident in maths when I was little. I
remember especially in the early years we would have maths
and I would get good marks.
Bianca: ...studying for it [mathematics test] and then, you know, doing
the test and then seeing “Oh, I‟ve done a good job”.
Mary attributed her self-confidence to the mathematics games that she
played.
Mary: [By] doing the games I was more confident.
Therefore, these teachers linked self-confidence to positive experiences, highlighting
the importance of providing children with positive mathematics experiences.
65
Mary‟s self-confidence was also developed through teacher feedback.
Mary: I think it [formation of her positive attitude] was when I was in
primary school. I think, my Year 2 and 3 teacher Mrs Hannah, I
still remember her name. We used to do maths all the time and
she always used to say “Oh (Name) is such a good, you’re so
good at maths” and used to get me to explain problems to the
class and get me to help other students. So, I think it was
mainly from then, thinking and putting that thought in my
head that “Oh I’m good at maths”. So, my attitude was
positive from then on. Even until I got to the higher end of
primary school I was still quite positive. (emphasis added)
Hence, teacher feedback played a major role in the development of Mary‟s positive
attitude, in particular her self-confidence. Recalling these memories during
interviewing indicates that these recollections have lasted long into her adult life.
Furthermore, positive use of her skills within the classroom appears to have assisted
in the development of her positive attitude. The teacher‟s recognition of Mary‟s
mathematical abilities was particularly successful in developing her self-confidence
in addition to the positive teacher feedback she received.
Motivation
Motivation to learn more mathematics by doing extra work was noted by Mary.
Extra work was something Mary was interested in doing at home with the support of
her parents.
Mary: I always did extra work at home and my parents always helped
me do more work. So, I was interested in maths.
Hence, Mary‟s positive attitude towards mathematics may have made her more likely
to engage in mathematics outside of the classroom when she was a child.
In summary, aspects of Mary and Bianca‟s primary school memories
included enjoyment (King, 2006; Schackow, 2005; Tapia, 1994), self-confidence
(Kloosterman, 1988; Schackow, 2005; Tapia, 1994) and motivation (e.g., Schiefele
& Csikszentmihalyi, 1995; Schackow, 2005; Tapia, 1994). The mathematical
experiences in primary school, recalled by Mary and Bianca, were all positive. This
suggests that for these teachers, primary school had a major effect on the
66
development of their positive attitudes. Mary had very strong memories relating to a
specific teacher, her Year 2 and 3 teacher. While Bianca did not recall a specific
teacher, her memories relate to teachers. Therefore, teachers had a major impact on
Mary and Bianca‟s attitude development.
4.4.2 Secondary school experiences
Both Mary and Bianca recalled secondary school experiences relating to enjoyment
(King, 2006; Schackow, 2005; Tapia, 1994). Bianca also recalled experiences
relating to self-confidence and motivation.
Enjoyment
The two positive teachers, Bianca and Mary, made comments regarding their
enjoyment of mathematics during their secondary school years. Bianca‟s comment
reflected how her enjoyment of mathematics continued from primary school through
to secondary school. She enjoyed all aspects of mathematics in secondary school.
Bianca: … I didn‟t pursue I guess the most academic maths, I only did
maths A. I still enjoyed that and enjoyed studying and learning
the different formula and being able to apply that …
Just as Bianca suggested that she enjoyed studying mathematics in primary school,
she also enjoyed studying mathematics in secondary school. Therefore, her positive
attitude contributed to her willingness to study.
Mary‟s statement indicates a change in her enjoyment of mathematics due to
the change in approach to teaching mathematics. In primary school Mary enjoyed
games, group work and hands-on activities. In contrast, Mary did not enjoy her
secondary school experiences.
Mary: I didn‟t enjoy maths as much in high school probably because it
was rote learning, working from textbooks and got a bit harder.
In contrast to Bianca, Mary did not enjoy mathematics as much due to the change in
the approach to teaching mathematics that she experienced. This may have been due
to Bianca‟s ability to adapt to the change in teaching approaches, where Mary was
not. Also, Bianca‟s willingness to put effort into her study may have influenced her
enjoyment.
67
Self-confidence
Bianca recalled the effects of studying.
Bianca: [Studying] helped me get a greater knowledge of it in my own
time and then when I was really able to understand, I felt a lot
more confident. I was able to do the exercises better and
perform better on the test and things like that.
Hence, the extra effort she dedicated to studying assisted in the development of her
self-confidence. Further, her positive attitude may have contributed to her
willingness to engage in mathematics outside of the classroom.
Motivation
Bianca remembered being motivated to engage in mathematics during her own time.
Bianca: I think when I was in high school, especially the studying
aspect I enjoyed more because it gave me a chance to go back
in my own time go through and read the maths text books and
go back through the exercises. It gave me more of a chance to
understand. I felt that in class we were sometimes a little bit
rushed and things like that but going back and studying for it
and looking at it again and again helped me understand it more.
Bianca‟s willingness to study in her own time, therefore, helped her to gain a better
understanding of mathematics concepts. A greater understanding of the concepts may
have assisted in making her mathematical experiences during class time more
positive, hence, impacting on her attitude towards the subject.
4.4.3 Tertiary experiences
Bianca was the only positive teacher to note tertiary (preservice teacher education)
experiences. Her comments related to enjoyment (King, 2006; Schackow, 2005;
Tapia, 1994) and self-confidence (Kloosterman, 1988; Schackow, 2005; Tapia, 1994).
Bianca‟s tertiary experiences included making maths games which she found
enjoyable. Her experiences also gave her the self-confidence to teach mathematics as
well as providing her with many skills to take with her into the classroom.
68
Enjoyment
For Bianca, discovering exciting and fun ways to teach mathematics provided her
with positive, enjoyable experiences.
Bianca: we got to make a lot of maths games and work out the best
activities and ways to teach maths and overviews as well. I
really enjoyed the maths games and I guess working out,
even working out the more difficult areas such as problem
solving and even division with two digit numbers. We had to
think about exciting ways to teach that ... So I guess for me
as a teacher, it [university] helped me understand how to teach
maths better and do that in more exciting ways. It got me
interested in it [teaching mathematics] and wanting to find out
more and making sure that I taught children maths in exciting
ways, engaging ways and real life. (emphasis added)
Hence, giving Bianca practical game ideas to take into her classroom ensured that
her enjoyment of and attitude towards mathematics remained positive.
Self-confidence
Bianca‟s self-confidence to teach mathematics was developed through her tertiary
studies. Not only did her university provide her with practical teaching ideas but it
gave her the opportunity to work with a child to gain real-life experience.
Bianca: When I was at uni, we had to choose a major and I chose maths
to major in. I chose it because I didn‟t feel confident to teach
maths. I wanted more information and it looked really
interesting ... we got to work with a child in a one-on-one
situation. It helped me, I guess, work out the best ways to work
one-on-one, help their learning difficulties and diagnose their
difficulties in maths and then work with them to overcome them
and help them gain a better understanding. (emphasis added)
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Bianca: I guess primary maths laid the foundations for a positive
attitude but I’d have to say that uni maths had the greatest
affect on my attitude towards teaching maths and in a
primary setting because it gave me the strategies and helped me
work out it wasn‟t just what we did but the why and the how
behind the activities. (emphasis added)
Therefore, practical teaching experience coupled with classroom teaching strategies
supported and enhanced Bianca‟s positive attitude towards mathematics. Further, it
gave her the self-confidence to teach mathematics to young children.
4.4.4 Summary
For the most part, Mary and Bianca‟s attitudes remained positive throughout their
primary, secondary and tertiary education. The exception was Mary‟s lack of
enjoyment of mathematics through secondary school. This finding suggests that
Mary‟s negative experiences in secondary school were not significant enough to
impact on the positive attitude she developed in primary school. Further, the absence
of memories relating to her tertiary experiences suggests that it was her primary
school experiences in isolation which developed her positive attitude towards
mathematics. This finding highlights that important role that primary school
experiences can play in the development of student attitudes towards mathematics.
4.5 Survey and Interview Results for Teachers with Positive
Attitudes
The following sections discuss the survey results in conjunction with the interview
results. In this way, consistencies, inconsistencies and interesting findings are
highlighted. When considering Mary and Bianca‟s survey results in conjunction with
their memories of primary school experiences, a clear picture of how their positive
attitudes formed is revealed. Both Mary and Bianca scored highly in all subscales of
the ATMI (Schackow, 2005), value, enjoyment, self-confidence and motivation.
However, interview data only revealed memories in relation to enjoyment, self-
confidence and motivation.
Mary and Bianca‟s percentages were high in the enjoyment subscale of the
ATMI (Schackow, 2005) (84.0% and 72.0%) (see Table 4.3). These percentages
suggest that both teachers enjoyed experiences and interactions with mathematics.
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This is consistent with the number of statements made by Mary and Bianca regarding
their enjoyment of mathematics during their primary school years. Both teachers
recalled only positive experiences from this stage of education and had clear
memories of specific activities and lessons, such as hands-on activities, group work
and games.
In comparison to the positive experiences recalled by both Mary and Bianca
during their primary school years, only Bianca found her secondary school years to
be a positive experience. Mary found the work harder and less enjoyable. Bianca‟s
positive comments reflect her percentage score of 72.0% in the enjoyment subscale
of the ATMI (Schackow, 2005). In contrast, Mary‟s more negative comments do not
reflect her percentage score of 84.0%. In isolation, Mary‟s score implies that she
encountered enjoyable experiences throughout her schooling, when in fact she did
not find her secondary school years enjoyable. The overall feeling of enjoyment
towards mathematics that was identified from the ATMI (Schackow, 2005) suggests
that Mary‟s experiences in secondary school, even though they were not positive, did
not contribute to her overall positive attitude towards mathematics (see Table 4.2).
This finding relates to attitude strength or the likelihood of an attitude changing
(Eagly & Chaiken, 1993). Strong attitudes are persistent over time and resistant to
change. In Mary‟s case, it would appear that her attitude is strong. In the absence of
more data, this topic would benefit from further investigation. Thus, the interviews
provided a more detailed investigation of positive attitudes than the survey results
alone.
Bianca was the only positive teacher to comment on her experiences during
her tertiary education. Her enjoyment came from learning many practical ideas to
take with her into her own classroom. In addition, the way that the subject was run
made her interested in finding out as much as she could about best mathematics
teaching practice. This finding suggests that the enjoyable preservice teacher
education subjects which included a hands-on teaching approach, contributed to
Bianca‟s positive attitude towards mathematics.
The ATMI (Schackow, 2005) scores for the self-confidence subscale were
high for both Mary (81.3%) and Bianca (85.3%) (see Table 4.3). Their scores suggest
that both teachers felt a high degree of self-confidence when engaged in
mathematical experiences. This is consistent with the comments made by Mary and
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Bianca, as both teachers recalled specific incidences which developed their self-
confidence in primary school. Mary believed that her Year 2 and 3 teacher and the
positive feedback that she received from this teacher, was responsible for making her
feel self-confident with mathematics. Bianca, however, believed that receiving good
grades reinforced her self-confidence. Therefore, reinforcement either through verbal
feedback or receiving good grades contributed to their self-confidence.
Only Bianca discussed the development of her self-confidence during her
secondary school years and her tertiary education. She recalled positive experiences
for both stages of education which also reflects her high self-confidence score
(85.3%). During secondary school she believed that studying developed her self-
confidence towards mathematics. Her willingness to study provided her with a
greater understanding of mathematics concepts which in turn made her classroom
experiences more positive. Her tertiary education developed her self-confidence to
teach mathematics. This was enhanced by the practical teaching ideas taught by her
lecturers. Having the opportunity to work with a child to gain real-life experience
also contributed to her feeling of self-confidence to teach the subject. Hence,
Bianca‟s self-confidence was developed through her willingness to study during her
secondary school years and the practical teaching ideas provided through her tertiary
education. These experiences built on the positive attitude that she developed during
her primary school years.
Both Mary and Bianca recalled being motivated to do extra mathematics
work in their own time. Mary‟s high motivation score (76%) reflects this willingness
to engage in mathematics outside of the classroom. Bianca‟s score of 64% is not as
suggestive of such willingness. Mary remembered during primary school, the extra
mathematics work that she did at home with the support of her parents. This positive
memory reflects her high motivation score. Bianca recalled being motivated to study
during secondary school in order to help develop her understanding of mathematical
concepts. In contrast to Mary‟s score, Bianca‟s lower score for motivation could
imply that she was not motivated to engage in extra mathematics or develop her
mathematics skills. Her comment, however, reflects the extra effort that she put in to
ensuring that she understood the mathematics work that she was taught. Hence, her
ATMI (Schackow, 2005) score along with her interview comment provided a more
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detailed understating of her attitude towards mathematics and the dimension of
motivation.
In summary, the use of both survey data and interview results to identify the
attitudes of the teachers with positive attitudes along with how their attitudes formed
was useful for the following reason. The interview comments made by Mary and
Bianca provided elaboration on the scores they obtained within each of the ATMI
(Schackow, 2005) subscales. In comparison to the study undertaken by Meyer (1980)
whereby data were collected through two open-ended questions alone (see Section
2.5.1), the use of both methods of data collection in this study allowed for
dimensions of attitude affecting the development of Mary and Bianca‟s positive
attitude to become clear. In addition, the elaborations identified some inconsistencies
between the interview and survey data. The use of only one data source, therefore,
may present findings which are misleading or incomplete, hence, it is recommended
that at least two sources of data collection are employed. The use of both survey data
and interview data proved to be important in understanding the attitudes of the
positive teachers as well as the formation of their attitudes. Thus, using the survey or
the interviews in isolation would have provided a much less descriptive picture and
in some cases an inaccurate picture of each teacher.
4.6 Understanding Teachers with Positive Attitudes
The interview data collected from Mary and Bianca can be interpreted in two ways.
First, the data can be situated within current literature relating to student attitudes and
mathematics (Duatepe-Paksu & Ubuz, 2009; Stipek, Salmon, Givvin, & Kazemi,
1998) (see Section 2.4). These studies have identified the impact that teaching
methods can have on students. These studies reported that students who were taught
mathematics concepts through more traditional methods of teaching, had more
negative attitudes towards mathematics. Interestingly, the results from this Master‟s
study revealed that one positive teacher (Bianca) enjoyed the more traditional
teaching methods employed during her secondary school years, while the other
positive teacher (Mary) did not. This finding presents a new dimension of the effects
of teaching methods on students which may be worth investigating in the future. The
contrasting feelings towards the more traditional teaching methods that Mary and
Bianca encountered, suggest that their positive attitudes did not influence the level of
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enjoyment they experienced. Rather, their preference for particular teaching methods
had the greatest impact. Hence, individual student‟s preferences to teaching methods
must be considered by teachers to ensure the positive development of their students‟
attitudes towards mathematics.
Second, Bianca‟s statements regarding the effect of her tertiary studies on
her attitude can be compared to current research with similar findings (Amato, 2004;
Philippou & Christou, 1998; Putney & Cass, 1998; Quinn, 1997; Schackow, 2005)
(see Section 2.3 and 2.4). These studies investigate the effects of preservice teacher
mathematics methods courses which used a hands-on approach. While it seems that
Bianca entered her tertiary studies with an already positive attitude towards
mathematics, she made particular mention of the use of hands-on methods of
teaching in her mathematics courses, commenting on their usefulness and the interest
they generated for her. Hence, the teaching methods employed by the university to
teach the mathematics course to Bianca were very effective in maintaining and
further developing her positive attitude towards the subject, and therefore must be a
consideration for tertiary institutions when developing their preservice teacher
mathematics subjects.
The similarities found between the findings from this study and the
literature are noteworthy and provide further evidence of the effects of schooling
experiences on the formation of attitudes. In addition, the findings have identified
experiences impacting on attitude development as discussed by practising teachers, a
participant group rarely focussed on (see Section 2.3).
4.7 Past Experiences of Teachers with Neutral Attitudes
Four teachers identified from the ATMI (Schackow, 2005) as having neutral attitudes,
discussed past experiences in primary and secondary school along with tertiary
experiences during their interviews. Their responses were divided into these stages of
education. Further, within these three stages of education, the responses were
grouped according to the four dimensions of attitude: value, enjoyment, self-
confidence and motivation (e.g., Hannula, 2002; King, 2006; Kloosterman, 1988;
Schackow, 2005; Schiefele & Csikszentmihalyi, 1995; Tapia, 1996).
These four teachers recalled experiences from primary school (Section
4.7.1), secondary school (Section 4.7.2) and tertiary studies (Section 4.7.3). Each
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teacher made comments regarding their experiences during their tertiary studies.
However, Linda did not recall any mathematical experiences from primary school
and Sandra did not discuss secondary school. The experiences noted from primary
and secondary school led to neutral and negative feelings these teachers developed
towards mathematics. However, each teacher recalled positive tertiary experiences.
4.7.1 Primary school experiences
For the four teachers with neutral attitudes towards mathematics, comments made
could be categorised into three of the dimensions of attitude being enjoyment, self-
confidence and motivation. Yvonne and Sandra spoke of memories relating to a lack
of enjoyment. Sandra, Lily and Linda discussed issues surrounding self-confidence
including lack of understanding and relevance.
Enjoyment
Lack of enjoyment was experienced by both Yvonne and Sandra during their primary
school years. Yvonne noted her lack of memories and the impact that a lack of
enjoyment had on her attitude towards mathematics.
Yvonne: Ok, at primary school I really did not like maths at all. I think I
have always been more language, creative way inclined than
mathematical ... I don‟t really have many recollections of
studying maths at school. I remember doing reading rotations or
writing certain things and doing science projects.
Yvonne: I think because I really didn‟t enjoy maths at primary school, I
didn‟t really put in a great deal of effort. I almost just switched
off I guess in maths lessons, so perhaps there were gaps in my
knowledge of maths.
Therefore, Yvonne‟s lack of enjoyment of mathematics during her primary school
years resulted in the absence of many memories along with reduced effort.
Consequently, Yvonne‟s content knowledge was compromised.
Sandra recalled when she believed her attitude towards mathematics formed
and how a lack of enjoyment affected her attitude development.
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Sandra: Ok, my maths [attitude] mainly formed when I got to upper
primary. I didn‟t really enjoy it as much. I think it became
harder as well and I didn‟t understand it.
A lack of understanding impacted on Sandra‟s feeling of enjoyment towards
mathematics which subsequently impacted on her attitude towards the subject.
Negative experiences with mathematics were the result of a lack of interest
for Yvonne and the inability to understand the work for Sandra. Hence, the absence
of enjoyment played a key role in the development of both teachers‟ neutral attitudes
towards mathematics.
Self-confidence
Sandra, Lily and Linda made varying responses relating to self-confidence. For
Sandra, a lack of understanding of specific concepts was noted as the main reason for
her low self-confidence.
Sandra: Ok, it was mainly the problem solving [that got harder] that I
didn‟t understand. I wasn‟t willing to delve, I didn‟t know how,
I wanted the quick answer and I didn‟t know how to delve into
it deeper ... Probably long division [impacted on my attitude].
When I was doing that, I did not get the concept at all. I did not
understand it and I felt just that I was defeated, so I
couldn’t do it. (emphasis added)
Sandra: I think I had ways I got around it [not understanding concepts]
because I felt defeated. Ways I got around doing maths and
stuff like that was having extra tutoring and stuff so I would get
the confidence in me.
Sandra: [I felt defeated] Because I was told I was wrong and I just
kept getting the wrong answer all the time. So, I think my
confidence just fell. It [teacher feedback] was mainly that they
said it was wrong but I still can‟t remember them actually
teaching me the right way of doing it. It was all like “you‟re
wrong, you‟re wrong” and it was like I had to do the problem
solving of how to get it right, I felt like no-one else was helping
me. (emphasis added)
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For Sandra, her low self-confidence was developed through her lack of achievement
and negative feedback received by teachers. She attempted to remedy this by getting
help from tutors. Hence, poor achievement was linked to Sandra‟s low self-
confidence and therefore contributed to her neutral attitude towards mathematics.
In contrast, Lily‟s self-confidence was developed through her Year 7
teacher‟s explanation of mathematical processes.
Lily: I had a primary school teacher, my Year 7 primary school
teacher, who used to stand at the front of the board and always
say “why are you doing it like this”. So, it would take 2 weeks
to teach us to do addition, but I really got a good
understanding of why I’m trading, why I’m doing the re-
grouping and he would make us explain it over and over
and over. That really cemented it for me in my head, how re-
grouping and trading works and that sort of thing. (emphasis
added)
Lily believed that her teacher‟s repetition and explanations of concepts enhanced her
learning which, in turn, developed her self-confidence and content knowledge.
Therefore, the teaching methods employed by Lily‟s teacher and the rate at which he
delivered the content had a positive effect on her self-confidence towards
mathematics.
For these teachers, primary school experiences including lack of
understanding and teacher explanation impacted on the development of their self-
confidence in both positive and negative ways. Hence, the importance of teacher
instruction relating to understanding is highlighted and shown to have had a major
impact on these teachers‟ attitudes. Interestingly, Sandra‟s (neutral teacher)
comments reflect the impact of teacher feedback which also featured in Mary‟s
(positive) interview responses (Section 4.4.1.3). The positive feedback received by
Mary affected her positive attitude where, the negative feedback Sandra received
contributed to her lack of self-confidence and neutral attitude.
Linda did not recall any experiences related to mathematics from primary
school. She believed that this may have been due to her sufficient ability level and
receiving neither positive nor negative feedback for her work. The only clear
memory from her primary school years involved her teacher commenting on her bad
cutting which Linda believed was not justified.
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Linda: There were no specific incidences that I remember in primary
school ... I think because I was quite capable of coping with all
of the curriculum in primary school. So, the only things I
remember from primary school are things where I was given
negative feedback.
Linda: I remember in Grade 3, in particular, a teacher asked me to do
some cutting for her because I was good at cutting. I had some
scissors that weren‟t very good that day, they were a bit stiff,
and so my cutting wasn‟t very good. I remember her not
chastising me but making a comment that it wasn‟t as good as I
normally do and I remember being devastated about that. So, I
think I only remember the negative feedback that I received and
because I was capable of doing the maths in primary school.
Hence, the absence of either positive or negative feedback relating to mathematics
resulted in Linda‟s lack of memories relating to mathematics and therefore may have
had no impact on the development of her attitude during this stage of schooling.
Motivation
Sandra recalled the way that she approached some mathematical challenges. This
related to motivation.
Sandra: I wanted the quick answer.
Sandra‟s neutral attitude towards mathematics appears to have been impacted
on by her lack of motivation to invest time in understanding problems in order
to find solutions. Hence, lack of motivation was linked to her neutral attitude
towards mathematics.
The primary school experiences of Yvonne, Sandra, Lily and Linda were all
very different. Similar to Mary and Bianca (positive), however, comments regarding
enjoyment, self-confidence and motivation were recalled during this stage of
education. In contrast to the positive teachers, their experiences were negative.
Yvonne and Sandra had only negative memories of mathematics in primary school.
Linda was unable to recall any memories involving mathematics from these years.
She believed that this may have been because she had no difficulties with it. Lily
only recalled one memory involving her teacher in Year 7 and it was positive. For
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these teachers, it seems that primary school did not have as great an impact on them
as it did on the positive teachers due to the limited memories shared during this stage
of education. Hence, negative primary school experiences contributed somewhat to
the development of the neutral teachers‟ attitudes towards mathematics. Responses
did fit within the same three dimensions of attitude: enjoyment, self-confidence and
motivation as with Mary and Bianca, however. This indicates the critical nature of
these three dimensions in the development of attitudes in children during their
primary school years.
4.7.2 Secondary school experiences
Only Yvonne, Lily and Linda recalled experiences from their secondary school years
in their interviews. Their responses could be categorised into three of the dimensions
of attitude: value, enjoyment and self-confidence. Yvonne and Lily discussed the
importance of relevance and real-life connections with secondary school
mathematics. Yvonne also specifically noted her lack of enjoyment of mathematics
in secondary school. Linda, Yvonne and Lily recalled a lack of self-confidence with
mathematics during these years noting not being able to understand concepts and
formulas as one of the major contributing factors for this.
Value
Valuing mathematics relates to relevance (Section 4.2.1). This was the case with
Yvonne and Lily who discussed the role of relevance in relation to the mathematics
they learnt in secondary school.
Yvonne: ... when I did maths at school, a lot of it, especially high school,
I thought I‟m never ever going to need any of these skills. So, it
didn‟t really seem very relevant.
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Lily: I’m going “I don’t want to know about this” and the
relevance I think. I couldn’t see the application of how to
apply it and I think that made it quite difficult as well ... In my
high school there was a lot of chalk and talk. So, it was just put
on the board and it was just “learn the formula”. Here‟s five
examples we‟re going to do as a group, learn the formula,
here‟s your questions in your book, sit and do them”. There was
not, it wasn‟t clearly explained for me to see the real life
application of it. I found because there was no real life
application, it was just theory, that I really didn‟t need to know.
Bad attitude, but yeah. (emphasis added)
Lily: I would like to have a better understanding of financial literacy,
more real life skills. I would have liked to have been given that
in high school. All the stuff that you learn day to day, how to
deal with money, how to invest money, that sort of stuff is what
I would have liked, more than the stuff that doesn‟t apply.
The role of the teacher in ensuring that children can see some relevance in what they
are learning is highlighted by these responses. Hence, for Yvonne and Lily, the
absence of real-life links to the mathematics they were learning impacted on their
attitude towards mathematics during secondary school.
Enjoyment
Enjoyment experienced during secondary school, was only discussed by Yvonne.
Yvonne: Then at high school, I continued to not enjoy mathematics. I did
do maths B but I did well and it was my sixth subject and I
really didn‟t enjoy it ... I pretty much did what I had to do to
pass but never enjoyed maths or got anything academically or
motivationally out of it.
Although Yvonne chose to do one of the harder mathematics subjects and noted
doing well in it, she did not enjoy it. It is interesting that Yvonne recalls doing well
in her mathematics subject but that she notes getting nothing academically out of it.
This may link back to her comments regarding relevance and feeling as though she
would never use the skills she was learning. Hence, Yvonne‟s lack of enjoyment
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meant that although she was doing well, her attitude towards the subject was poor
highlighting the critical link between enjoyment and positive attitude.
Self-confidence
Lack of self-confidence during secondary school was discussed by Linda, Yvonne
and Lily. Each teacher believed that issues around content knowledge contributed to
their lack of self-confidence. Linda remembered getting help with concepts that she
did not understand.
Linda: I‟ve never been good at maths. That became apparent when I
became a high school student. I just could never ever
understand the concepts, particularly past Grade 10. I would
say ... I remember specifically my teacher spending a lot of,
especially in Year 11 and 12. I think that‟s when I struggled the
most. He spent a lot of time 1 on 1 trying to help me understand
concepts. Even with that help, I just couldn’t wrap my head
around what he was trying to teach me. I couldn’t either
remember the formula or I couldn’t apply the formula
correctly. I would get frustrated. I suppose that I just couldn‟t
get it when I could understand so many other things and didn‟t
have any other problems in other subjects. (emphasis added)
Linda‟s poor achievement might have contributed to her lack of self-confidence,
which then might have influenced her neutral attitude towards mathematics.
Moreover, receiving one-on-one help seemed to not only fail in assisting her to
understand the concepts but contributed to lowering her self-confidence further.
Yvonne recalled being able to remember formulas but not actually
understanding the process behind them.
Yvonne: In Years 11 and 12, doing maths B, all of our assessment was
through tests. So I used to rote memorise formulas and certain
procedures that you had to do for equations but didn‟t actually
understand the process.
Even though Yvonne could recall formulas, she knew there was a deficit in her
understanding. This deficit led to her lack of self-confidence with her abilities,
contributing to her neutral attitude towards mathematics.
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For Lily, her inability to remember equations and formulas made
mathematics very difficult for her.
Lily: I failed a lot of my high school, not the top maths, the second
maths in high school and I failed it in Grade 11 and 12. I just
scraped through because my last semester was computing and I
aced the computing and it was enough for me to scrape a pass
mark. It was just too technical for me. All the equations don‟t
click for me really well. It’s something that I find really
difficult ... I‟m really good at all the abstract stuff, but when it
came to all the formulas, I just could never remember the
formulas and they never clicked really easily. It was talking
about the formulas of triangles and things like that; it was just a
little bit beyond my skills. Basic stuff I could do. (emphasis
added)
Hence, Lily‟s experiences during secondary school resulted in her feeling like she
did not understand the work. This led to her lack of self-confidence and contributed
further to her neutral attitude towards mathematics.
For Yvonne, Lily and Linda, relevance and content knowledge featured
strongly in their memories from their secondary school years. For these teachers,
secondary school provided them with only negative experiences which seem to have
had a major impact on their developing attitudes towards mathematics. Hence, issues
surrounding value, enjoyment and self-confidence only exacerbated these neutral
teachers‟ already poor attitudes towards mathematics.
4.7.3 Tertiary experiences
Responses made by Yvonne, Sandra, Lily and Linda could be categorised into three
dimensions of attitude being value (Hannula, 2002; Schackow, 2005; Tapia, 1994),
enjoyment (King, 2006; Schackow, 2005; Tapia, 1994) and self-confidence
(Kloosterman, 1988; Schackow, 2005; Tapia, 1994). Lily discussed the role that her
tertiary studies played in teaching her the real-life application of some mathematics
concepts as well as how learning mathematics from lecturers she knew made it seem
more interesting to her. Sandra‟s self-confidence was developed through the subjects
where she learnt how to teach children in the most effective ways. Yvonne
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experienced a similar improvement in her self-confidence due to learning particular
ways to teach children mathematics.
Value
Lily valued the mathematics which was delivered to her by lecturers that she knew.
She felt as though it gave the mathematics more relevance.
Lily: Maybe at uni, the stuff was a bit more, or I could see how it
was a bit more applicable to real life. Whereas, in high school
it was just things of angles and you‟re just going, I don‟t need
to know ... I guess the maths stuff didn‟t really click until I did
my business degree and I did a basic statistics course. I knew a
lot of the lecturers, the theorists that we were studying. I
personally knew them through my mum, so it was a bit more
relevant. (emphasis added)
Hence, relevance and real life application of mathematics contributed to Lily‟s value
of mathematics, giving her a more positive attitude towards the subject.
Enjoyment
Enjoyment of mathematics was assisted for Lily through her experiences with
lecturers whom she knew through her mother.
Lily: These were people that I knew you know, so it was even though
it wasn‟t stuff that I could apply it was stuff that was interesting
because I knew the person. I could connect to the actual
scientist rather than the theories that they were doing ... So it
became a lot more interesting, I suppose, and I had that
connection to the people writing the things ... I was studying
people that I actually knew, so it was a lot more interesting.
Whereas, I didn‟t have that in high school, you know, I‟m
studying my friends and their knowledge. (emphasis added)
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Lily: It was scientists that I knew through my mum. One of the guys
did a lot of stuff for NASA and his maths was incredibly
technical and I didn‟t understand it but what I was studying was
a very basic statistical analysis. Because I knew the man
personally and I had met him and visited him in overseas at his
university and all that sort of stuff, that I‟m actually studying
someone that I actually know. Even though I didn’t
understand his more technical things, what I was studying
was the basics and it was more interesting for me. Some of
the other people that I knew in Australia through my mum, they
were people that I knew, so I was a bit more interested in
studying it. It wasn‟t just some application to analyse this data
that wasn‟t relevant or I‟m just going “yeah it‟s some stranger
who‟s written something which is really exciting if you are into
it”. These were people that I knew you know, so it was even
though it wasn’t stuff that I could apply it was stuff that was
interesting because I knew the person and I could connect to
the actual scientist rather than the theories that they were
doing. (emphasis added)
Having lecturers whom she knew, made the mathematics for Lily seem more relevant
to her but it also made it more interesting. Interest, therefore, was linked to Lily‟s
attitude towards the mathematics she encountered during her tertiary studies. Hence,
interest and enjoyment contributed significantly to the more positive attitude that
Lily had towards mathematics during her tertiary studies.
Self-confidence
The self-confidence of Sandra, Yvonne and Linda was developed through their
experiences during their tertiary studies. Sandra believed that her experiences in
university actually developed her content knowledge which in turn increased her
self-confidence towards the subject.
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Sandra: I have had more understanding of it [mathematics], going
through uni, just learning more of the skills ... It [university]
was a hands-on approach as well just looking at different ways
that children had different thinking. We looked at how they
would use those strategies and how you would steer them in the
right direction. So, there wasn‟t just one right way but different
ways of finding the answer ... I think learning different ways [of
teaching at university, has impacted on my teaching practises].
So if children don‟t know how to do it, I find a different way [to
teach it] and see where their thinking is at as well. (emphasis
added)
Further, university had a positive impact on her self-confidence towards teaching
early years mathematics.
Sandra: Actually, teaching mathematics in the early years I‟ve found
easier to do. I‟m more confident in that early childhood part, but
when I have to go, like if I had to do teaching in the upper
primary, I don‟t think I would feel more confident.
Sandra‟s self-confidence improved during university and this gave her the
confidence to teach mathematics to young children. However, Sandra would not be
confident to teach mathematics in higher grades. Her degree had an early years focus
which would explain her trepidation towards teaching beyond the early years of
schooling. Hence, subjects which build self-confidence can affect attitudes in a
positive way.
Yvonne‟s tertiary experiences gave her an understanding of how to develop
children‟s mathematical skills.
Yvonne: When I was at uni, the mathematics subjects that I studied were
through Mr. B. He encouraged us to explore games and
concrete materials as a way of learning mathematics. After the
children were comfortable with that, we moved in to recording
sums and numbers and symbols, more your traditional style.
Then it moved on to applying those skills to problem-based
scenarios. So, that made a lot of sense I guess. It seemed to
work well.
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Yvonne‟s neutral attitude towards mathematics was positively influenced by the
lecturers and content taught during her tertiary studies. Hence, the practical, detailed
instruction given to Yvonne regarding the teaching of mathematics impacted upon
her neutral attitude in a positive way.
Linda believed that her self-confidence towards teaching mathematics was
developed through her experiences at university, in particular with a practicum
teacher
Linda: Mostly what I learnt at uni about how children learn best [is
what I have implemented in my classroom]. Also, I had one
particular fantastic prac teacher who we would talk a lot about
teaching of maths and the best way to teach maths ... I think
this particular prac teacher was the first instance where I
was able to see what uni was telling us was best practice
teaching which was hands-on learning. I was able to see that
in practice with her in her classroom. Whereas, previous
pracs, the children were learning maths from a textbook or not
learning maths as the case may be. So, I think actually seeing it
in practice seeing how it can work, learning about how to
arrange and organise maths groups, how to come up with
activities for them was really beneficial. (emphasis added)
Through Linda‟s practicum‟s, she was able to see the theory she learnt at university
put into practice and be very effective. For Linda, therefore, theories taught at
university relating to best teaching practise coupled with a supportive and
knowledgeable practicum teacher influenced her attitude towards mathematics in a
positive way.
4.7.4 Summary
Similar to the positive teachers who remained positive for the majority of their
education, the four teachers with neutral attitudes towards mathematics appear to
remember their attitudes remaining negative and neutral right up to their tertiary
years. Tertiary experiences seem to have provided them with opportunities to see
mathematics in more positive ways, however. Issues surrounding value, enjoyment
and self-confidence were discussed by the teachers, highlighting the broad effect that
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preservice education had on their attitudes towards mathematics. Hence, positive
tertiary experiences can counter existing negative attitudes of preservice teachers.
4.8 Survey and Interview Results for Teachers with Neutral
Attitudes
The following sections compare Yvonne, Sandra, Lily and Linda‟s survey results
with their interview data, highlighting consistencies, inconsistencies and any
interesting findings. When considering the survey results of Yvonne, Sandra, Lily
and Linda in conjunction with their memories of primary school experiences, a clear
picture of how their neutral attitudes formed is revealed.
During primary school, Yvonne and Lily recalled memories relating to
valuing the relevance of the mathematics being taught. Both teachers discussed how
they felt that the mathematics they were being taught had no relevance and that the
lack of relevance contributed to their disengagement. This finding is consistent with
the high percentages scored in the value subscale of the ATMI (Schackow, 2005)
where Yvonne scored 80.0% and Lily scored 84.0%. Their high value scores and
clear memories of when relevance was not achieved, indicate the strong impact that
these experiences had on them. These memories have lasted into adulthood,
Lily also recalled valuing the relevance of the mathematics that she was
taught during her tertiary studies. Throughout her interview, the importance of
relevance was noted on numerous occasions. This finding is consistent with her high
value score (84%). The frequency of comments relating to relevance suggests that
the lack of relevance she experienced during her education had a major impact on her.
Further, it highlights the importance she placed on the relevance attached to
mathematical concepts and hence, her high score in this area of the inventory.
Each of the neutral teachers scored highly in the value subscale of the ATMI
(Schackow, 2005). Lily scored 84.0%, Linda scored 82.0% and Yvonne and Sandra
scored 80.0% (see Table 4.3). Even though this appeared to be an important
dimension of the teachers‟ attitudes, only Lily and Yvonne made comments during
the interviews relating to this area. The survey results alone may indicate that the
most positive component to the neutral teachers‟ attitudes towards mathematics are
those relating to value. The lack of comments relating to this dimension of attitude
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found in the teachers‟ interviews suggest that valuing mathematics did not have a
major impact on the development of their attitudes.
Lack of enjoyment was discussed by Yvonne and Sandra in relation to their
experiences with mathematics in primary school. Their comments noting lack of
enjoyment were consistent with their overall ATMI (Schackow, 2005) enjoyment
subscale percentages which were both very low: Yvonne scored 48.0% and Sandra
scored 44.0%. Although Yvonne stated that she did not enjoy mathematics during
primary school, she found it hard to recall anything specific apart from her lack of
effort which she believed resulted in gaps in her mathematical knowledge. Similarly,
Sandra did not go into any specific detail but stated that she felt as though the work
got harder and it was this fact that contributed to her lack of enjoyment. In both cases,
it seems that it was not a particular experience that shaped their neutral attitude but
rather their entire experience with mathematics in primary school.
Yvonne was the only teacher who discussed her lack of enjoyment of
mathematics during her secondary school years. Her ATMI (Schackow, 2005)
enjoyment subscale percentage was consistent with this finding (48.0%). Even
though she remembered doing well in the mathematics subjects that she took, she
still did not enjoy it. In relation to the literature, Yvonne‟s lack of enjoyment of
mathematics while still achieving good grades provides an interesting topic for
further research, expanding on current findings which suggest that poor attitude and
high achievement is more common amongst Asian students (Leung, 2002; Stevenson,
Chen, & Lee, 1993).
In contrast to Yvonne and Sandra, Lily remembered enjoying the
mathematics she encountered during her tertiary studies. This was due to the
relationship she had with the lecturers. This finding was inconsistent with her
enjoyment score which was low (42%). This would suggest that her negative
experiences in high school had the greatest impact on her overall neutral attitude and
that the enjoyment she experienced during her tertiary studies was not enough to alter
this.
Issues relating to self-confidence during primary school were discussed by
Sandra, Lily and Linda, although all of them were quite different. Sandra recalled
that she lacked self-confidence due to her inability to understand the concepts taught.
She also felt like nobody was helping her to understand them. These comments
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reflect the low self-confidence score she received in the ATMI (Schackow, 2005)
(45.3%). In contrast, Lily‟s self-confidence was increased through her Year 7
teacher‟s explanation of mathematical processes which assisted her understanding of
the concepts taught. This comment does not reflect her self-confidence score of 56%.
Her survey data alone does not reveal this positive experience. Sandra and Lily‟s
memories suggest that teacher support or lack thereof, had a great impact on their
self-confidence levels.
Linda had a completely different recollection relating to her self-confidence
during primary school, being that she received neither positive nor negative feedback
due to her sufficient ability level. Her belief that she was capable of doing the
mathematics work suggests that her self-confidence was not low during this stage of
education. This is inconsistent with her overall self-confidence score from the ATMI
(Schackow, 2005) which was low (43%). In comparison to Sandra and Lily, she was
unable to recall anything specific but rather attempted to explain her lack of
memories.
Low self-confidence during secondary school was discussed by Lily,
Yvonne and Linda. Their interview comments are consistent with their self-
confidence percentages from the ATMI (Schackow, 2005). Lily scored 56.0%,
Yvonne scored 57.0% and Linda scored 43.0%. For each of the three teachers, their
memories related to a lack of understanding or the inability to remember or use
formulas correctly. The similarities between the teachers‟ experiences may account
for the similarities in their ATMI (Schackow, 2005) scores.
Sandra, Yvonne, Linda and Lily reported their self-confidence levels
increasing during their tertiary studies experiences. This finding was inconsistent
with the self-confidence subscale scores they obtained in the ATMI (Schackow,
2005). For Sandra and Yvonne, their tertiary experiences developed their self-
confidence by giving them strategies for teaching mathematics to young children as
well as providing them with practical ideas to use in their own classrooms. Linda‟s
self-confidence was developed in an entirely different way. She attributes her
teaching practicum experiences with the development of her self-confidence.
Common to all teachers is the positive nature of their tertiary experiences. For each
teacher, their experiences with mathematics in primary and secondary school were
not entirely positive and it is these memories which may have had the greatest impact
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on them, hence having low self-confidence scores. Their survey results in isolation
suggest that they may have had minimal positive experiences with mathematics.
Their survey results coupled with their interview comments reveal that each of these
teachers had very positive experiences with mathematics during their tertiary studies.
In summary, as with the positive teacher results, the survey and interview
results collected from the neutral teachers may be better understood when analysed
together. Similar to the data collection methods of Trujillo and Hadfield (1999) (see
Section 2.6.1), using both quantitative and qualitative methods of data collection
allowed for elaboration of responses along with the identification of any
inconsistencies between the two data sources. Further, a greater understanding of the
role that experiences played in the development of the teachers‟ attitudes was
obtained.
4.9 Understanding Teachers with Neutral Attitudes
The interview data collected from the neutral teachers can be interpreted within
current attitude research. Yvonne noted the lack of enjoyment that she experienced
during her secondary school years. She also noted the fact that even with a lack of
enjoyment that she was still achieving at a high level. This finding may suggest that
there is not always a direct link between positive attitude and achievement but that
high achievement is still possible even when a student is not enjoying the subject.
Research conducted by Leung (2002) and Stevenson, Chen, and Lee (1993) report on
findings which support this notion (Section 2.5). These studies were conducted in
Asia or used Asian students as participants and the results indicated that positive
attitudes were not always present in students with high achievement scores (Leung,
2002; Stevenson, Chen, & Lee, 1993). Although Yvonne‟s comments can be linked
to results within previous studies relating to attitude and achievement, hers is a
unique case within this study. As such, further research may be warranted in order to
identify whether the trend of high performing individuals not enjoying mathematics
is not just isolated to schools in Asia or where Asian students have participated.
Lily and Yvonne noted that a major influence, which contributed to their
neutral attitudes towards mathematics, was the lack of relevance or real-life
application that was conveyed during mathematics learnt during their secondary
school years. Duatepe-Paksu and Ubuz (2009) conducted a study which compared
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differing teaching methods employed within secondary school classes and the effects
of these teaching methods on the students‟ attitudes towards mathematics. The
results suggested that the students who were taught using the teaching method which
included activities related to real-life situations and scenarios had more positive
attitudes compared to those who were not taught in this way. Hence, teaching
methods can impact upon student attitudes in a significant way. Teachers need to be
aware of this impact to ensure that their planning and delivery of mathematical
concepts is providing students with experiences which promote positive attitudes not
experiences which diminish them.
Although the four neutral teachers (Lily, Linda, Sandra, Yvonne) recalled
negative experiences from their primary and secondary school years, all teachers
noted the positive impact that their tertiary experiences had on their attitudes towards
mathematics and mathematics teaching. Similar findings have been reported in
studies conducted by Philippou and Christou (1998), Putney and Cass (1998), Quinn
(1997) and Schackow (2005). These studies show the benefit of providing preservice
teachers with quality mathematics preservice education designed to improve attitudes.
Hence, the results from this study along with previous studies relating to the topic of
preservice teacher education provide universities with strong evidence supporting the
important role that tertiary subjects play in the development or change of attitudes
towards mathematics. Further, Lily and Yvonne‟s discussion of the impact of
teaching methods which focus on relevance and real-life scenarios in mathematics,
suggest that this is an important area of investigation. This finding supports research
conducted by Duatepe-Paksu and Ubuz (2009) adding to the notion that teaching
methods can greatly influence a student‟s attitudes towards mathematics. Further, the
positive impact of tertiary subjects on preservice teacher attitudes is very
encouraging and adds to the large body of work (Philippou & Christou, 1998; Putney
& Cass, 1998; Quinn, 1997; Schackow, 2005) advocating for quality preservice
education which focuses on the development of positive attitudes.
Lack of understanding was noted as one of the major contributing factors to
Yvonne‟s lack of enjoyment of mathematics during her secondary school years.
Interestingly, later she discussed how this was remedied once she began teaching
(see Section 4.10). Hence, Yvonne‟s neutral attitude, which was developed during
her secondary education due to her lack of content knowledge, was positively
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changed through her teaching experiences. Wilkins (2002) found that content
knowledge does not always mean that a teacher will teach well. In fact, Wilkins
(2002) found that positive attitude is more important than content knowledge. The
positive change in Yvonne‟s attitude coupled with an increased content knowledge or
understanding, therefore, makes it likely that she will teach well.
4.10 Comparison of Teachers with Positive and Neutral
Attitudes
When comparing the survey and interview results of the positive teachers with the
neutral teachers five similarities along with three main differences are evident. The
first similarity relates to the teachers‟ comments relating to how their experiences
have affected their own teaching practices. The positive teachers use many of the
activities and teaching methods that they experienced in primary school, including
games which have been found to be an experience which elicits enjoyment and fun in
students (Bragg, 2007). Many of the neutral teachers, not having any positive
experiences in primary or secondary school, have ensured that the teaching methods
they employ are different to those they experienced. In particular, Lily felt that her
mathematical experiences in school were not related enough to real-life scenarios and
often she could not see the relevance. She commented that her teaching includes
these aspects for her children. These findings indicate that the teaching practices used
by these teachers have been influenced by their own schooling experiences.
The second similarity found between the positive and neutral teachers‟
results relates to the negative secondary school experiences noted by all teachers
except for Bianca. This finding was particularly interesting for Mary who had a
positive attitude overall. The fact that all of these teachers recalled their secondary
school experiences in a negative way highlights the importance of this stage of
schooling in attitude formation. Studies reported on in Chapter 2 (Duatepe-Paksu &
Ubuz, 2009; Stipek, Salmon, Givvin, & Kazemi, 1998) which investigated the
effects of particular teaching methods on student attitudes have shown the impact
that different teaching methods can have on student attitudes. The findings from this
study contribute to this body of work.
The third similarity found between the positive teachers‟ and neutral
teachers‟ results is that all teachers, except for Mary, discussed how they have
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transferred what they learnt during their tertiary studies, into their own classrooms.
As with previous studies (Philippou & Christou, 1998; Putney & Cass, 1998; Quinn,
1997; Schackow, 2005), these findings suggest that tertiary experiences can have a
significant impact on the way that teachers teach mathematics when they join the
workforce.
The fourth similarity found between the positive teachers and the neutral
teachers is that not only did all teachers except for Mary discuss how they have
transferred what they learnt at university into their own classrooms but also that the
tertiary mathematics subjects they completed developed their self-confidence
towards mathematics and teaching mathematics. This finding is very positive for the
universities where these teachers completed their degrees. Not only did the teachers
believe that what they learnt was valuable enough to be used in the classroom, but
their otherwise very low self-confidence (except for Bianca) was developed through
these subjects. This shows that even if teachers have negative experiences at school
which contribute to low self-confidence, experiences during their tertiary years can
assist in building self-confidence.
The final similarity between the positive and the neutral teachers‟ results is
that within the teachers‟ interview data, the subscale of enjoyment and self-
confidence were common within both groups‟ interview comments. This indicates
that the attitudes of these teachers were primarily formed through education
experiences which were linked to enjoyment or self-confidence. This finding is
important for teachers due to the implications for lesson planning and teaching
within their own classrooms. Making mathematics enjoyable and teaching
mathematics in a way that builds student self-confidence appear to contribute to the
development of positive attitudes towards mathematics.
Three main differences can be identified when comparing the survey and
interview results of the positive and neutral teachers. The first difference is that two
of the neutral teachers discussed issues surrounding value. However, neither of the
positive teachers made comments related to this dimension of attitude. Both Yvonne
and Lily made value comments regarding relevance and real-life connection
experienced during their secondary and tertiary years of education. Interestingly, Lily
specifically noted how because she did not experience relevance and real-life
connection in her mathematics learning at school, she makes sure that the
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mathematics that she teaches is linked to real-like scenarios as well as trying to
explain the relevance of what she is teaching. This finding suggests that even though
the teachers highly value mathematics, memorable experiences which may have
contributed to this are minimal and value may be developed in other ways.
The second difference in survey and interview results when comparing the
positive teachers with the neutral teachers is that the positive teachers recalled many
memories relating to mathematical experiences which they enjoyed. Conversely, the
neutral teachers noted the opposite, recalling many experiences which they did not
enjoy. This finding was evident in both the survey data (see Table 4.3) and interview
data (see Sections 4.4 and 4.6). Therefore, the attitude dimension of enjoyment
appears to have had a considerable effect on the development of the positive attitudes
in Mary and Bianca.
The third difference in results when comparing the positive teachers with
the neutral teachers is that their self-confidence and enjoyment scores had the greatest
percentage difference for these subscales. For self-confidence, the positive teachers
scored an average of 83.0% where the neutral teachers had an average score of
50.3%. For enjoyment, the positive teachers scored an average of 78.0% where the
neutral teachers had an average score of 47.5%. Further, both the positive teachers
and neutral teachers made comments relating to self-confidence and enjoyment.
These comments related to each stage of schooling also. This finding suggests that
for these teachers, self-confidence had an effect on the development of either their
positive attitude or neutral attitude towards mathematics.
4.11 Impact of Past Experiences on Teaching
Past schooling experiences have had a major impact on all of the teachers. Their
implementation of activities and lessons experienced as children, within their own
classrooms, highlight the impact that education experiences had on these teachers.
These findings suggest that memories related to mathematics, which elicited an
attitudinal response, have remained with these teachers into their adult lives.
Primary school experiences that Mary and Bianca recalled as being positive
were used by both teachers when they entered the workforce. Mary discussed how
she used positive feedback with her students, modelled on the feedback that she
received during primary school.
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Mary: I think a lot of positive encouragement from the teachers [has
the greatest impact on student attitudes towards mathematics]. I
think teachers have a main part in forming children’s
attitude towards maths. I know a boy we had last year was not
the best at maths but we kept encouraging and telling him if
he did something great that it was excellent and he would
come in “I love maths, I love maths are we doing maths, are we
doing maths yet?”. It wasn‟t because he was the best student in
the class, it was because we did a lot of positive, you know,
“you can do this, it‟s very easy if you just keep trying”. So, I do
think as soon as you put the kids down and tell them that they
can‟t do it that they are not going to have any enjoyment in
doing maths at all. So we try and, I know I try and hype them
up a bit and tell them “Oh you‟re great, you should go up to
Grade 2 maths, you could do Grade 2 maths right now”. So I
guess to make their heads a bit bigger and tell them that they
can do it and that it is easy for them if they have a positive
attitude to it (emphasis added).
Teacher feedback was noted by Mary as being the major influence which contributed
to her positive attitude towards mathematics. Her use of this teaching strategy within
her own classroom highlights the long-term influence that her teacher had on her.
Mary also went on to discuss how she has incorporated games, hands-on
activities and group work into her classroom.
Mary: I do remember with Mrs. Hannah, she used to do a lot of group
work, so in my classroom now we do a lot of group work.
There‟s a lot of manipulatives, there‟s not too many worksheets.
I remember playing „Around the world‟ with kids, other kids in
the class, and we play that game now and we try and play a
game at the end of each lesson to build their confidence and
enjoyment of maths, not to make it all you known rote learning,
boring maths. So I do think from those experiences with her
that I have been able to adapt some of them but use a lot of
them in the classroom (emphasis added).
Enjoyable mathematics that Mary experienced in primary school, therefore, impacted
on her teaching practices later in life highlighting the longevity of these memories.
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Bianca mentioned her use of cooking activities within her own classroom as
a way to teach mathematical concepts.
Bianca: I try to do cooking which is an activity that I remember from
primary school so it‟s something I think the children will enjoy
and it also helps them learn maths in a more real life setting.
Hence, positive experiences encountered during primary school can last long into
adulthood and can be transferred into teaching practices for individuals who go on to
become teachers (see Section 2.4.5).
Secondary school experiences that Lily and Yvonne recall as being negative
have influenced their teaching practice in a positive way. Lily and Yvonne discussed
how their experiences relating to the relevance of mathematics has influenced their
own teaching.
Lily: Then I kind of lost the plot in high school because it was chalk
and talk. There was no real life application. So, I try to bring
back into my classroom that real life application. That there
is a reason why we are doing it, that it is something that we can
use, that the skills have a purpose. That it‟s not just something
you just have to know (emphasis added).
Yvonne: I made like a conscious effort to make maths more hands on
and fun so we do like a lot of games and linking it to I
guess real life skills. That‟s because when I did maths at school,
a lot of it, especially high school, I thought I‟m never ever
going to need any of these skills so it didn‟t really seem very
relevant. I try to link it in as much as I can so that the kids
can see the point in doing it and just making it instead of
worksheets or drills or tests that was what I did mainly at school
for maths. Just making it more hands on, problem solving, not
always right and wrong and just a little bit more creative I guess
(emphasis added).
For Lily and Yvonne, the negative experiences they encountered during secondary
school resulted in neutral or negative attitudes towards mathematics but influenced
their teaching practices in a positive way. They both made sure that they did not
provide their students with the types of experiences that they believe contributed to
their neutral attitudes towards mathematics.
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Tertiary studies and the experiences encountered during this stage of
education influenced Bianca, Yvonne, Sandra, Lily and Linda in a positive way.
Similar to the lasting effects of the positive experiences encountered by Bianca
during her primary school years, her tertiary experiences had a major impact of the
teaching methods she employed in her own classroom.
Bianca: I guess in uni when we made a lot of games. I’ve used a lot of
the games in a Prep and Year 1 setting. Games to develop
one-to-one correspondence, board games to develop simple
addition skills. I‟ve got some board games and memory games
to develop money skills, money recognition and simple coin
adding. I guess to I try to do cooking which is an activity that I
remember from primary school, so it‟s something I think the
children will enjoy and it also helps them learn maths in a more
real life setting (emphasis added).
Positive tertiary experiences therefore, had a major impact on the teaching practices
employed by Bianca when she began teaching. While Bianca recalled having a
positive attitude throughout her childhood and into her adulthood, her comments
highlight the critical role of tertiary educators in the development and support of
positive attitudes towards mathematics.
Yvonne remembered the process for teaching children mathematical
concepts taught by her lecturer making sense to her.
Yvonne: When I was at uni, the mathematics subjects that I studied were
through Mr. B. He encouraged us to explore games and
concrete materials as a way of learning mathematics and after
the children were comfortable with that we moved in to
recording sums and numbers and symbols, more your
traditional style. Then it moved on to applying those skills to
problem based scenarios. So, that made a lot of sense I guess. It
seemed to work well. So, that‟s what I started when I first left
university, when I first started teaching. Since then we have
done a lot of work in our school with mathematics consultants
which has also tied in with having games and developing skills
until children are comfortable with that and then applying it to
real life situations.
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Yvonne‟s tertiary experiences provided her with an understanding of how to teach
children mathematical concepts effectively. As a result, she has implemented the
process taught by Mr. B. within her own classroom, highlighting the impact that
tertiary subjects can have on a teacher‟s future teaching practice.
Sandra also discussed how her tertiary experiences provided her with an
understanding of how to teach children.
Sandra: I think learning different ways [of teaching]. So, if children
don‟t know how to do it, I find a different way [to teach it] to
find ways and see where their thinking is at as well.
Sandra‟s tertiary education had a positive impact on her attitude. She was provided
with a variety of teaching strategies to use within her classroom and used them when
she entered the workforce. Hence, her tertiary education had a direct impact on the
teaching strategies she implemented with her own students.
Linda, Yvonne and Lily also discussed their confidence to teach early years
mathematics. Linda and Yvonne feel confident to teach mathematical concepts to
young children. Lily, however, is not confident to teach early years mathematics.
Linda discussed her self-confidence to teach concepts that she understands to her
students.
Linda: I feel quite comfortable teaching maths in prep and Grade 1. I
really enjoy being able to teach it with hands on resources in a
way that will facilitate their understanding. I think I feel
comfortable with it because I completely understand all of the
concepts that I am required to teach them. If I had to teach in an
upper primary classroom, I think I would be more hesitant.
Therefore, self-confidence that Linda developed during her early years of primary
school assisted with her self-confidence to teach early years mathematics in her own
classroom.
Similarly, Yvonne‟s self-confidence and content knowledge that were
developed in university have been built upon through her teaching of early years
mathematics.
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Yvonne: Since teaching it [early years mathematics] and going back to
basics and doing it that way, I quite enjoy teaching maths. The
more that I have taught it, I guess I am more willing to
approach mathematics. Even professional development, I‟m
more interested in it now than I would have been when I was in
school ... Since having to go back from the beginning and
looking at how I would explain it and you know all the nitty
gritty kinds of things, I‟ve found it more enjoyable and I do
quite enjoy teaching maths which I never thought I probably
would.
Therefore, Yvonne believed that through her planning and teaching, she was been
able to re-learn basic mathematical concepts, making teaching mathematics more
enjoyable.
Lily spoke at length about her lack of confidence and effort to teach young
children.
Lily: You have to work as a teacher a lot harder to integrate maths
and you have to spend the time to create activities that do
integrate a lot more. Then you tend to go “nah I don‟t have time
for it”. It‟s the last thing you get to. I come into it with the
attitude that I’m not great at maths, so it is the last thing I
get to because it is a bit of a chore for me to do. I have to put
the effort in to plan for those lessons. So, because I have that
background in me maybe I don‟t always put the best into doing
the kids maths lessons because it is a bit of a challenge for me
to make it real life, to make it interesting to make it easier for
the children to understand ... Because I haven‟t had good
experiences with it, it does make it a challenge. Even coming up
with the ideas of how to link it in (emphasis added).
As a teacher, Lily believed that her negative attitude and low self-confidence meant
that she did not find mathematics easy to teach. Further, she found it hard to get
motivated to plan her lessons.
In addition, later in her interview, Lily discussed her inability to understand
mathematics that is more complex.
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Lily: Maybe in primary school, where it is more of the foundation
stuff, how to add, how to subtract, how to read a clock, to know
what a square and a shape is, that foundation stuff is easy. I can
do that stuff. When it gets up to higher Grade 6, Grade 7, into
high school maths when it is more the abstract stuff, the
formulas that I struggle with myself. Trying to teach it to
someone else is a bit of a challenge when I’m struggling to
understand it ... We did a Science unit that used all those
powers of 10 and when I‟m struggling to understand it, I would
be writing it on the board wondering if I had the right number
of zeros in it. If adults are struggling to understand the
application, then we are not teaching it very well to kids and we
are struggling to impart that knowledge to kids. Kids were
picking it up faster that I was which you know is not setting a
really good example but I don‟t have that knowledge to give to
kids. The kids were teaching me more than I was teaching them
because they could pick it up faster than I could (emphasis
added).
Lily recognised her lack of self-confidence and content knowledge and the negative
impact it had on the children she was trying to teach. She acknowledged that she was
unable to teach her class effectively due to her lack of content knowledge and poor
self-confidence. Therefore, attitudes developed during her education years had a
major effect on her teaching capabilities. She does, however, make a conscious effort
to address this by attending professional development sessions.
Lily: I really chase any PD‟s that are offered to do with maths and try
to develop my own skills on it and get new ways to teach it,
new ideas to teach it, new strategies to try something different.
Doing some of the maths program at school that I either love or
hate, whatever I can get my hands on. I‟ll have a go at, to try to
improve my own skills and then try to teach it in a different way
or develop my own skill in a different way. I think because I
know that I am not good at it, it is something that I do try to
work hard at to improve knowing that it is a fault of mine.
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Hence, even though Lily‟s attitude towards mathematics and towards her
mathematical abilities was negative, she strives to improve her perceived deficits
through professional development opportunities.
The long-term impact that the experiences encountered by both the positive
and neutral teachers is evident in their discussion of how they have or have not
incorporated what they encountered in their own classrooms. This finding is
consistent with a study by Wilkins (2002) which showed that teachers tended to
teach as they were taught themselves, thereby, showing the intergenerational impact
of teaching approaches. Similar results have been found in other studies (Ball,
Lubienski, & Mewborn, 2001; Brown, McNamara, Hanley, & Jones, 1999;
Middleton, 1992), highlighting the impact of teachers and teaching methods on
students, some of whom will go on to become teachers themselves. Experiences from
primary school, secondary school and tertiary studies have all influenced the way
that these early years teachers reported they teach in their own classrooms.
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5 Conclusion
5.1 Chapter Overview
The previous chapter presented the results of the study and provided a discussion of
the types of experiences encountered by teachers which contributed to their attitude
development. Further, the stages of education in which the early years teachers
believe these attitudes were formed were identified. This final chapter concludes the
thesis. There are four further sections to this chapter. The first section summarises
the findings according to each of the two research questions (Section 5.2).
Limitations of the study are identified in the second section of this chapter (Section
5.3). The third section discusses the implications for future research (Section 5.4).
The fourth section provides an overview of the chapter (Section 5.5).
5.2 Summary of Findings
This study investigated the types of attitudes held by practising early years teachers
and how these attitudes formed. Consistent with Yin‟s (2003) explanatory case study
design, multiple forms of data were collected. Data from the ATMI survey
(Schackow, 2005) were used to answer research question one relating to the attitudes
that early years teachers held towards mathematics (see Section 5.2.1). Open-ended
interviews were analysed using explanation building (Yin, 2003) and pattern coding
(Miles & Huberman, 1994) in order to answer research question two relating to
attitude formation (Section 5.2.2). Where relevant, the survey data were also used to
investigate this question. The two research questions will be addressed in turn.
5.2.1 Practising early years teachers’ attitudes towards
mathematics
The first research question was: What attitudes do practising early years teachers
hold towards mathematics? Four key findings were identified using the teachers‟
ATMI (Schackow, 2005) scores. First, no teachers were found to have negative or
strongly negative attitudes after scoring the 20 teachers‟ ATMI‟s (Schackow, 2005).
Interestingly, out of the 20 early years teachers surveyed, 75.0% scored within the
positive or strongly positive range.
102
Second, there was a distinct difference between the positive teachers‟ and
the neutral teachers‟ scores for the subscales of enjoyment and self-confidence. For
the subscale of enjoyment, the positive teachers (Bianca, Mary) had an average
percentage score of 78.0%. The neutral teachers (Lily, Linda, Sandra, Yvonne),
however, had an average percentage score of 47.5%. For the subscale of self-
confidence, the positive teachers (Bianca, Mary) had an average percentage score of
83.0%. The neutral teachers (Lily, Linda, Sandra, Yvonne) however, had an average
percentage score of 50.5%. This difference may indicate a link between a positive
attitude and experiencing enjoyment and high self-confidence. This is in contrast to a
link between teachers with neutral attitudes lack of enjoyment and low self-
confidence.
Third, no distinct difference was found between the positive teachers‟ scores
and the neutral teachers‟ scores for the subscale of motivation. The two positive
teachers (Bianca, Mary) along with two neutral teachers (Linda, Sandra) had
percentage scores between 64.0% and 76.0%. The other two neutral teachers (Lily,
Yvonne) had percentage scores of 48.0% and 44.0%. This would suggest that the
teachers‟ overall attitudes were not affected by motivation.
Finally, all teachers scored similarly for the subscale value. All teachers
scored within 80.0% - 90.0%. This indicates that they valued mathematics, had a
desire to develop their mathematical skills and valued the role that mathematics plays
in our everyday and professional lives. This finding is similar to the initial survey
results reported by Schackow (2005). Schackow (2005) did not report on individual
scores but included the mean score for each subscale with the subscale of value
scoring the highest out of the four subscales (value, enjoyment, self-confidence,
motivation). This indicates that the pre-service teachers surveyed in Schackow‟s
(2005) study also highly valued mathematics. The findings from Schackow‟s (2005)
study and this study indicate that value is an integral dimension of both teachers with
neutral attitudes and positive attitudes. However, the lack of comments made by the
positive teachers regarding value, suggests that it may play a greater role in the
overall attitude of the neutral teachers only.
103
5.2.2 The formation of early years teachers’ attitudes towards
mathematics
The second research question was: How did the teachers’ mathematics attitudes form?
This question was designed to elaborate on the results obtained through the ATMI
(Schackow, 2005). Six teachers with varying attitudes (Bianca, Lily, Linda, Mary,
Sandra, Yvonne) participated in open-ended interviews in order to answer this
question. Four key findings were identified through the analysis of the teachers‟
interview responses.
First, all teachers attributed their education experiences to the development
of their attitude towards mathematics. The nature of the open-ended question allowed
them to discuss the factors that they believed contributed to their attitude formation.
Their responses identified schooling experiences as the major contributing factor to
their attitude formation. These experiences were encountered during three stages of
education: primary, secondary and tertiary. The stages of education discussed varied
amongst the teachers as did the types of experiences. This suggests that education
experiences encountered at different times in a student‟s life contribute to the
development of attitudes but that these experiences can vary amongst teachers with
similar and different attitudes.
Second, the experiences noted by the participants as contributing to their
attitude formation, all involved teachers they had experienced during their education.
These experiences varied amongst the two groups (neutral, positive) and within the
stages of education. As discussed earlier (Section 2.3), other research findings imply
the critical impact of teacher attitudes on teaching and learning although none
provided concluding evidence to support these claims (e.g., Brown, McNamara,
Hanley, & Jones, 1999; Philippou & Christou, 1998; Quinn, 1997; Trujillo &
Hadfield, 1999). Hence, there is a critical need for future research into this area. The
findings from this study do, however, provide vital information regarding the impact
that teachers can have on students‟ attitudes. This is particularly important for
practising teacher professional development and future pre-service teacher education.
Third, the positive teachers (Bianca, Mary) believed that it was the
experiences encountered during their primary school education which developed
their attitudes towards mathematics. This finding is consistent with literature
identifying this stage of schooling as critical in the development of student attitudes
104
towards mathematics (Brown, McNamara, Hanley, & Jones, 1999; Meyer, 1980;
Trujillo & Hadfield, 1999). Further, for the group of six teachers interviewed in this
study, only the teachers who encountered positive primary school experiences
developed positive attitudes towards mathematics. Hence, positive primary school
experiences were directly linked to their positive attitudes.
Finally, education experiences had a major impact on the teaching practices
employed by all the teachers involved in this study. For Mary and Bianca it was the
positive experiences in primary school which they took into their own classrooms.
Lily and Yvonne also used experiences from their schooling to inform their teaching.
In contrast to Mary and Bianca‟s positive experiences, Lily and Yvonne‟s teaching
included aspects of mathematics that they believed were missing from their
experiences. All teachers, except Mary, discussed the positive impact that their
tertiary studies had on their teaching. Hence, this study has shown that in these cases,
the Preliminary Cycle of Teachers‟ Attitudes is accurate (see Figure 2.2).
The results from the study of early years teachers‟ attitudes towards
mathematics provide the means to elaborate on the preliminary model and create a
Cycle of Early Years Teachers‟ Attitudes Towards Mathematics (Figure 5.1).
Teacher attitudes impact upon their teaching behaviours and teaching methods
(Uusimaki, 2004; Wilkins, 2002). This, in turn, impacts upon student attitudes.
Specific schooling experiences impact on the formation of positive or negative
attitudes in students. Schooling experiences which can impact students‟ attitudes in a
positive way include games, group work, hands-on activities, positive teacher
feedback and relevance. Schooling experiences which can impact students‟ attitudes
in a negative way include insufficient help, teaching rushed, negative feedback and
lack of relevance. At this point, without intervention, it is the attitude that the student
exits school with that they may potentially carry through with them into their own
classroom. Teacher education courses can alter the attitudes of some students,
however, helping them develop more positive attitudes. The attitude that remains
with student on the completion of their teacher education course is carried through
into their career unless challenged.
For Mary and Bianca, their experiences follow the Cycle of Early Years
Teachers‟ Attitudes Towards Mathematics (see Figure 5.1) whereby the positive
teaching methods employed by their teachers assisted in the development of their
105
positive attitudes. Their positive attitudes continued throughout their stages of
education (except for Mary‟s secondary school experiences) and went on to influence
the teaching methods they employed when they became teachers. For the neutral
teachers however, the cycle varies slightly whereby their neutral or negative attitudes
developed through primary and secondary school were influenced positively during
their teacher education courses. This is in comparison to the positive teachers whose
attitudes remained relatively constant throughout.
106
Figure 5.1. Cycle of Early Years Teachers‟ Attitudes Towards Mathematics.
107
5.3 Limitations of the Study
There are nine limitations associated with this study. These issues and the ways they
have been addressed in the study are discussed in turn.
First, explanatory case study (Yin, 2003) research is labour intensive.
Collecting data in two phases requires a larger timeframe as opposed to using an
embedded design which involves collecting qualitative and quantitative data
simultaneously (Creswell, 2008). Similarly, open-ended interviews are labour
intensive. However, allocating an appropriate amount of time for each interview
would ensure the depth and elaboration needed to create an accurate narrative
regarding the respondent‟s perception of how their attitude formed (Rubin & Rubin,
2005). These issues were addressed by allowing sufficient time for data collection.
Working at the same site provided easy access and time flexibility for the open-
ended interviews.
Second, some teachers were unwilling to participate due to existing
workloads and fearing scrutiny according to responses. This issue was addressed by
clearly stating the voluntary nature of participation, prior to commencement and was
assisted by an already existing rapport with the teachers and time flexibility due to
my role as a curriculum support person for these teachers.
Third, teachers may have been unwilling to participate or divulge
information to the researcher who is a colleague of participants. To address this issue,
the researcher informed participants of the special care that was taken to safeguard
confidentiality of all information received. Also, the option of withdrawal at any
point without comment or penalty was communicated to the participants. The
teachers were invited to approach either the Junior School Principal or Junior School
Heads of Curriculum (HOC) to support them in their decision to participate. Both the
Junior School principal and HOC‟s were provided with an information sheet and
given time to ask the researcher any questions regarding the process.
Fourth, participants did not read through the researcher‟s interpretations of
their interview data. Due to the timing of this project, not all teachers were
contactable once interpretations were completed due to work relocation. Greater
trustworthiness and credibility may have been achieved if interpretations had been
reviewed.
108
Fifth, a potential bias which may have arisen from this research involved
participant selection. Researchers may select participants whom they believe will
generate desired results. Although convenience sampling was adopted, the entire
early years‟ population within the selected site was invited to participate, and hence,
results were obtained from a variety of teachers. The survey instrument was used to
identify interview participants, removing researcher choice in who participated.
Sixth, potential biases and preconceptions of the researcher also needed to
be considered in this study. Bias and preconceptions can be a problem during the
data analysis phase of the study as the researcher may interpret findings based on
personal viewpoints or already perceived ideas related to the investigation. It is
suggested that because qualitative research requires human investigation, mistakes
can be made and personal biases can interfere (Merriam, 1998). Reflexivity or
critical self-reflection was employed and every effort was made to mitigate research
bias by remaining conscious of the influence of biases and preconceptions.
Additionally, to counteract bias in this study, interpretations and conclusions were
peer reviewed by another researcher (i.e., supervisor). This peer was encouraged to
be critical, challenging the researcher to provide evidence supporting the
interpretations and conclusions.
Seventh, transferability or statistical generalisations cannot be made using
the results from this study due to the use of convenience sampling for participant
selection. In most cases, convenience sampling does not provide a group of
individual‟s representative of the population (Creswell, 2008), therefore, results
cannot be transferred to the general population.
Eighth, the ATMI (Schackow, 2005) was originally designed for use with a
student population. Although Schackow adapted the instrument for use with
preservice teachers and generated meaningful results, a robust assessment of its
psychometric properties has not been conducted with a teacher population. In this
Master‟s study, the ATMI dimensions were used to organise the qualitative
responses and were not used for statistical purposes.
Finally, the selection and analysis of teachers with varying attitudes was
limited by the number of teachers surveyed and the results that were obtained. If a
greater number of participants were included, a broader range of attitudes might have
been identified. Although the ATMI (Schackow, 2005) did not identify participants
109
for each of the three original attitude groups (strongly positive, neutral, strongly
negative), the teachers selected obtained the closet scores to each of these attitude
levels.
5.4 Implications of the Study
Three main implications have emerged from this study. The implications relate to
future research (Section 5.4.1), pre-service education (Section 5.4.2) and practising
teacher professional education (Section 5.4.3).
5.4.1 Implications for future research
There are two avenues for future research arising from the findings of this study.
First, Yvonne (neutral teacher) commented on the fact that during her secondary
school years, she experienced a lack of enjoyment whilst still achieving good grades.
This contradicts findings from studies conducted in Western countries (Iben, 1991;
Ma, 1997; Ma & Kishor, 1997; Tocci & Engelhard, 1991), but supports studies
conducted in Asia or with Asian students (Leung, 2002; Stevenson, Chen, & Lee,
1993). Further research into this area will help to establish the factors which
contribute to either a positive or negative relationship between achievement and
attitude and therefore provide a greater understanding as to how to develop both a
positive attitude and high achievement in students.
Second, Mary‟s (positive teacher) comments relating to a lack of enjoyment
experienced during secondary school whilst still scoring in the positive range of the
ATMI (Schackow, 2005) indicate that the positive attitude which she developed
during primary school was resilient against negative experiences later in her
education. This finding relates to attitude strength or the likelihood of an attitude
changing (Eagly & Chaiken, 1993) which suggests that strong attitudes are persistent
over time and resistant to change. This appears to be applicable to Mary‟s case.
Further research would investigate this complex aspect of attitude in more depth,
providing a greater understanding of the resilience of strong attitudes.
5.4.2 Implications for preservice teacher education
An important finding emerging from this study is that of the positive impact of pre-
service teacher education on the neutral teachers‟ attitudes towards mathematics.
Whilst all four neutral teachers (Lily, Linda, Sandra, Yvonne) recalled negative
110
experiences from their primary and secondary school years, all teachers noted the
positive impact that their tertiary experiences had on their attitudes towards
mathematics and mathematics teaching. Similar findings have been reported in
studies conducted by Philippou and Christou (1998), Putney and Cass (1998), Quinn
(1997), and Schackow (2005). Pre-service teacher education has had a positive
impact on the attitudes of the participants. The neutral teachers discussed the
enjoyable nature of their tertiary experiences along with the way that these
experiences, helped to build their self-confidence in teaching mathematics. These
findings suggest that tertiary institutions play a vital role in ensuring that teachers
leave university with a positive attitude to mathematics.
5.4.3 Implications for professional development
The research findings identified three main issues for practising early years teachers.
First, this study has identified specific experiences encountered in primary school
which affected the participants in both positive and negative ways when they were
students. Professional development opportunities can be used to highlight the types
of experiences which develop positive attitudes in students.
Second, the participants in this study identified teachers and schooling
experiences as playing a vital role in their attitude formation when they were students.
It is important for practising early years teachers to recognise the vital role that they
play in the formation of their students‟ attitudes, hence ensuring that their
interactions and teaching methods employed in their classrooms promote positive
attitude development in their students.
Third, the comments made by the participants in this study have revealed
that students with negative attitudes can be affected in many ways. Issues raised by
the neutral teachers in this study included switching off, causing gaps in knowledge,
and feeling defeated. Understanding the effect that negative attitudes can have on
students should help to encourage teachers to make every effort to ensure that their
students have positive experiences and attitudes towards mathematics.
5.5 Chapter Summary
This study revealed that amongst the 20 practising early years teachers surveyed,
75.0% scored within the positive or strongly positive range with no negative or
strongly negative attitudes recorded. A distinct difference was identified between the
111
strongly positive teachers‟ and the neutral teachers‟ scores for the subscales of
enjoyment and self-confidence. High enjoyment along with high self-confidence was
common among the positive teachers, whereas lack of enjoyment and low self-
confidence were common to the neutral teachers. In contrast, no distinct difference
was identified between the positive and neutral teachers in the subscale of motivation
as a mix of positive and neutral teachers scored above 72.0% whilst two neutral
teachers scored below 48.0%. All teachers scored similarly for the subscale value.
Amongst the six teachers who participated in the open-ended interviews, all
attributed their education experiences to the development of their attitude towards
mathematics. Further and most importantly, the education experiences noted by the
participants as contributing to their attitude formation, all involved teachers. The six
teachers‟ interview responses revealed the impact their education experiences had on
their current teaching practices employed by them once they began teaching. Also,
the positive teachers (Bianca, Mary) believed that it was the experiences they
encountered during their primary school education which developed their attitudes
towards mathematics.
Future research implications arising from this study include investigating
further the link between positive attitude and achievement as well as how students
can experience a lack of enjoyment whilst still achieving at a high level. Also,
investigating factors attributing to the development of attitudes resilient to change
would prove beneficial in this area of research. Implications for tertiary institutions
relate to the effect that mathematics subjects can have on pre-service teachers‟
attitudes towards mathematics. For practising teachers, implications for professional
development include identifying the types of schooling experiences which contribute
to both positive and negative attitudes in students, the vital role that teachers play in
the formation of student attitudes towards mathematics and the effects that negative
attitudes towards mathematics can have on students‟ learning.
112
113
References
Aiken, L. (2000). Psychological testing and assessment. Boston, MA: Allyn and
Bacon.
Ajzen, I. (1989). Attitude structure and behaviour. In A. R. Pratkanis & S. J. Breckler
(Eds.), Attitude structure and function (pp. 241-274). Hillsdale, NJ: Erlbaum.
Ajzen , I., & Fishbein, M. (1975). Attitude-behaviour relation: A theoretical analysis
and review of empirical research. Psychological Bulletin, 84, 888-918.
Albarracin, D., Zanna, M., Johnson, B., & Kumkale, G. (2005). Attitudes:
Introduction and scope. In D. Albarracin, B. Johnson, & M. Zanna (Eds.),
The handbook of attitudes (pp. 3-20). Mahwah, NJ: Lawrence Erlbaum.
Allport, G. (1935). Attitudes. In C. Murchison (Ed.), The handbook of social
psychology (Vol. 2) (pp. 798-844). Worcester, MA: Clark University Press.
Amato, S. (2004). Improving student teachers‟ attitudes to mathematics. In M.
Haines & A. Fuglestad (Eds.), Proceedings of the 28th
Conference of the
International Group for Psychology of Mathematics Education (Vol. 2, pp.
25-32). Bergen, Norway: Bergen University College.
Australian Association of Mathematics Teachers. (1998). Policy on numeracy
education in schools. Retrieved April 1, 2010, from
http://www.aamt.edu.au/Documentation/Statements/Policy-on-Numeracy-
Education-in-Schools-1998.
Australian Association of Mathematics Teachers. (2006). Position paper on early
childhood mathematics. Retrieved April 1, 2010, from
http://www.aamt.edu.au/Documentation/Statements/Position-Paper-on-Early-
Childhood-Mathematics-print-friendly.
Australian Curriculum, Assessment and Reporting Authority. (2009). Australian
curriculum. Retrieved October 10, 2009 from
http://www.acara.edu.au/curriculum.html.
Aşkar, P. (1986). The development of a Likert type attitude scale toward
mathematics, Education and Science, 62(11), 31-36
Balfanz, R. (1999). Why do we teach young children so little mathematics? Some
historical considerations. In J. Copley (Ed.), Mathematics in the early years
(pp. 3-10). Reston, VA: The National Council of Teachers of Mathematics.
114
Ball, D., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics:
The unsolved problem of teachers‟ mathematical knowledge. In V.
Richardson (Ed.), Handbook of research on teaching (4th
ed.) (pp.433-456).
New York: Macmillan.
Baroody, A., & Wilkins, J. (1999). The development of informal concepts, number,
and arithmetic skills and concepts. In J. Copley (Ed.), Mathematics in the
early years (pp. 48-65). Reston, VA: The National Council for Teachers of
Mathematics.
Baroody, A., Lai, M., & Mix, K. (2006). The development of young children‟s early
number and operation sense and its implications for early childhood
education. In B. Spodek & O. Saracho (Eds.), Handbook of research on the
education of young children (pp. 187-221). Mahwah, NJ: Lawrence Erlbaum
Associates.
Bobis, J. & Anderson, J. (2006). Reform-oriented teaching practices and the
influence of school context. Retrieved October 10, 2009 from
http://www.merga.net.au/documents/RP72006.pdf
Bobis, J., & Cusworth, R. (1994). Teacher education: A watershed for preservice
teachers‟ attitudes towards mathematics. In G. Bell, B. Wright, N. Leeson, &
J. Geake (Eds.), Challenges in mathematics education: Constraints on
construction Proceedings of the 17th
annual conference of the Mathematics
Education Research Group of Australasia (Vol. 1, pp. 113-120). Lismore,
Australia: MERGA.
Bragg, L. (2007). Student‟s conflicting attitudes towards games as a vehicle for
learning mathematics: a methodological dilemma. Mathematics Education
Research Journal, 19(1), 29-44.
Brown, T., McNamara, O., Hanley, U., & Jones, L. (1999). Primary student teachers‟
understanding of mathematics and its teaching. British Educational Research
Journal, 25(3), 299-322.
Burns, R. (2000). Introduction to research methods (4th
ed.). Melbourne, Australia:
Longman Cheshire.
Caezza, J. (1970). A study of teacher experience, knowledge of and attitude toward
mathematics and the relationship of these variables to elementary school
115
pupils‟ attitudes toward and achievement in mathematics. Unpublished
doctoral dissertation, Syracuse University.
Chamberlain, S. (2010). A review of instruments created to assess affect in
mathematics. Journal of Mathematics Education, 3(1), 167-182.
Charalambous, C., Panaoura, A., & Philippou, G. (2009). Using the history of
mathematics to induce changes in preservice teachers‟ beliefs and attitudes:
Insights from evaluating a teacher education program. Educational Studies in
Mathematics, 71(2), 161-180.
Cornell, C. (1999). “I hate math! I couldn‟t learn it, and I can‟t teach it!” Childhood
Education, 75(4), 225- 231.
Creswell, J. (2008). Educational research: Planning, conducting, and evaluating
quantitative and qualitative research (3rd
ed.). Upper Saddle River, NJ:
Pearson.
Creswell, J. (1998). Qualitative inquiry and research design: Choosing among five
traditions. Thousand Oaks, CA: SAGE.
Department of Education, Employment and Workplace Relations. (2008). Quality
education: The case for an education revolution in our schools. Retrieved
January 6, 2008 from
http://www.deewr.gov.au/Schooling/Resources/Documents/Publications/Qual
ityEducationEducationRevolutionWEB.pdf
De Vaus, D. (2002). Surveys in social research (5th
ed.). New South Wales, Australia:
Allen & Unwin.
Duatepe-Paksu, A., & Ubuz, B. (2007). Development of a geometry attitude scale.
Academic Exchange Quarterly, 11(2), 205-209.
Duatepe-Paksu, A., & Ubuz, B. (2009). Effects of drama-based geometry instruction
on student achievement, attitudes, and thinking levels. Journal of Educational
Research, 102(4), 272-286.
Dutton, W., & Adams, L. (1961). Arithmetic for teachers. Englewood Cliffs, NJ:
Prentice Hall.
Eagly, A., & Chaiken, S. (1993). The psychology of attitudes. Fort Worth, TX:
Harcourt Brace Jovanovich.
Entwisle, D., & Hayduk, L. (1988). Lasting effects of elementary school. Sociology
of Education, 61(3), 147-159.
116
Erdogan, S. & Baran, G. (2009). A study on the effect of mathematics teaching
through drama on the mathematics ability of six-year old children. Eurasia
Journal of Mathematics, Science and Technology Education, 5(1), 79-85.
Fennema, E., & Franke, M. (1992). Teachers‟ knowledge and its impact. In D.
Grouws (Ed.), Handbook of research on mathematics teaching and learning
(pp. 147-164). New York: Macmillan.
Fennema, E., & Sherman, J. (1976). Fennema-Sherman Mathematics Attitudes
Scales: Instruments Designed to Measure Attitudes toward the Learning of
Mathematics by Females and Males. Journal for Research in Mathematics
Education, 7(5), 324-326.
Fritz, R. (2008). The power of a positive attitude: Discovering the key to success.
New York: AMACOM. Retrieved May 23, 2009 from Electronic Book
Library Database
http://books.google.com.au/books?id=plpecfV97e0C&pg=PA105&lpg=PA10
5&dq=The+power+of+a+positive+attitude:+Discovering+the+key+to+succes
s&source=bl&ots=nzioYZsB4_&sig=BxBR_izFqIVi9UhWQ83XY4ASwCs
&hl=en&ei=XGbmSvzBONf-
kAXH_KCeAQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAoQ
6AEwAA#v=onepage&q=&f=false
Furner, J., Yahya, N., & Duffy, M. (2005). Teach mathematics: Strategies to reach
all students. Intervention In School and Clinic, 41(1), 16-23.
Gay, L., Mills, G., & Airasian, P. (2006). Educational research: Competencies for
analysis and applications. Upper Saddle River, NJ: Pearson Prentice Hall.
Gillham, J., Shatté, A., Reivich, K., & Seligman, M. (2001). Optimism, pessimism,
and explanatory style. In E. Chang (Ed), Optimism & pessimism: Implications
for theory, research, and practice, (pp. 53-75). Washington, DC: American
Psychological Association.
Ginsburg, H., & Baroody, A. (1990). Children‟s mathematical learning: A cognitive
view. Journal for Research in Mathematics Education, Monograph, (4), 51-
210.
Ginsburg, H., Cannon, J., Eisenband, J., & Pappas, S. (2002). Mathematical thinking
and learning. In K. McCartney & D. Phillips (Eds.), Blackwell handbook of
early childhood development (pp. 208-230). Malden, MA: Blackwell.
117
Gomez-Chacon, M. (2000). Affective influences in the knowledge of mathematics.
Educational Studies in Mathematics, 43(2), 149-168.
Goolsby, C. (1988). Factors affecting mathematics achievement in high-risk college
students. Research and Teaching in Development Education, 4(2), 18-27.
Grootenboer, P., Lomas, G., & Ingram, N. (2008). The affective domain and
mathematics education. In H. Forgasz, A. Barkatsas, A. Bishop, B. Clarke, S.
Keast, W. Seah, & P. Sullivan (Eds.), MERGA: Research in mathematics
education in Australasia 2004-2007 (pp. 255-269). Rotterdam: Sense
Publishers.
Hannula, M. (2002). Attitude towards mathematics: Emotions, expectations and
values. Educational Studies in Mathematics, 49(1), 25-46.
Iben, M. (1991). Attitudes and mathematics. Comparative Education, 27(2), 135-142.
Jasalavich, S. M. (1992). Preservice elementary teachers’ belief about science
teaching and learning and perceived sources of their beliefs prior to their
first formal science teaching experience. Paper presented at the Annual
Meeting of the National Association for Research in Science Teaching.
Boston, MA.
Kelly, J. (2000). Rethinking the elementary science methods course: a case for
content, pedagogy, and informal science education. International Journal of
Science Education, 22(7), 775-777.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children
learn mathematics. Washington, DC: National Academy Press.
King, B. (2006). Elementary teachers’ attitudes towards mathematics and their
preparation to teach mathematics. Retrieved October 19, 2009 from
ProQuest Dissertations and Theses (Identifier:
http://proquest.umi.com.ezp01.library.qut.edu.au/pqdweb?did=1221706631&
Fmt=7&clientId=14394&RQT=309&VName=PQD
Kloosterman, P. (1988). Self-confidence and motivation in mathematics. Journal of
Educational Psychology, 80(3), 345-351.
Koehler, M., & Grouws, D. (1992). Mathematics teaching practices and their effects.
In D. Grouws (Ed.), Handbook of research on mathematics teaching and
learning (pp. 115-126). New York: Macmillan.
118
Kolstad, R., & Hughes, S. (1994). Teacher attitudes toward mathematics. Journal of
Instructional Psychology, 21(1), 44-48.
Lacefield, W. (1999). A study of elementary teachers’ attitudes toward mathematics
instruction and mathematics teaching methods used in the elementary
classroom. Retrieved October 19, 2009 from ProQuest Dissertations and
Theses (Identifier:
http://proquest.umi.com.ezp01.library.qut.edu.au/pqdweb?did=732037431&F
mt=7&clientId=14394&RQT=309&VName=PQD
Leung, F. (2002). Behind the high achievement of East Asian students. Educational
Research and Evaluation, 8(1), 87-108.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ:
Erlbaum.
Ma, X. (1997). Reciprocal relationships between attitude toward mathematics and
achievement in mathematics. Journal of Educational Research, 90(4), 221-
229.
Ma. X., & Kishor, N. (1997). Assessing the relationship between attitude toward
mathematics and achievement in mathematics: A meta-analysis. Journal for
Research in Mathematics Education, 28(1), 26-47.
McDevitt, T., Heikkinen, H., Alcorn, J., Ambrosio, A,. & Gardner, A. (1993).
Evalution of the preparation of teachers in science and mathematics:
Assessment of preservice teachers‟ attitudes and beliefs. Science Education,
77(6), 593-610.
McLeod, D. (1992). Research on affect in mathematics education: A
reconceptualisation. In D. Grouws (Ed.), Handbook of research on
mathematics teaching and learning (pp. 575-596). New York: Macmillan.
McLeod, D., & McLeod, S. (2002). Synthesis – Beliefs and mathematics education:
Implications for learning, teaching and research. In G. Leder, E. Pehkonen, &
G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp.
115-123). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Merriam, S. (1998). Qualitative research and case-study applications in education.
San Francisco, CA: Jossey-Bass Publishing.
119
Meyer, R. (1980). Attitudes of elementary teachers toward mathematics. Retrieved
October 3, 2008, from Education Resources Information Centre (ERIC)
Database. (ERIC document No ED190388).
Middleton, J. A. (1992). Teachers’ vs. students’ beliefs regarding intrinsic
motivation in the mathematics classroom: A personal constructs approach.
Paper presented at the annual meeting of the American Educational Research
Association, San Francisco, CA.
Miles, M. & Huberman, A. (1994). Qualitative data analysis : A sourcebook of new
methods (2nd
ed.). Newbury Park, CA: Sage.
Mullholland, J., & Wallace, J. (1996). Breaking the cycle: Preparing elementary
teachers to teach science. Journal of Elementary Science Education, 8(1), 17
- 38.
Moustakas, C. (1994). Phenomenological research methods. London: SAGE.
National Association for the Education of Young Children. (2008). NAEYC position
statement. Retrieved November 11, 2008. from
http://www.naeyc.org/ece/critical/math.asp
National Association for the Education of Young Children & National Council for
Teachers of Mathematics (2002). Early childhood maths: Promoting good
beginnings. Retrieved October 1, 2008, from
http://www.naeyc.org/about/positions/pdf/psmath.pdf
National Council of Teachers of Mathematics. (2000). Principles and standards for
school mathematics. Reston, VA: National Council of Teachers of
Mathematics.
Nisbet, S. (1991). A new instrument to measure preservice primary teachers‟
attitudes to teaching mathematics. Mathematics Education Research Journal,
32(2), 34-56.
Palmer, D. (2002). Factors contributing to attitude exchange amongst preservice
elementary teachers. Science Education, 86(1), 122-141.
Pederson, J. & McCurdy, D. (1992). The effects of hands-on, minds-on teaching
experiences on attitudes of preservice elementary teachers. Science
Education, 76(2), 141-146.
120
Philippou, G., & Christou, C. (1998). The effects of a preparatory mathematics
program in changing prospective teachers‟ attitudes towards mathematics.
Educational Studies in Mathematics, 35(2), 189-206.
Plake, B., & Parker, C. (1982). The development and validation of a revised version
of the Mathematics Anxiety Rating Scale. Educational and Psychological
Measurement, 42(2), 551-557.
Putney, D., & Cass, C. (1998). Preservice teacher attitudes toward mathematics:
Improvement through a manipulative approach. College Student Journal,
32(4), 626-631.
Queensland Studies Authority. (2006). Early years curriculum guidelines. Retrieved
October 10, 2009, from http://www.qsa.qld.edu.au/learning/981.html
Queensland Studies Authority. (2007). Essential learnings. Retrieved October 10,
2009, from http://www.qsa.qld.edu.au/learning/7296.html
Queensland Studies Authority. (2008). Scope and sequence guide. Retrieved October
10, 2009, from
http://www.qsa.qld.edu.au/downloads/learning/qcar_ss_maths_number.pdf
Quinn, R. (1997). Effects of mathematics methods courses on the mathematical
attitudes and content knowledge of preservice teachers. The Journal of
Educational Research, 91(2), 108-119.
Ragin, C. (1994). Constructing social research: The unity and diversity of method.
Thousand Oaks, CA : Pine Forge Press.
Robinson, S., & Adkins, G. (2002). The effects of mathematics methods course on
preservice teachers’ attitudes towards mathematics and mathematics
teaching. Retrieved October 19, 2009, from Electronic Resources Information
Centre (ERIC) database. (ERIC document No ED474445).
Rubin, H & Rubin, I. (2005). Qualitative interviewing: The art of hearing data (2nd
Ed.). London: SAGE.
Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics.
Educational Studies in Mathematics, 35, 1-18.
Sarama, D., & Clements, J. (2008). Mathematics in early childhood. In O. Saracho &
B. Spodek (Eds.), Contemporary perspectives on mathematics in early
childhood education (pp. 67-94). Charlotte, NC: Information Age Publishing.
121
Schackow, J. (2005). Examining attitudes toward mathematics of preservice
elementary school teachers enrolled in an introductory mathematics methods
course and the experiences that have influenced the development of these
attitudes. Unpublished doctoral dissertation. University of South Florida,
USA. Retrieved June 14, 2009 from University of South Florida database
(Identifier:
http://kong.lib.usf.edu:8881/R/CB5F947NNYIJU4E355KJGLNF2R3NYLP
P1QU19K8P8EAXDKKSS01259?func=dbinjumpfull&object_id=72248&loc
al_base=GEN01&pds_handle=GUEST).
Schiefele, U., & Csikszentmihalyi, M. (1995). Motivation and ability as factors in
mathematics experience and achievement. Journal for Research in
Mathematics Education, 26(2), 163-181.
Seidman, I. (2006). Interviewing as qualitative research: A guide for researchers in
education and the social sciences (3rd
ed.). New York: Teachers College
Press.
Seligman, R. (1998). Learned optimism: How to change your mind and your life.
New York: Vintage Press.
Seo, K., & Ginsburg, H. (2004). What is developmentally appropriate in early
childhood mathematics education? Lessons from new research. In D.
Clements, J. Sarama, & A. DiBiase (Eds.), Engaging young children in
mathematics: Standards for early childhood mathematics education (pp. 91-
104). Mahwah, NJ: Lawrence Erlbaum.
Singh, K. Granville, M., & Dika, S. (2002). Mathematics and science achievement
effects of motivation, interest, and academic engagement. Journal of
Educational Research, 95(6), 323-332.
Stefanich, G. & Kelsey, K. (1989). Improving science attitudes of preservice
elementary teachers. Science Education, 73(2), 187-194.
Stevenson, H., Chen, C., & Lee, S. (1993). Mathematics achievement of Chinese,
Japanese and American children: Ten years later. Science, 259(5091), 53-58.
Stipek, D., Givvin, K., Salmon, J., & Kazemi, E. (1998). The value (and convergence)
of practices suggested by motivation research and promoted by mathematics
education reformers. Journal for Research in Mathematics Education, 29(4),
465-489.
122
Talsma, V. L. (1996). Science autobiographies: What do they tell us about
preservice elementary teachers: Attitudes towards science and science
teaching? Paper presented at the Annual Meeting for the National
Association for Research in Science Teaching. St. Louis, MO.
Tapia, M. (1996). The attitudes towards mathematics instrument. Retrieved June 2,
2009 from Education Resources Information Centre (ERIC) database. (ERIC
document No ED404165).
Tapia, M., & Marsh, G. (2002). Confirmatory factor analysis of the attitudes towards
mathematics inventory. Retrieved June 2, 2009 from ERIC database
http://www.eric.ed.gov/ERICWebPortal/custom/portlets/recordDetails/detail
mini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED471301&ERIC
ExtSearch_SearchType_0=no&accno=ED471301
Tashakkori, A., & Teddlie, C. (1998). Mixed methodology: Combining qualitative
and quantitative approaches. Thousand Oaks, CA: SAGE.
Thompson, A. (1992). Teachers‟ beliefs and conceptions: A synthesis of the research.
In D. Grouws (Ed.), Handbook of research on mathematics teaching and
learning (pp. 127-146). New York: Macmillan.
Thorndike-Christ, T. (1991). Attitudes toward mathematics: Relationships to
mathematics
achievement, gender, mathematics course-taking plans, and career interests.
WA: Western Washington University (ERIC Document Reproduction
Service NO. ED 347066).
Tocci, C., & Engelhard, G. (1991). Achievement, parental support and gender
differences in attitudes towards mathematics. Journal of Educational
Research, 84(5), 280-286.
Trujillo, K., & Hadfield, O. (1999). Tracing the roots of mathematics anxiety through
in-depth interviews with preservice elementary teachers. College Student
Journal, 33(2), 219-232.
Uusimaki, L. S. (2004). Addressing preservice student teachers’ negative beliefs and
anxieties about mathematics. Retrieved November 20, 2008 from
Australasian Digital Thesis Program (Identifier:
http://www.eprints.qut.edu.au/15921/)
123
Van de Walle, J. (1973). Attitudes and perceptions of elementary mathematics
possessed by third and sixth grade teachers as related to student attitude and
achievement in mathematics. Retrieved October 10, 2009 from Electronic
Resources Information Centre (ERIC) database. (ERIC document No
ED076425).
Van Hiele, P. (1986). Structure and insight. New York: Academic Press.
Varol, F., & Farran, D. (2006). Early mathematical growth: How to support young
children‟s mathematical development. Early Childhood Journal, 33(6), 381-
387.
Westwood, P. (2008). What teachers need to know about teaching methods. Victoria:
ACER Press. Retrieved May 23, 2009 from Electronic Book Library
Database
http://search.informit.com.au.ezp01.library.qut.edu.au/browsePublication;res
=IELHSS;isbn=9780864319128
Wigfield, A. (1994). The role of children‟s achievement values in the self-regulation
of their learning outcomes. In D. Schunk & B. Zimmerman (Eds.), Self-
regulation of learning and performance: Issues and educational application
(pp. 101-124). Hillsdale, NJ: Lawerence Erlbaum Associates.
Wilkins, J. (2002). The impact of teachers’ content knowledge and attitudes on
instructional beliefs and practices. Retrieved October 19, 2009 from
Electronic Resources Information Centre (ERIC) database. (ERIC document
No ED471775).
Wilson, P. (2008). Promoting positive attitudes. Retrieved November 10, 2008 from
Electronic Resources Information Centre (ERIC) database. (ERIC document
No EJ815090).
White, A., Way, J., Perry, B., & Southwell, B. (2005/2006). Mathematical attitudes,
beliefs and achievement in primary preservice mathematics teacher education.
Mathematics Teacher Education and Development, 7, 33-52.
Yin, R. K. (1994). Case study research: Design and methods (2nd
ed.). Thousand
Oaks, CA: Sage.
Yin, R. (2003). Case study research: Design and methods (3rd
ed.). Thousand Oaks,
CA: Sage Publications.
124
Yin, R. (2009). Case study research: Design and methods (4th
ed.). Thousand Oaks,
CA: Sage Publications.
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Appendices
Appendix A: Attitude towards mathematics inventory (Schackow,
2005)
Directions: This inventory consists of 40 statements about your attitude towards
mathematics. There are no correct or incorrect responses. Read each item carefully.
Please think about the item that best describes your attitude. Use the following
response scale to respond to each item.
Please circle a response for each of the 40 items.
1. Mathematics is a very worthwhile and necessary subject.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
2. I want to develop my mathematical skills.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
3. Mathematics helps develop the mind and teaches a person to think.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
4. Mathematics is important in everyday life.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
5. Mathematics is one of the most important subjects for people to study.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
6. Math courses would be very helpful no matter what grade level I taught.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
7. I think of many ways that I use maths outside of school.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
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8. I think studying advanced mathematics is useful.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
9. I believe studying maths helps me with problem solving in other areas.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
10. A strong math background could help me in my professional life.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
11. I get a great deal of satisfaction out of solving a mathematics problem.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
12. I have usually enjoyed studying mathematics in school.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
13. I like to solve new problems in mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
14. I would prefer to do an assignment in math than to write an essay.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
15. I really like mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
16. I am happier in math class than in any other class.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
17. Mathematics is a very interesting subject.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
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18. I am comfortable expressing my own ideas on how to look for solutions to a
difficult problem in math.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
19. I am comfortable answering questions in math class.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
20. Mathematics is dull and boring.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
21. Mathematics is one of my dreaded subjects.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
22. When I hear the word mathematics, I have a feeling of dislike.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
23. My mind goes blank and I am unable to think clearly when working with
mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
24. Studying mathematics makes me feel nervous.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
25. Mathematics makes me feel uncomfortable.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
26. I am always under terrible strain in math class.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
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27. It makes me nervous to even think about having to do a mathematics problem.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
28. I am always confused in my mathematics class.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
29. I feel a sense of insecurity when attempting mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
30. Mathematics does not scare me at all.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
31. I have a lot of self-confidence when it comes to mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
32. I am able to solve mathematics problems without too much difficulty.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
33. I expect to do fairly well in any math class I take.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
34. I learn mathematics easily.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
35. I believe I am good at solving problems.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
36. I am confident that I could learn advanced mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
37. I plan to take as much mathematics as I can during my education.
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Strongly Disagree Disagree Neutral Agree Strongly
Agree
38. The challenge of math appeals to me.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
39. I am willing to take more than the required amount of mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
40. I would like to avoid teaching mathematics.
Strongly Disagree Disagree Neutral Agree Strongly
Agree
DETAILS
Name: __________________________________
Contact Details: Ph.: ___________________________
Email: _________________________
130
Appendix B: Interview stimulus questions
The main questions were created from the research topic (Rubin & Rubin, 2005).
For example,
Your results from the ATMI (Tapia, 1996) suggest that you have a strongly
positive/strongly negative/neutral attitude towards mathematics. Can you tell
me more about your attitude to mathematics?
Can you tell me about how or when this attitude formed?
Can you recall specific incidences which might have contributed to the
formation of your attitude towards mathematics?
How does your attitude towards mathematics affect your teaching of
mathematics?
Follow-up questions related directly to what the participant had stated during
the conversation. For example,
Your attitude was identified as positive yet you have recounted
experiences in a negative manner which contradicts your survey
responses. Can you explain the difference between your survey response
and your interview response?
The probes were used to extend the conversation, ensuring that enough
detail and clarification was obtained throughout the conversation. For example,
I noticed that you mentioned particular teaching methods in your preservice
course as contributing to the formation of your attitude towards mathematics.
Can you elaborate further?
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Appendix C: Information and consent forms for teachers and principals
PARTICIPANT INFORMATION for QUT RESEARCH PROJECT
Teachers
Early years teachers’ attitudes towards mathematics
Research Team Contacts
Kylie Sweeting MEd Research Student
Faculty of Education, QUT
Dr Ann Heirdsfield / Professor Carmel Diezmann
Faculty of Education 0410 465 359 3138 3171 / 3138 3333
[email protected] [email protected] /
Description This project is being undertaken as part of a Master of Education (Research) project for Kylie Sweeting. The project is unfunded. The purpose of this project is to investigate teacher attitudes to mathematics and how these attitudes were formed. The researcher requests your assistance to contribute to information about the attitudes of practising early years teachers, because your opinions and personal experiences are considered to be extremely valuable. The data collected will help the researcher understand the types of attitudes held by early years teachers and the types of experiences that led to the formation of these attitudes. This understanding will then inform professional support offered to early years teachers. Participation Your participation in this project is voluntary. If you do agree to participate, you can withdraw from participation at any time during the project without comment or penalty. If you choose to withdraw, any data collected from you will be removed from the data set and destroyed immediately. Your decision to participate will in no way impact upon your current or future relationship with QUT or with Calamvale Community College. Your participation will involve:
1. Completing an attitude towards mathematics survey. This will take approximately 15 minutes and can be completed at a time convenient to you.
2. Receiving confidential follow up feedback about your attitudes (as measured in the survey) at a time and place convenient to you.
3. Considering an offer to participate in an open-ended interview to further explore how your attitudes towards mathematics were formed. As part of this research, I am interested in different types of attitudes and would like to interview teachers with different attitudes for the second phase of the research. In the feedback session, I will identify approximately 6 teachers with different attitudes and will ask you to consider participating in an
132
interview with me. Interviews will take approximately 90 minute and will be conducted at Lower Creek School in a private office outside of school hours.
Expected benefits The research may not benefit you immediately, however, it may prompt greater understanding of your attitudes towards mathematics and it may help inform future provision of professional support to teachers. Risks This is a low risk project meaning that the only identified risk for you is likely to be one of discomfort during or following the survey or interview process. Should you experience anything more than discomfort, for example if you become distressed, please let me know so that I can offer support. In this instance, QUT provides for limited free counselling for research participants of QUT projects, who may experience distress as a result of their participation in the research. Should you wish to access this service please contact the Clinic Receptionist of the QUT Psychology Clinic on 3138 0999. Please indicate to the receptionist that you are a research participant. Confidentiality Your survey responses will be identifiable until the point at which feedback is provided to each individual respondent and then removed. Identifying details on the surveys will be replaced by codes so that participant identities are known only by Kylie Sweeting and her supervisors. Pseudonyms for both the school and participants will be used in all reporting to ensure anonymity. Interviews will be audio recorded and then transcribed by Kylie Sweeting for data analysis. Audio recordings will be destroyed once they have been transcribed. The researcher and her supervisors will have access to the transcribed data. Prior to analysis, interview participants will be provided with a transcript of their interview and given an opportunity to verify the data collected, ensuring that a true and accurate portrayal of their responses has been recorded. Consent to Participate We would like to ask you to sign a written consent form (enclosed) to confirm your agreement to participate. Questions / further information about the project Please contact the researcher or her supervisors, named above, to have any questions answered or if you require further information about the project. Concerns / complaints regarding the conduct of the project QUT is committed to researcher integrity and the ethical conduct of research projects. However, if you do have any concerns or complaints about the ethical conduct of the project you may contact the QUT Research Ethics Coordinator on 3138 2091 or [email protected]. The Research Ethics Coordinator is not connected with the research project and can deal with your concern in an impartial manner.
133
CONSENT FORM for QUT RESEARCH PROJECT
Teachers
Early years teachers’ attitudes towards mathematics
Research Team Contacts
Kylie Sweeting MEd Research Student
Faculty of Education, QUT
Dr Ann Heirdsfield / Professor Carmel Diezmann
Faculty of Education 0410 465 359 3138 3171 / 3138 3333
[email protected] [email protected] /
Statement of consent By signing below, you are indicating that you:
have read and understood the information document regarding this project
have had any questions answered to your satisfaction
understand that if you have any additional questions you can contact the research team
understand that you are free to withdraw at any time, without comment or penalty
understand that you can contact the Research Ethics Coordinator on 3138 2091 or [email protected] if you have concerns about the ethical conduct of the project
understand that the participation in the project involves i) completing a survey; ii) receiving feedback on my attitudes as measured in the survey; iii) possibly participating in an interview if invited
understand that the interview in the project will include audio recording and give my permission for this audio recording
agree to the publication of excerpts of de-identified interview transcripts
agree to participate in the project
Name
Signature
Date / /
How is it best to contact you for follow up?
134
PARTICIPANT INFORMATION for QUT RESEARCH PROJECT
Principal
Early years teachers’ attitudes towards mathematics
Research Team Contacts
Kylie Sweeting MEd Research Student
Faculty of Education, QUT
Dr Ann Heirdsfield / Professor Carmel Diezmann
Faculty of Education 0410 465 359 3138 3171 / 3138 3333
[email protected] [email protected] /
Description This project is being undertaken as part of a Master of Education (Research) project for Kylie Sweeting. The project is unfunded. The purpose of this project is to investigate teacher attitudes to mathematics and how these attitudes were formed. The researcher requests permission to conduct this research with the Lower Junior teachers at your school. Participation Your school’s participation in this project is voluntary. If you do agree to allow the teachers to participate, you or they can withdraw from participation at any time during the project without comment or penalty. If a teacher withdraws from the project data collected from that teacher will be removed from the data set and destroyed immediately. Each teacher’s decision to participate will in no way impact upon their current or future relationship with QUT. Teachers’ participation will involve:
1. Approximately 20 Lower Junior teachers completing an attitude towards mathematics survey. This will take approximately 15 minutes and can be completed at a time convenient to the teacher.
2. Receiving confidential follow up feedback from the researcher about their attitudes
3. 6 teachers will be invited to participate in an open-ended interview to further explore how their attitudes towards mathematics were formed. Interviews will take approximately 90 minutes in order to explore the topic. These interviews will be conducted at Lower Creek School in a private office outside of school hours.
Expected benefits The research may not benefit your school directly however, the teachers at Calamvale Community College may develop greater understanding of their own attitudes via participation in the project. The results of the study may help inform professional support to primary teachers. Risks This is a low risk project meaning that the only identified risk for participants is that of
135
discomfort during or following the survey or interview process. However, in the event that a participant experiences more than discomfort, for example if they experience distress, QUT provides for limited free counselling for research participants of QUT projects, who may experience discomfort or distress as a result of their participation in the research. Should teachers wish to access this service they can contact the Clinic Receptionist of the QUT Psychology Clinic on 3138 0999. Confidentiality The survey responses will be identifiable until the point at which feedback is provided to each individual respondent. Identifying details on the surveys will be coded so that participant identities are known only by Kylie Sweeting and her supervisors. Pseudonyms for both the school and participants will be used in all reporting to ensure anonymity. Interviews will be audio recorded and then transcribed by Kylie Sweeting for data analysis. Audio recordings will be destroyed once they have been transcribed. The researcher and her supervisors will have access to the transcribed data. Prior to final inclusion, interview participants will be provided with a transcript of their interview and given an opportunity to verify the data collected, ensuring that a true and accurate portrayal of their responses has been recorded. Consent to Participate We would like to ask you to sign a written consent form (enclosed) to confirm your agreement to allow the teachers at your school to participate. Questions / further information about the project Please contact the researcher or her supervisors, named above, to have any questions answered or if you require further information about the project. Concerns / complaints regarding the conduct of the project QUT is committed to researcher integrity and the ethical conduct of research projects. However, if you do have any concerns or complaints about the ethical conduct of the project you may contact the QUT Research Ethics Coordinator on 3138 2091 or [email protected]. The Research Ethics Coordinator is not connected with the research project and can deal with your concern in an impartial manner.
136
CONSENT FORM for QUT RESEARCH PROJECT
Principal
Early years teachers’ attitudes towards mathematics
Research Team Contacts
Kylie Sweeting
MEd Research Student Faculty of Education, QUT
Ann Heirdsfield / Carmel Diezmann Faculty of Education
0410 465 359 3138 3171 / 3138 3333
[email protected] [email protected] /
Statement of consent By signing below, you are indicating that you:
have read and understood the information document regarding this project
have had any questions answered to your satisfaction
understand that if you have any additional questions you can contact the research team
understand that teachers are free to withdraw at any time, without comment or penalty
understand that you can contact the Research Ethics Coordinator on 3138 2091 or [email protected] if you have concerns about the ethical conduct of the project
agree to allow Lower Junior teachers at your school to participate in the project
School Name
Principal Name
Signature
Date / /
137
Appendix D: Interview transcripts
Mary – Positive attitude
Your results from the ATMI suggest that you have a positive attitude towards
mathematics, how and when do you believe this attitude formed?
I think it [attitude development] was when I was in primary school. I think, my Year
2 and 3 teacher Mrs Hannah, I still remember her name. We used to do maths all the
time and she always used to say “Oh Mary is such a good, you‟re so good at maths”
and used to get me to explain problems to the class and get me to help other students.
So, I think it was mainly from then, thinking and putting that thought in my head that
“Oh I‟m good at maths”. So, my attitude was positive from then on. Even until I got
to the higher end of primary school I was still quite positive. I always did extra work
at home and my parents always helped me do more work so I was interested in maths.
I think it was from that teacher telling me and putting those thoughts in my head that
made me keep thinking “I can do it, I can do it”. So yeah, but with English it wasn‟t
the same so I think I went maths, maths, maths.
You mentioned your teacher telling you that you were good at maths and including
you in the lessons in different ways, can you think of anything else that may have
attributed to your positive attitude?
I do remember doing fun maths games. I don‟t really remember Year 1 but I do
remember Year 2 and 3 doing group activities and lots of maths games. Not just sit
and learn, rote learning. So, I guess because I enjoyed it, doing the games I was more
confident.
You just talked about some of the ways your teacher taught maths, can you discuss
that further
I only remember doing testing in Grades 5, 6 and 7 maybe. I remember sitting there
doing the worksheets. Oh, we used to do Mad Minutes which was where we used to
138
whatever we were up to, addition or subtraction and we would time ourselves every
week. I was very good at that so of course I liked doing that but then you could see
the kids that weren‟t confident. You know, I sort of felt a bit sorry for them. I
remember doing that, but apart from that I don‟t remember doing too many other
worksheets.
In your survey you recorded a neutral feeling towards studying advanced maths and
thinking that it is useful can you discuss that
Uh, well I think in early childhood I know enough about the maths that I‟m teaching
to these kids and I‟ve got really not much interest in teaching it [advanced
mathematics]. I didn‟t enjoy maths as much in high school, probably because it was
rote learning, working from text books and [it] got a bit harder. So really I don‟t have
much interest in doing that unless it‟s, you know, advanced maths for the younger
kids.
In the statement that asks whether you will take as much maths as you can you
recorded a neutral response, can you discuss that
Uh, I like doing maths and I like taking extra maths outside of what we do in the
classroom but I also like doing other learning areas as well. So, yeah I don‟t think
everything comes down to learning all about maths and whenever I can I also like to
do other things
What impacts on a person’s mathematics attitude?
I think a lot of positive encouragement from the teachers. I think teachers have a
main part in forming childrens‟ attitudes towards maths. I now a boy we had last year
was not the best at maths but we kept encouraging and telling him if he did
something great that it was excellent. He would come in “I love maths, I love maths,
are we doing maths, are we doing maths yet?”. It wasn‟t because he was the best
student in the class, it was because we did a lot of positive, you know, “you can do
this, it‟s very easy if you just keep trying”. So, I do think as soon as you put the kids
139
down and tell them that they can‟t do it that they are not going to have any
enjoyment in doing maths at all. So we try and, I know I try and hype them up a bit
and tell them “Oh your great, you should go up to grade 2 maths, you could do grade
2 maths right now”. So, I guess to make their heads a bit bigger and tell them that
they can do it and that it is easy for them if they have a positive attitude to it.
What experiences from your past have influenced your teaching?
I do remember with Mrs. Hannah, she used to do a lot of group work, so in my
classroom now we do a lot of group work. There‟s a lot of manipulatives, there‟s not
too many worksheets. I remember playing „Around the world‟ with kids, other kids
in the class, and we play that game now and we try and play a game at the end of
each lesson to build their confidence and enjoyment of maths, not to make it all you
known rote learning, boring maths. So, I do think from those experiences with her
that I have been able to adapt some of them but use a lot of them in the classroom.
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Bianca – Positive attitude
The results from your ATMI suggest that you have a positive attitude towards
mathematics, can you discuss how and when you feel your attitude formed.
I guess my attitude to maths formed when I was in primary school. It started off, I
remember, we had maths groups and things like that and I always enjoyed them. I
think I felt quite confident in maths when I was little. I remember especially in the
early years we would have maths and I would get good marks and I kind of enjoyed
it. We got to do lots of hands-on activities. I really liked the games and things like
that and I also enjoyed when we would do maths tests and things like that, studying
for it and then, you know, doing the test and then seeing “oh I‟ve done a good job”. I
guess as I got older, my confidence sort of dropped a little bit but I did enjoy it. Even
in high school, even though I didn‟t pursue I guess the most academic maths, I only
did maths A, I still enjoyed that. I enjoyed studying and learning the different
formula and being able to apply that. When I was at uni, I did a few good maths
courses and had some really good lecturers. So, I guess for me as a teacher, it helped
me understand how to teach maths better and do that in more exciting ways. It got
me interested in it and wanting to find out more and making sure that I taught
children maths in exciting ways, engaging ways and real life.
So you’ve noted a lot of positive experiences in primary school so I’m wondering if
you can recall any specific incidences that you feel impacted on your attitude.
I remember in Grade 2, we had maths groups and I was in the kangaroos maths group.
We got to do different games and the parents came in to help and it was once a week
I think. We got to rotate through the different games and I think we also got to do
cooking and I really enjoyed the cooking in maths, the counting and the measuring
and all that. So, I guess that‟s something specific that I remember and all the games
and stuff the teacher would make. I really enjoyed doing them so they‟re probably
the main areas I remember, the cooking and the games.
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So you’ve talked about the studying part both in your primary years and your high
school years and enjoying doing well out of that. Can you elaborate on that for me?
I think when I was in high school, especially the studying aspect I enjoyed more
because it gave me a chance to go back in my own time go through and read the
maths text books and go back through the exercises. It gave me more of a chance to
understand and I felt that in class we were sometimes a little bit rushed and things
like that. But, going back and studying for it and looking at it again and again helped
me understand it more. It helped me get a greater knowledge of it in my own time
and then when I was really able to understand. I felt a lot more confident. I was able
to do the exercises better and perform better on the test and things like that.
So you’ve talked about your uni maths courses and having really great lecturers and
that you’ve brought a lot of that into the classroom, can you elaborate on that.
When I was at uni, we had to choose a major and I chose maths to major in. I chose it
because I didn‟t feel confident to teach maths. I wanted more information and it
looked really interesting. I particularly liked the last subject in that major because we
got to work with a child in a one-on-one situation. It helped me, I guess, work out the
best ways to work one-on-one, help their learning difficulties and diagnose their
difficulties in maths and then work with them to overcome them and help them gain
a better understanding. Also, I really enjoyed, we got to make a lot of maths games
and work out the best activities and ways to teach maths and overviews as well. I
really enjoyed the maths games and I guess working out, even working out the more
difficult areas such as problem solving and even division with two digit numbers, we
had to think about exciting ways to teach that. I guess that made me think “What‟s
the best way to teach maths?” It‟s not just when they get a bit older a text book, that
you can still use maths games and things like that.
You’ve talked about your experiences in primary school in a positive way and you’ve
talked about your uni maths courses and how they’ve really impacted on you in a
positive way. Which do you feel has had the greatest impact on your attitude and
your teaching practises?
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That‟s hard. I guess primary maths laid the foundations for a positive attitude but I‟d
have to say that uni maths had the greatest affect on my attitude towards teaching
maths and in a primary setting. It gave me the strategies and helped me work out it
wasn‟t just what we did but the why and the how behind the activities.
So can you think of specific activities that you’ve either brought with you from your
experiences in primary school or that you learnt in uni and thought were really great?
I guess in uni when we made a lot of games. I‟ve used a lot of the games in a Prep
and Year 1 setting. Games to develop one-to-one correspondence and board games to
develop simple addition skills. I‟ve got some board games and memory games to
develop money skills, money recognition and simple coin adding. I guess too, I try to
do cooking which is an activity that I remember from primary school, so it‟s
something I think the children will enjoy and it also helps them learn maths in a more
real life setting.
So you touched on a bit earlier about how you really enjoyed studying and you
enjoyed getting things back to know that you were doing well, so can you talk about
how you did know that you did well in maths.
I guess I knew I was doing well or that I was good at maths because I felt I
understood it. Especially through going back and doing exercises again. I guess I felt
that I understood it and was more confident with it and I could go to the more tricky
exercises or in the next lesson. I was able to do the exercises and keep up with the
rest of the class and things like that, so I guess I felt I understood. Then you get back
tests and things like that, especially in high school it is very test based, and if you got
a good mark then that sort of reaffirmed my feeling in that stage of life.
So you’ve talked about primary school, high school and uni having an impact on the
development of your attitude. Is there anything else which may have contributed to
your attitude towards mathematics?
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I guess when I was at uni and stuff and had a part-time job we had to count out
change and add up the prices of things and work out percentages off when we had
sales because I worked in a shop. So doing all those things, you had to do them in
your head and be good at them and quick at them and accurate at them otherwise the
business wasn‟t going to be happy. When we had to add up the cost of things at the
end of the day and even working out the cost price of things that would come in, we
had to add 10% and double that to work out the price we would sell it at. We had to
do all those things so I guess as a teacher it is important to me. Especially with
money and coin recognition at this early stage, that children learn that and are able to
do that because obviously when they get older through work and things like that,
they have to know money. They have to know how to add and they have to be able to
realise that their answers are reasonable as well otherwise, especially in a business, it
won‟t work.
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Linda – Neutral attitude
The results from the ATMI suggest that you have a neutral attitude towards
mathematics. Can you discuss how and when you believe this attitude formed?
There were no specific incidences that I remember in primary school. I don‟t, I‟ve
never been good at maths. That became apparent when I became a high school
student. I just could never ever understand the concepts, particularly past grade 10, I
would say. So, I think my struggling with maths and being aware that I was
struggling has made me aware, has made me neutral towards maths I suppose about
not being good. I think if I was better at it I would probably have a more positive
attitude towards it.
So you said that you can’t recall any specific incidences in primary school. Can you
discuss some of your experiences after primary school though?
I remember specifically my teacher spending a lot of, especially in year 11 and 12. I
think that‟s when I struggled the most, he spent a lot of time 1 on 1 trying to help me
understand concepts. Even with that help, I just couldn‟t wrap my head around what
he was trying to teach me. I couldn‟t either remember the formula or I couldn‟t apply
the formula correctly. I would get frustrated, I suppose, that I just couldn‟t get it
when I could understand so many other things and didn‟t have any other problems in
other subjects.
So at the moment you are teaching in the early years and as a teacher in the early
years you have to teach mathematics to children. Can you discuss that for me.
I feel quite comfortable teaching maths in the early years. I really enjoy being able to
teach it with hands-on resources in a way that will facilitate their understanding. I
think I feel comfortable with it because I completely understand all of the concepts
that I am required to teach them. If I had to teach in an upper primary classroom, I
think I would be more hesitant. I still get quite anxious at staff PD session, staff
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mathematics sessions where maths games are played and I worry that I am not going
to know the answer in front of other staff.
So what has led you to the particular teaching methods for mathematics that you use
in your classroom?
Mostly what I learnt at uni about how children learn best. Also, I had one particular
fantastic prac teacher who we would talk a lot about teaching of maths and the best
way to teach maths. I also have friends who are teachers and we talk about what,
good ways to teach mathematics to young children. We have professional
development at school which continues to inform my teaching and I still do reading
of articles and things I come across through school, just to keep updated with best
teaching practice.
You have recalled memories from high school onwards relating to mathematics. Can
you recall any memories from primary school? If not why do you think that is?
No, I don‟t have any that I remember except like I think because I was quite capable
of coping with all of the curriculum in primary school so the only things I remember
from primary school are things where I was given negative feedback. I remember in
Grade 3 in particular, a teacher asked me to do some cutting for her because I was
good at cutting. I had some scissors that weren‟t very good that day, they were a bit
stiff, and so my cutting wasn‟t very good. I remember her not chastising me but
making a comment that it wasn‟t as good as I normally do and I remember being
devastated about that. So, I think I only remember the negative feedback that I
received and because I was capable of doing the maths in primary school. I don‟t
remember any specific negative feedback.
Can you go back and elaborate on your experiences with your prac teacher?
I think this particular prac teacher was the first instance where I was able to see what
uni was telling us was best practice teaching which was hands-on learning. I was able
to see that in practice with her in her classroom. Whereas, previous pracs, the
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children were learning maths from a text book or not learning maths as the case may
be. So, I think actually seeing it in practice seeing how it can work, learning about
how to arrange and organise maths groups, how to come up with activities for them
was really beneficial.
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Yvonne – Neutral attitude
Your results from the ATMI suggest that you have a neutral attitude towards
mathematics can you tell me about how and when you believe this attitude formed?
Ok, at primary school I really did not like maths at all. I think I have always been
more language, creative way inclined than mathematical. Then, at high school I
continued to not enjoy mathematics. I did do maths B but I did well and it was my
6th subject and I really didn‟t enjoy it. Then after school, I didn‟t do too much maths
but since teaching it and going back to basics and doing it that way, I quite enjoy
teaching maths. The more that I have taught it, I guess I am more willing to approach
mathematics. Even professional development, I‟m more interested in it now than I
would have been when I was in school.
You mentioned enjoying maths since ‘going back to basics’ can you discuss this for
me
I think because I really didn‟t enjoy maths at primary school, I didn‟t really put in a
great deal of effort. I almost just switched off I guess in maths lessons. So, perhaps
there were gaps in my knowledge of maths. Since having to go back from the
beginning and looking at how I would explain it and you know all the nitty gritty
kinds of things, I‟ve found it more enjoyable. I do quite enjoy teaching maths which I
never thought I probably would.
Does your attitude towards mathematics affect you in any way?
I made like a conscious effort to make maths more hands-on and fun. So, we do like
a lot of games and linking it to I guess real life skills. That‟s because when I did
maths at school, a lot of it, especially high school, I thought I‟m never ever going to
need any of these skills so it didn‟t really seem very relevant. I try to link it in as
much as I can so that the kids can see the point in doing it and just making it, instead
of worksheets or drills or tests, that was what I did mainly at school for maths, just
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making it more hands on, problem solving, not always right and wrong and just a
little bit more creative I guess.
You mentioned teaching your children with hands on experiences, using problem
solving and teaching them that there is not always a right and wrong answer. Can
you discuss this further?
When I was at uni, the mathematics subjects that I studied were through Mr. B. He
encouraged us to explore games and concrete materials as a way of learning
mathematics and after the children were comfortable with that we moved in to
recording sums and numbers and symbols, more your traditional style. Then it
moved on to applying those skills to problem based scenarios. So, that made a lot of
sense I guess. It seemed to work well. So, that‟s what I started when I first left
university, when I first started teaching. Since then we have done a lot of work in our
school with mathematics consultants which has also tied in with having games and
developing skills until children are comfortable with that and then applying it to real
life situations.
Can you recall any specific incidences involving mathematics that have had an
impact on you?
At high school when we did maths B and I forget what I was going to say - Have
there been any specific incidences that have impacted on you – in Years 11 and 12,
doing maths B, all of our assessment was through tests. So, I used to rote memorise
formulas and certain procedures that you had to do for equations but didn‟t actually
understand the process. I pretty much did what I had to do to pass but never enjoyed
maths or got anything academically or motivationally out of it. When I was in lower
primary, from probably preschool to Year 4, I don‟t really have many recollections
of studying maths at school. I remember doing reading rotations or writing certain
things and doing science projects. In Year 3 I remember we did a maths test and
there were shapes on the page and I don‟t know if it was a labelling or we had to do
something with the shapes but I obviously hadn‟t listened or I didn‟t understand the
task. I thought it was a Mr. Squiggle drawing so I turned it into this lovely boat or
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whatever it was which wasn‟t obviously what they were after. So my mum and dad
had to come up to school and we had a little meeting about why I had done an art
activity in a maths exam. I don‟t think mum was very impressed about the whole
thing but dad thought it was a good drawing so it didn‟t affect him too much.
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Lily – Neutral attitude
The results from the ATMI suggest that you have a neutral attitude towards
mathematics. Can you discuss how and when you believe this attitude formed?
I don‟t think that I have been very good at maths throughout school. It‟s something
that I have always struggled with and I found it difficult because my mum is a
statistician at university so she‟s very, very good at maths. So, because of that, I have
found it a bit of a challenge. I was never allowed to get a tutor because she was a
statistician. So, my mum always tutored me which did create arguments in our
household, huge arguments. Maths probably never clicked until I got to university
and did it in my business degree, not in my education degree. I do think I have skills
for everyday life but I don‟t have great skills for everyday life. I think that that has
really shaped my attitude towards it.
You said that you do not feel like you are very good at maths, how do you know that?
I failed a lot of my high school, not the top maths, the second maths in high school
and I failed it Grade 11 and 12. I just scraped through because my last semester was
computing and I aced the computing and it was enough for me to scrape a pass mark.
It was just too technical for me. All the equations don‟t click for me really well. It‟s
something that I find really difficult. I‟m really good at all the abstract stuff but when
it came to all the formulas I just could never remember the formulas and they never
clicked really easily. It was something, because it was talking about the formulas of
triangles and things like that, it was just a little bit beyond my skills. Basic stuff I
could do but that was just a bit too you know „pie‟ „tan‟ all that stuff. I‟m going “I
don‟t want to know about this” and the relevance I think. I couldn‟t see the
application of how to apply it and I think that made it quite difficult as well. Maybe
at uni, the stuff was a bit more, or I could see how it was a bit more applicable to real
life. Whereas, in high school it was just things of angles and you‟re just going “I
don‟t need to know”.
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You said that during high school, in particular you couldn’t see the application for
the maths you were doing. Can you discuss this further?
In my high school there was a lot of chalk and talk. So, it was just put on the board
and it was just learn the formula. Here‟s five examples we‟re going to do as a group,
learn the formula, here‟s your questions in your book, sit and do them. There was not,
it wasn‟t clearly explained for me to see the real life application of it and I found
because there was no real life application, it was just theory, that I really didn‟t need
to know. Bad attitude, but yeah. At university in my education degree, I did a
primary school maths subject which was more about how to teach maths. It was done
by Mr. B and I actually had him in my class as a prac teacher. He was one of the
teachers that came in as I was on prac and to see him in the classroom, he had no
clue. He had the theory but could not do any application in the classroom. It was
shocking, absolutely unbelievable but he had the theory behind it. He wasn‟t my uni
lecturer though I just happened to see him on prac as a student teacher and then I
studied his book. I thought that he applied more real life activities, more games, more
child focussed. I guess the maths stuff didn‟t really click until I did my business
degree and I did a basic statistics course. I knew a lot of the lecturers, the theorists
that we were studying, I personally knew them through my mum, so it was a bit more
relevant. I was studying people that I actually knew, so it was a lot more interesting.
Whereas, I didn‟t have that in high school, you know, I‟m studying my friends and
their knowledge. So, it became a lot more interesting I suppose and I had that
connection to the people writing the things.
You said that in uni you studied people you knew, why do you think that made it more
interesting?
It was scientists that I knew through my mum. One of the guys did a lot of stuff for
NASA and his maths was incredibly technical and I didn‟t understand it but what I
was studying was a very basic statistical analysis. Because I knew the man
personally and I had met him and visited him in overseas at his university and all that
sort of stuff, that I‟m actually studying someone that I actually know. Even though I
didn‟t understand his more technical things, what I was studying was the basics and
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it was more interesting for me. Some of the other people that I knew in Australia
through my mum, they were people that I knew, so I was a bit more interested in
studying it. It wasn‟t just some application to analyse this data that wasn‟t relevant or
I‟m just going yeah it‟s some stranger who‟s written something which is really
exciting if you are into it. These were people that I knew you know, so it was even
though it wasn‟t stuff that I could apply it was stuff that was interesting because I
knew the person and I could connect to the actual scientist rather than the theories
that they were doing.
You talked about a lot of your high school experiences, the chalk and talk, not seeing
relevance but then in uni seeing more of the real life application through games and
a child focus. How have these experiences impacted on your teaching?
I really think it‟s more to do real life problems and explain to children where the
application is of doing these activities like if it‟s working out. Like, you might give
them a problem, you know a sausage sizzle. How many sausages am I going to buy?
How much will we sell them for? It might have something to do with camp, how
much will it cost? So that they can see that the maths has an application. I had a
primary school teacher, my year 7 primary school teacher, who used to stand at the
front of the board and always say “Why are you doing it like this”. So, it would take
two weeks to teach us to do addition, but I really got a good understanding of why
I‟m trading, why I‟m doing the re-grouping and he would make us explain it over
and over and over. That really cemented it for me in my head, how re-grouping and
trading works and that sort of thing. Then, I kind of lost the plot in high school
because it was chalk and talk. There was no real life application. So, I try to bring
back into my classroom that real life application, that there is a reason why we are
doing it. That it is something that we can use. That the skills have a purpose. That it‟s
not just something you just have to know. I was going to say that maybe because
maths can be abstract and it is hard to see that real life application for it, because it is
taught or is quite frequently taught as a separate subject away from being integrated
[that it is hard to teach and learn]. It‟s not like you‟re writing an invitation to invite
someone to a party because that‟s what we do in the classroom and that‟s what we do
in real life. Quite often it is or does sit separately and it‟s not an integrated subject or
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its not problem based enough to become an integrated subject. It does have that
separation to it and it does sit by itself. You can integrate Science, SOSE and
Technology into whatever unit you are doing. Whereas, it‟s a lot harder to integrate
maths. You have to work as a teacher, a lot harder to integrate maths and you have to
spend the time to create activities that do integrate a lot more. Then, you tend to go
nah, I don‟t have time for it it‟s the last thing you get to. I come into it with the
attitude that I‟m not great at maths, so it is the last thing I get to because it is a bit of
a chore for me to do. I have to put the effort in to plan for those lessons. So, because
I have that background in me maybe I don‟t always put the best into doing the kids
maths lessons because it is a bit of a challenge for me to make it real life, to make it
interesting to make it easier for the children to understand.
What is the challenge?
Because I haven‟t had good experiences with it, it does make it a challenge. Even
coming up with the ideas of how to link it in. I would like to have a better
understanding of financial literacy, more real life skills. I would have liked to have
been given that in high school. All the stuff that you learn day to day, how to deal
with money, how to invest money, that sort of stuff is what I would have liked, more
than the stuff that doesn‟t apply. Maybe in primary school, where it is more of the
foundation stuff, how to add, how to subtract, how to read a clock, to know what a
square and a shape is, that foundation stuff is easy. I can do that stuff. When it gets
up to higher Grade 6, Grade 7, into high school maths when it is more the abstract
stuff, the formulas that I struggle with myself. Trying to teach it to someone else is a
bit of a challenge when I‟m struggling to understand it. We did a Science unit that
used all those powers of 10and when I‟m struggling to understand it, I would be
writing it on the board wondering if I had the right number of zeros in it. If adults are
struggling to understand the application, then we are not teaching it very well to kids
and we are struggling to impart that knowledge to kids. Kids were picking it up faster
that I was which you know is not setting a really good example but I don‟t have that
knowledge to give to kids. The kids were teaching me more than I was teaching them
because they could pick it up faster than I could.
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You have discussed how you have on occasions felt that you didn’t understand what
you had to teach, can you elaborate on this.
I really chase any PD‟s that are offered to do with maths and try to develop my own
skills on it and get new ways to teach it, new ideas to teach it, new strategies to try
something different. Doing some of the maths program at school that I either love or
hate, whatever I can get my hands on. I‟ll have a go at, to try to improve my own
skills and then try to teach it in a different way or develop my own skill in a different
way. I think because I know that I am not good at it, it is something that I do try to
work hard at to improve knowing that it is a fault of mine.
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Sandra – Neutral attitude
Your results from the ATMI suggest that you have a neutral attitude towards
mathematics. Can you discuss how and when you believe this attitude formed.
Ok, my maths [attitude] mainly formed when I got to upper primary. I didn‟t really
enjoy it as much. I think it became harder as well and I didn‟t understand it.
So you said that in upper primary you felt that the maths got a lot harder and you
didn’t understand it, can you discuss that further for me.
Ok, it was mainly the problem solving that I didn‟t understand. I wasn‟t willing to
delve, I didn‟t know how, I wanted the quick answer and I didn‟t know how to delve
into it deeper.
Your results from the ATMI suggest that your self-confidence is very low but you
strongly disagree with wanting to avoid teaching mathematics. Can you discuss this.
Actually, teaching mathematics in the early years I‟ve found easier to do. Mainly
because I have had more understanding of it, going through uni, just learning more of
the skills. I‟m more confident in that early childhood part but when I have to go, like
if I had to do teaching in the upper primary, I don‟t think I would feel more confident.
So you said at uni that that really helped your understanding of mathematics so was
there anything in particular that they did that had an impact on that do you think?
It (university) was a hands-on approach as well just looking at different ways that
children had different thinking. We looked at how they would use those strategies
and how you would steer them in the right direction. So, there wasn‟t just one right
way but different ways of finding the answer.
Can you recall any specific incidences which you think may have impacted on your
attitude toward mathematics?
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Right, probably long division [impacted on my attitude]. When I was doing that, I
did not get the concept at all. I did not understand it and I felt just that I was defeated.
So, I couldn‟t do it. I think I had ways I got around it because I felt defeated. Ways I
got around doing maths and stuff like that was having extra tutoring and stuff so I
would get the confidence in me.
So, how do you know that you were defeated, how do you know that that was the case?
Because I was told I was wrong and I just kept getting the wrong answer all the time.
So I think my confidence just fell.
Can you discuss that a bit further for me, so when the teachers were giving you
feedback about how you were going, like what did that entail?
It (teacher feedback) was mainly that they said it was wrong but I still can‟t
remember them actually teaching me the right way of doing it. It was all like “you‟re
wrong you‟re wrong” and it was like I had to do the problem solving of how to get it
right. I felt like no-one else was helping me.
So have your past experiences impacted on your teaching in any way?
I think learning different ways [of teaching]. So, if children don‟t know how to do it,
I find a different way [to teach it] to find ways and see where their thinking is at as
well.
What experiences are you referring to?
Because of uni and my experiences as well. So, it‟s a whole holistic approach
basically.
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So is there anything else in particular from your schooling experiences that you have
tried to re-create in your teaching or that you have avoided in your teaching because
of your experiences?
You want to do the best teaching practices you can and you sometimes feel like
you‟re struggling because you don‟t get it, then you won‟t be able to teach it the best
way. I do try to teach as best I can so the children do get it.