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Learning, Culture and Social Interaction

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Tapping into the mental resources of teachers' workingknowledge: Insights into the generative power ofintuitive pedagogy

Lina Markauskaite ⁎, Peter Goodyear 1

Centre for Research on Computer Supported Learning and Cognition (CoCo), Faculty of Education & SocialWork (A35), The University of Sydney, Sydney, NSW 2006, Australia

a r t i c l e i n f o

⁎ Corresponding author at: Centre for Research on Coof Sydney, NSW 2006, Australia. Tel.: +61 2 9036 5320

E-mail addresses: [email protected] Tel.: +61 2 9351 4708; fax: +61 2 9036 5205.

2210-6561/$ – see front matter © 2014 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.lcsi.2014.01.001

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a b s t r a c t

Article history:Received 13 February 2013Received in revised form 29 November 2013Accepted 3 January 2014Available online xxxx

This paper provides novel insights into the kinds of mental resources on which teachers drawin their pedagogical sense-making (about everyday teaching decisions), and into the origins ofthese mental resources. The paper examines how teachers' knowledge is grounded in diversesocial, cognitive and metacognitive experiences of learning and teaching phenomena. Itcontributes to the development of new ways of theorising the links between (a) experientialknowledge resources, which originate in specific activities and interactions, and (b) anintegrated conceptual understanding that organises professional sense-making across diversesituations and contexts. By combining conceptual ideas about knowledge fragmentation withoriginal empirical observations from a study of the form and functioning of teachers' workingknowledge in higher education, the paper advances two lines of theoretical argument. Firstly,teachers' working knowledge is better seen as contextualised and fragmented rather than as asystematic personal theory. There are advantages to pedagogical ‘knowledge-in-pieces’ thatcan be activated and combined in different ways in interaction with various contexts.Secondly, pedagogical ideas and ways of knowing that originate in one's personal experience(‘intuitive pedagogy’) can be a productive resource in teacher thinking, action and professionallearning. The paper suggests that the view of professional learning in, and through, practiceshould be expanded from its traditional focus on social and material interactions to alsoinclude the consideration of simultaneous interactions with one's mind.

© 2014 Elsevier Ltd. All rights reserved.

Keywords:Teacher working knowledgeMental resourcesIntuitive pedagogyHigher educationSociocultural–cognitive perspective

1. Introduction

1.1. Background: teachers' working knowledge

Research on teachers' knowledge and expertise broadly agrees about the complexity of teacher knowledge and knowing(e.g. Bromme, 1994; Calderhead, 1996; Minstrell, 1999; Shulman, 1986, 2004; Winch, 2004). It includes not only propositionalknowledge, facts and formal concepts, but also skills, hunches and beliefs. This paper focuses on what Yinger and Lee called ‘workingknowledge’ in teaching: the kind of knowledge that is “particularly useful to get things accomplished in practical situations” (Yinger& Hendricks-Lee, 1993, p. 100). Other terms have been used for similar kinds of knowledge and knowing, such as ‘knowingin action’ (Schön, 1995), ‘actionable knowledge’ (Argyris, 1999), ‘action-oriented understanding’, ‘personal practical knowledge’

mputer Supported Learning and Cognition (CoCo), Faculty of Education and Social Work (A35), The University, fax: +61 2 9036 5205.u (L. Markauskaite), [email protected] (P. Goodyear).

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, & Goodyear, P., Tapping into the mental resources of teachers' working knowledge:ing, Culture and Social Interaction (2014), http://dx.doi.org/10.1016/j.lcsi.2014.01.001

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(Clandinin, 1985), ‘metis’ (Baumard, 1999) and ‘sense-making’ (Weick, 1995). This knowledge includes various kinds of thinking andunderstanding, including conceptual or structural knowledge (‘What’), procedural knowledge (‘How’), strategic knowledge (‘Why’)and contextual knowledge (‘When’) (Atkinson & Claxton, 2000; Jonassen, 2003; Shavelson, Ruiz-Primo, & Wiley, 2005). However,working knowledge is distinct from the formal concepts, strategies or rules of reasoning that are often held to constitute professionalknowledge bases. Working knowledge involves diverse knowledge resources that are used functionally to organise one'sunderstanding, make plausible sense of encountered situations and act sensibly (cf. Greeno, 2012).

A professional's ‘working knowledge’ involves explicit and implicit components (Collins, 2010; Eraut, 2000, 2007; Perry, 1965;Sternberg & Horvath, 1999). Explicit knowledge is knowledge that a person can articulate with relative ease. It often refers to moresystematic types of knowledge – including normative and empirical – that can be characterised by a unified conceptual basis andlogical connections between parts (Winch, 2004). Such accessible and integrated knowledge is seen as a key ingredient ofexpertise in most accounts of teacher professional practice, whether rationalistic, reflective or critical (Furlong, 2000). Implicitknowledge is less readily available to consciousness and is harder to put into words. Such knowledge is often grounded inexperience and useful for practical decisions. However, it can rarely be represented in an articulated, systematic fashion orjustified without referring to one's ‘commonsense’ (Atkinson & Claxton, 2000; Collins, 2010; Perry, 1965).

Implicit knowledge can arise in several ways. For example, repetition and practice in professional work can lead to somemental processes becoming automatic — not requiring conscious attention. In some cases, this knowledge originates in explicitlylearnt principles which experts can articulate when requested. In other cases, it is deeply tacit and not readily available forintrospection (cf. Collins, 2010; Ohlsson, 2011). The ability to use implicit knowledge in fluent expert performance is highlyvalued in complex individual and collective professional work, including teaching (Atkinson & Claxton, 2000; DiBello, Missildine,& Struttman, 2008; Sternberg & Horvath, 1999; Torff & Sternberg, 2001).

In contrast, some other kinds of implicit knowledge, such as the knowledge that arises from everyday experience, is not sohighly valued and is often referred to as a ‘folk’ or ‘naïve’ way of understanding. Examples include the ‘naïve conceptions’ (or‘alternative conceptions’ or even ‘misconceptions’) identified by researchers in science education (e.g. Driver, 1989; Vosniadou,2002). Similar kinds of ‘commonsense’, ‘folk’ or ‘naïve’ ways of understanding learning and pedagogy – acquired througheveryday experiences – are typically also considered as primitive, inconsistent and counterproductive in the development ofteacher expertise (e.g. Torff, 1999). Just as the ‘everyday conceptions’ of scientific phenomena, acquired through directengagement with the physical world, are sometimes held to interfere with the adoption of scientifically accepted ways ofunderstanding those phenomena, so, it is argued, everyday personal experiences of learning, teaching and other social andcognitive phenomena create a ‘folk pedagogy,’ and ‘folk psychology’ (Olson & Bruner, 1996), which is held to interfere with theadoption of more systematic, evidence-based, theoretically coherent ways of understanding teaching and learning phenomena,and therefore should be confronted and replaced with ‘expert like’ pedagogical understanding (e.g. see Ho, 2000; Ryan & Healy,2008; Torff, 1999).

Sharp oppositions between tacit and explicit, commonsense and specialised, functional and formal, fragmented and coherenttypes of knowledge have been contested in both professional practice and education. It is proposed that some kinds of intuitiveknowledge cannot be replaced by explicit or specialised knowledge (Collins, 2010; Greeno, 2012; Gupta, Hammer, & Redish,2010; Perry, 1965; Polanyi, 1966/2009). For example, Perry (1965) argued that different kinds of knowledge often draw on eachother, and while “(1) commonsense is not sufficient for problems that require specialised treatment, (2) it is needed in additionto specialised knowledge to make complete sense of the specialised treatment by relating it to general experience” (p. 126–127).Perry identified several distinct functions of commonsense knowledge. First, commonsense provides a body of knowledgewhich is not set before people in specialised technical discussions, but is needed to make these conversations intelligible. Second,while specialised knowledge facilitates deep investigations, commonsense helps to establish the relevance of different kinds ofspecialised knowledge to practical situations. Third, Perry suggests that there is a close interaction between the development ofspecialised knowledge and experiential, commonsense understanding. Different types of specialised knowledge arise fromexperience and, when specialised knowledge is available, commonsense draws on ideas from specialised knowledge to makeexperience intelligible.

Further, a number of studies have questioned whether experts always draw on one coherent, formally articulated conceptualbase in their practical decisions. For example, Chi and Ohlsson (2005) noted that knowledgeable people often operate withinconsistency and that this might indicate an intellectual flexibility rather than a lack of expertise. Similarly, Gupta et al. (2010)have depicted physicists flexibly and productively drawing upon, and switching between, scientifically correct and ‘naïve’ontological categories in their reasoning about complex scientific phenomena. They argue that multiple ways of thinking, whichare sensitive to the context, are an important part of expert epistemology. Similarly, studies of concept formation in professionalactivities provide increasing evidence that manifold ways of meaning making, and fluent use of “formal” and “everyday” concepts,are key enablers of shared meaning making, learning and conceptual change (e.g. see Engeström & Sannino, 2012; Greeno, 2012).

In the current intellectual climate of evidence-based practice and reflective thought, explicit, articulated forms of knowledge,and deliberative, conscious, thinking and reflection tend to be the main focus of teacher development programmes and research.In contrast, less internally consistent and less well articulated forms of knowledge and learning tend to be under-theorised andundervalued (Atkinson & Claxton, 2000; Eraut, 2000).

Further, as Billett (2006) points out, some accounts of professional learning tend to privilege the role of social aspects, such asthose provided by communities of practice and activity systems in specific situations. In so doing they downplay the role ofindividual aspects, such as the contributions of one's earlier experiences, intentionality and subjectivity, all of which guidecognition and learning throughout a working life. As Billett points out, the concept of learning and development over a life span

Please cite this article as: Markauskaite, L., & Goodyear, P., Tapping into the mental resources of teachers' working knowledge:Insights into the generative power..., Learning, Culture and Social Interaction (2014), http://dx.doi.org/10.1016/j.lcsi.2014.01.001


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requires a far more detailed analysis of the relational interdependence between individual cognition and social interaction.Similarly, it demands far greater attention be paid to the obscured connections amongst primordial feelings, action and theconscious mind (Barsalou, Breazeal, & Smith, 2007; Damasio, 2012; Siegel, 2012).

1.2. Aims

In this paper, we aim to provide some insights into the relationship between the individual and the social contributions byexploring how teachers' professional sense-making and knowledge are grounded in diverse social,material and cognitive interactionsand experiences. Drawing on insights from our empirical research and the theoretical perspective of ‘mental resources’ and‘knowledge-in-pieces’ (cf. diSessa, 1993, 2000; Hammer & Elby, 2002; Minsky, 2006), we aim to suggest a new way to theoriseintuitive pedagogical ideas and to investigate their role in teachers' working knowledge. Our perspective contrasts with a moretraditional view of commonsense pedagogical understanding as a primitive, unproductive, and generally problematic resource thathas to be superseded by more sophisticated forms of pedagogical knowledge or reflected professional experiences. We propose thatexperiential ideas and ways of creating knowledge alongside other kinds of knowledge and knowing play a constitutive role inteachers' pedagogical sense-making, actions and learning. Rather than treating all initial intuitive knowledge resources andcommonsense ways of knowing as crude and unproductive, we recommend paying more attention to their generative features.

In Section 2, we elaborate our arguments about the nature and form of teachers' knowledge and the role of direct experiencein its formation. We summarise two different perspectives on knowledge, knowing, and personal epistemology and introduce thenotion of ‘knowledge-in-pieces’. To illustrate and advance our theoretical argument, in Section 3 and Section 4, we present amethodology and some findings from a study of teachers' working knowledge. We draw on a series of observations andstimulated interviews with an early career university teacher and explore two main questions:

(1) What sorts of mental resources did the teacher typically draw upon during her explanations of teaching decisions?(2) What were the main origins and sources of these mental resources?

We illustrate how the teacher's working knowledge can be understood as contextualised and fragmented – as ‘knowledge-in-pieces’ that can be combined in different ways in various contexts – rather than as a uniform, systematic personal theory or belief.Then, we show how ideas about teaching and learning that originate in direct personal experience can be productive resources inteacher's everyday sense-making and learning.

In Section 5, we provide a theoretically-grounded interpretation of the empirical outcomes that foreground our claims about(a) the explanatory power of this fine-grained conception of working knowledge (‘knowledge-in-pieces’), and (b) the generativepower of intuitive pedagogy, and its connections to professional learning. Section 6 draws conclusions and outlines possibilitiesfor further research.

By ‘intuition’ we mean “a loose-knit family of ‘ways of knowing’ which are less articulate and explicit than normal reasoningand discourse” (Claxton, 2000, p. 49). We use the term ‘intuitive pedagogy’ (Johansson & Kroksmark, 2004), to describe thoseaspects of a teacher's working knowledge which are derived from direct personal interaction and experience, and which oftentake an implicit commonsense form, rather than being expressed in formal language or as articulated principles.

2. Conceptual perspectives on knowledge, knowing and personal epistemology: coherence vs. fragmentation

2.1. Professional knowledge as coherent ('theory-like')

Theories of professionalism have generally claimed that professional knowledge is:

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usually systematic, having a unified theoretical basis with close logical connections between its main parts, whethernormative or empirical. Piecemeal and inconsistent theoretical bases are unlikely to count as professional knowledge, norare empirical bases that are not generally accepted as true.

[(Winch, 2004, p. 181)]

Similarly, studies of expertise have also suggested that experts generally possess a coherent, well-integrated ‘theory-like’abstracted knowledge that can be retrieved in large, systematically organised chunks when the situation is right (e.g. see Ericsson,Charness, Feltovich, & Hoffman, 2006). Further, not only experts, compared to lay people, possess a more complete body ofknowledge, but also their knowledge is organised differently, they attend to different features of the situation and they approachproblems in a fundamentally different manner.

Some influential theories of learning and conceptual change have followed a similar ‘theory-like’ line of argument. For example,they have related students' difficulties in understanding scientific concepts to the possession of ‘theory-like’ misconceptions oralternative belief systems (cf. Chi & Roscoe, 2002; Vosniadou, 2002). This view suggests that learning must involve a ‘radicalconceptual change’ during which a misconception, or entire false theory, is reconstructed and replaced with a correct one. Suchchange might happen over a shorter or a longer period of time, but it should be precipitated by an explicit ‘cognitive conflict’ andrational argument that enable students to abandon their existing ‘naïve’ conceptualisations (e.g. Slotta & Chi, 2006).

Just as people possess conceptual knowledge for making sense of physical phenomena, they also possess epistemic knowledgeor beliefs for making sense of cognitive phenomena. Some dominant perspectives on personal epistemology have similarly

e cite this article as: Markauskaite, L., & Goodyear, P., Tapping into the mental resources of teachers' working knowledge:hts into the generative power..., Learning, Culture and Social Interaction (2014), http://dx.doi.org/10.1016/j.lcsi.2014.01.001



claimed that one's beliefs about knowledge and learning are quite stable and coherent (e.g. see Brownlee, Schraw, & Berthelsen,2011; Hofer & Pintrich, 2002). They are said to develop in quite an orderly fashion, in several stages, from naïve simplisticviews to increasingly more sophisticated understandings of epistemic phenomena. People may shift to a more sophisticatedepistemological position, but once they have shifted, they do not move back, and they typically apply a consistent epistemologicalframework across a broad range of situations.

Research has commonly conceptualised teachers' pedagogical conceptions – beliefs about teaching and students' learning –

in a similar, ‘theory-like’, way (for a review see Kane, Sandretto, & Heath, 2002). Teachers' understandings of pedagogicalphenomena have commonly been classified into a small set of relatively coherent and stable categories, ranging broadly between“teacher-centred” and “student-centred” conceptions. As Kane et al. (2002) point out, many studies have found that teachers'beliefs “exist in a tacit or implicit form”, are “difficult to articulate” and are “robust and resistant to change” (p. 180).

Studies following this theoretical line have successfully identified certain general categories of pedagogical conceptions.However, many of them are less successful at explaining observed inconsistencies between ‘espoused’ teachers' views and theirnumerous ‘theories in use’ — how to act in specific teaching situations (e.g. Eley, 2006; McAlpine, Weston, Berthiaume, &Fairbank-Roch, 2006). Some studies have noted that teachers' conceptions of epistemic and pedagogical phenomenamay be moreflexible and context-dependent (cf. Brownlee et al., 2011; Gonzalez, 2010; Khine, 2008). Nevertheless, most have implied thatteachers' beliefs are generally systematic, abstract, developmentally coherent and hard to change.

2.2. Professional knowledge as fragmented (‘knowledge-in-pieces’)

In contrast, some research on conceptual change and personal epistemologies in science education has been challenging theassumption that people's understanding of scientific ideas, and of the nature of knowledgemore generally, is best thought of in this‘theory-like’ way. This new line of argument has its origins in Toulmin's (1979) ideas about conceptual ecology, and has beenadvanced (empirically) mainly through the work of diSessa and colleagues on the development of understanding in physics(diSessa, 1993; Hammer, 1996).More recently, it has been extended to the area of personal epistemologies (Hammer& Elby, 2002)and the re-conceptualisation of transfer (diSessa, Elby, & Hammer, 2003; Hammer, Elby, Scherr, & Redish, 2005; Wagner, 2006).

According to this approach, one's conceptual resources include a large array of (mostly implicit) knowledge ‘in pieces’, whichdiSessa (1993) called ‘phenomenological primitives’ (or ‘p-prims’). These enable an individual to understand the phenomena ofthe physical world. P-Prims form a layer of knowledge between ‘hard-wired’ direct experience and conscious concepts. Theyconsist of an individual's interpretation of an observable phenomenon, which is repurposed to explain the same or similarphenomena encountered in the world. This kind of knowledge is readily activated when the context is right. Similarly, peoplepossess a large array of epistemic resources that enable them to understand cognitive phenomena (Elby & Hammer, 2010;Hammer & Elby, 2002). These too can be seen as context-sensitive, rather than deeply systematic. While these intuitiveknowledge resources might sometimes be activated incorrectly, which would lead to a misinterpretation, in general, p-primsprovide a powerful generative mechanism for building one's conceptual understanding. Learning, from this point view, does notinvolve rejecting intuitive ideas, so much as refining and integrating experiential resources into a stronger, more normativeconceptual system. This perspective also offers a powerful reconceptualisation of transfer, in the context of situated learning, whichcan be understood,

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… not as the all-or-nothing transportation of an abstract knowledge structure across situations, but as the incrementalgrowth, systematization, and organization of knowledge resources that only gradually extend the span of situations inwhich a concept is perceived as applicable.

[(Wagner, 2006, p. 10)]

While most empirical studies have applied the ‘knowledge-in-pieces’ framework in well defined knowledge domains, such asphysics and mathematics, Minsky (2006) has applied a similar line of argument to various everyday situations that combineunderstandings from multiple realms. He suggests that human resourcefulness with respect to creativity and practicaldecision-making comes not from one's ability to entertain systematically one particular point of view, but from the capacity tointerpret situations flexibly by switching between different frames of reference and entertaining simultaneously knowledgeresources from multiple realms.

Knowledge of teaching, like knowledge of physics, has a similar character — intuitive, grounded in culture, experience andinteraction (Olson & Bruner, 1996; Ratcliffe, 2006). As Strømsø and Bråten (2011) argue, teachers in higher education rarelyundertake any formal study of teaching and their understanding of learning, teaching and knowledge is likely to be grounded intheir own experiences as students, and in other encounters with epistemic phenomena, such as in their research (see also Kane etal., 2002). While the knowledge required to be an effective teacher may be related to a systematised body of pedagogical theory,much of it depends on sensitivity to the environment, flexibility and situational awareness (Winch, 2004).

Nevertheless, issues in teaching tend to be epistemologically more diverse and open than those in physics. For example,Shulman (1986) argued that teaching decisions involve not only knowledge of general pedagogy, but also knowledge ofdiscipline, students, curriculum, and other aspects of the teaching context. From this perspective, an answer to a specificteaching question might not only be a matter of one's knowledge of normative pedagogical theory, but rather of one's goals andthe situation which requires the simultaneous activation and combination of knowledge resources from multiple realms.




In short, we suggest that a teacher's working knowledge is likely to be dynamic, largely experiential and situationally-crafted,rather than coherent and theory-like. Such knowledge develops gradually by integrating ideas and experiences from diversesituated encounters of a pedagogical phenomenon, rather by undergoing stage-like developments or radical replacements ofone's folk pedagogical theorieswith expert views. This knowledge can, therefore, bemore precisely depicted by various combinationsof fine-grainedmental resources activated in specific situations, rather thanmore coarse constructs, such as “theory-like” conceptionsof, and approaches to, teaching.

We now illustrate the potential of this theoretical perspective using examples from a study in which we investigated types ofknowledge and ways of knowing in pedagogical meaning-making. (This is part of a larger study of the development of epistemicfluency in professional practice. See Goodyear and Markauskaite (2009); Kali, Goodyear and Markauskaite (2011); Markauskaiteand Goodyear (2009, 2011, forthcoming). Our goal is not to provide a detailed analysis of teachers' mental resources, but to offeran existence argument about: (a) a more fragmented (multi-frame) conception of the nature of teachers' knowledge; and (b)multiple sources and diverse epistemic roots of teachers' pedagogical ideas. We illustrate some generative features of teacherexperiential understanding when the teacher makes sense of encountered pedagogical phenomena, learns and makes decisionson how to act in specific situations.

3. Method

Over one semester, we tracked how a young university teacher (pseudonym: Sophie) retrospectively explained for us (a) theteaching decisions she made prior to each lesson, and (b) the actions she took during each lesson. Sophie was teaching part of aone semester course on systems modelling and change to a group of master's students studying learning technology. Sophie hadrecently completed a PhD on a closely related topic and was knowledgeable about systems modelling and its use in educationalcontexts. The course was mainly taught online, using a mix of synchronous (real-time) and asynchronous communicationmethods. Amongst other challenges, the students had to learn how to build system dynamics models using the modellingsoftware STELLA. This was Sophie's third year of teaching the course. (Single participant (‘n = 1’) studies are common in similarconceptual-exploratory research in this area. For a detailed rationale and examples see (diSessa et al. (2003), Goodyear (2002)and Wagner (2006)).

We observed all but one class, collected and analysed all Sophie's teaching resources and notes, and recorded a series of eightsemi-structured interviews with her. We met with Sophie the day after each of the synchronous online teaching sessions andasked her to recall and elaborate retrospectively on (a) the teaching decisions she had made prior to each lesson, and (b) thelesson as she experienced it. Each interview typically included a set of questions, with prompts, about the overall design of thatsession, and selected one or two specific tasks. The interviews were based on the principles of critical decision-making (Hoffman,Crandall, & Shadbolt, 1998) and epistemic interviewing (Brinkmann, 2007). There is an extensive literature on the pros and consof retrospective interviews (e.g. Calderhead, 1981; Ericsson & Simon, 1993; Marcos & Tillema, 2006). As we were interested in thenature of the mental resources that underpin a teacher's working knowledge, tapping into the process of decision-making was notour main purpose. Sophie's accounts of her teaching were anchored in our shared knowledge of what had transpired in theteaching sessions we observed. We have come to believe that such retrospective interviewing, combining critical decision making(Hoffman & Lintern, 2006) with epistemic and phenomenological questioning (cf. Brinkmann, 2007; Smith & Osborn, 2003),provides deeper insights into the ecological nature of teachers' working knowledge than do process-oriented methods, such as“think-aloud” or direct observation.

We used materials and transcripts recorded during the online observations as prompts and posed a number of in-depthepistemic questions, asking Sophie to explain such things as:

(1) Why various decisions were made (e.g. “Could you explain to me why …?”).(2) How she came up with these ideas (e.g. “Where did this idea come from?”, “What inspired you to do it this way?”).(3) Whether she could suggest, and compare her decisions with, possible alternatives (e.g. “Are there other possibilities?”,

“Why have you chosen this design?”).

Our initial questions focused on three main educational design components: tasks, social groupings (e.g. how the studentsshould work together, divide their labour), and the selection of tools and resources (Goodyear, 2005). Then, we asked aboutSophie's and the students' experiences with these tasks and about unplanned teaching decisions made during the class.

The interviews took 45–90 min each and were audio-recorded. The recordings were transcribed in full. We adapted andfollowed an interpretative phenomenological analysis procedure (Smith, Flowers, & Larkin, 2009; Smith & Osborn, 2003). Ouranalysis included four main phases: (a) repeated reading of transcripts and making initial notes; (b) development of emergingthemes; (c) search for connections across the initial themes, using such strategies as abstraction, subsumption and polarisation,and development of the broader categories; and (d) final exploration of relationships and interpretations. That is, we jointlyexplored the language and epistemic meanings in what Sophie was saying. We then identified and labelled themes, reflecting (a)frames of reference, in which knowledge and meanings were situated, and (b) sources or origins of these ideas. Subsequently, weclustered these themes into a smaller number of broader-based categories. In the final stage, we explored key features andrelationships amongst the categories in various contexts, triangulated evidence, and produced final interpretations. Each of thefour stages involved 2–4 iterations. During the last two stages, the outcomes and interpretations were presented for review totwo other researchers, who were familiar with the study aims and approach, but were not involved in the analysis. Their




feedback indicated that the identified categories and interpretations were convincing and communicable, and did not needfurther revisions.

4. Results

4.1. What kinds of mental resources were used for explaining teaching decisions?

Our initial identification of mental resources focussed on the realms (Minsky, 2006) or frames of reference that were salient inSophie's explanations. We found seven such frames of reference. Three (GF1–GF3) refer to more generalmental resources that arenot tightly linked to a specific context. These can be labelled: (GF1) nature of subject matter; (GF2) how people learn; and (GF3)how to teach. Four frames (CF4–CF7) are more contextual and experiential: (CF4) the course; (CF5) the educational environment;(CF6) the students; and (CF7) herself as the teacher (Kali, Goodyear, & Markauskaite, 2011). Short descriptions, and someexamples from each category, are provided in Table 1.

We will focus on four key findings, summarised in the next four subsections: (1) Sophie's constant reference to the contextualframes (CF4–7); (2) the ways in which many of the elements in Sophie's accounts of her teaching integrated ideas associated withseveral frames of reference; (3) the role of personal experience in making judgments; and (4) the contrast between the localcoherence of her explanations of context-specific decisions, and the challenges she hadmaking more distant or abstract connections.

Table 1Examples of the frames of reference.

Frame of reference and description Example

GF1. Disciplinary content and subject nature: ontology and epistemologyof the disciplinary knowledge, key theories and concepts, skills, tools,relationships to practice, etc.

• “The topics are the building blocks” (0828Q20)• “[It] explains a lot of the concepts that you need to know about systemdynamics” (0828Q20)• “They have to understand system dynamics to manipulate the model, butthat's not what they need to communicate to the audience” (1016Q02)• “Because that's what happens in real life. Very few systems are allowed tojust grow exponentially for as long as they want. There's always going to bea limit ….” (1009Q04)

GF2. How people learn: cognitive and social processes, constraints andconditions for successful learning, etc.

• “You need to understand those concepts” (0828Q20)• “If they get a chance to do it themselves and then discuss, they tend tounderstand” (0828Q20)• “It's not something you would normally physically see, so you have to noticethe behaviour of a system over a period of time ….” (1009Q15)

GF3. How to teach: instructional strategies and other pedagogical ideas fordesigning tasks and teaching different kinds of knowledge and skills.

• “The chat I find really good for communicating information ….” (0821Q18)• “It's not much good me just showing them example after example” (0828Q20)• “The small group task [is] for the transfer, that's so they get experience intrying to figure out the transfer options, but again in a group, so they candiscuss it ….” (0821Q18)

CF4. Course: aims, scope, topics covered, expected outcomes and otheraspects of the overall course design.

• “The rest of the subject is about organisational change and about learning tochange, so it's a good tool that fits” (0828Q01)• “It [today's class] goes into that broader systems thinking, being able to applyit in their real lives” (0926Q24)• “The aims are still the same and the general experience is the same. What'schanged this year, I changed the actual task that they'll be doing in their teamsto make it a bit more authentic, to make it something that will also tie in nicelywith the rest of the units” (0821Q08)

CF5. Educational environment: affordances and constraints of the learningenvironment, including time, teaching mode, available tools and otherresources and infrastructure.

• “It's far easier, we have the whiteboard tool there” (0828Q20)• “It's not a big enough class to do that and I would want more lead up time, morepractice modelling before they did that, and it's not the case in this class” (0925Q30)• “I send the materials out early, so if you're doing it online with people in theirworkplaces or homes, send out a model beforehand and get them to downloadit and make sure that it works for the lesson.” (1009Q27)

CF6. Students: learners' previous and expected knowledge, needs,interests, motivation, experiences, etc.

• “I'm not expecting every single one of them to be an expert system dynamicsmodeller at the end, but I want them all to have experience in it” (0821Q18)• “Sometimes I think it's good to do a team task that's really relevant to your job;sometimes, I think, people are happy not to and to experience something new.So, I think it will be good…” (0904Q42)• “That [task] assumes that students have carried out all the other lessonsleading up to that, so it assumes more detail knowledge than these studentshave” (1023Q10)

CF7. Teacher: instructor's aims, experience, knowledge, preferences,feelings, etc.

• “It's too big of a task and it doesn't give me the opportunity to see how they'regoing, to check where they're up to” (0904Q30)• “I prefer for them all to have the same baseline for this particular skill” (0904Q20)• “For me it's mainly to do with what I end up feeling comfortable with” (1023Q36)




4.1.1. Frequent reference to contextual framesAll four of the contextual frames of referencewere common in Sophie's explanations. In particular, Sophie referred very frequently

to different aspects of students' experience (CF6) in her descriptions of her teaching decisions. For example, she typically talked about:the relevance of what she teaches to students: “I made it a bit more authentic” (0821Q8); experience that students already have:“I think it's too hard at this stage” (0828Q44); students' class experience: “they were comfortable in the class” (0828Q38); andstudents' projected experience: “we will discuss them in a couple of weeks once they have some experience in building a model”(0828Q16). (Note: The codes in brackets refer to segments of the interview transcripts. Each of Sophie's quotes is identified with adate and question number, MMDDQnn.)

4.1.2. Integrating ideas across framesDifferent general and contextual frames of reference were often interconnected. For example, Sophie's explanations included

general statements about teaching and learning (i.e. how to teach; how people learn), and statements blended with the subjectmatter (i.e. system dynamics), course aims, students' experiences, etc. In some cases, almost all the categories were intertwined. Forexample, in one of the first interviews, we discussed the history and established pedagogical approaches for teaching this subject inhigher education. Sophie readily named the leading educators and described differences between their “schools of thought”. Whenasked, “Against this background, what does your [course] unit look like?What school do you subscribe to?”, she answered as follows.(Note: here and in later quotes, frames of reference are noted in italic inside square brackets, using the numbering system in Table 1.)

PleasInsig

Mine is a mash of all of them. I like what Forrester and his group has produced [GF1 Disciplinary content] but I have timerestrictions [CF5 Educational environment] so I use some of them with the class in about week 4 or week 5 to look attransfer, because there are really good examples [GF1 Disciplinary content] and really good ways of explaining that [GF3How to teach]. I use the Sterman book for big chunks of information [GF1 Disciplinary content] they read or for examples thatwe talk about in class, or I get them to participate in as a group [GF3 How to teach]. I don't use too many of his [GF1Disciplinary content] because they're very in-depth examples [CF4 Course]. I use the Diana Fisher book [GF1 Disciplinarycontent] for how to learn how to use the software involved rather than the concepts behind it [GF3 How to teach]. So I reallymeld them together …. (0828Q9)

Similarly, Sophie provided explanations combining multiple frames of reference even when asked questions about the designof one class or a small specific task. Most of the examples in Table 1 feature in a single answer to a question about the design ofone lesson: “How did you come up with this design, the area of topics and activities?”

The area of topics — the topics are the building blocks [GF1 Disciplinary content]. They are what's fairly consistent betweenall the different schools of thought on how you should be teaching it [GF3 How to teach], that you need to understand thoseconcepts [GF2 How people learn]. The way of doing causal loop diagrams [GF1 Disciplinary content], it just made sense to me[GF3 How to teach]. It's far easier, we have the whiteboard tool there [CF5 Educational environment], it's not much good mejust showing them example after example [GF3 How to teach]. If they get a chance to do it themselves and then discuss,they tend to understand [GF2 How people learn]. (0828Q20)

4.1.3. Personal experience in making judgementsWhen asked, “Why do you think this is a goodway to do it?”, Sophie's explanationwas directly grounded in her personal experience:

Because that's how I learned it, I read all of these parts and I didn't just go through one of these separately and instantlyunderstand it [CF7 Teacher]. I needed to gather more information from all these different areas and I had to practice in allthese different ways [CF7 Teacher] and that's the way I chose to teach it [GF3 How to teach] because that's the way it madesense in my head [CF7 Teacher]. (080828Q10)

Further probing, aimed at exploring sources, did not lead to any normative answer:

Q: What is your general philosophy of teaching or your general pedagogical approach with this [course] unit?Sophie: I wouldn't be able to name you a theory that I subscribe to, but the way I approach it andwhat I try to keep inmy headwhen I'm teaching is that a little bit of chaos is fine. I don't want to be the teacher telling them all the information…. (0828Q11)Q: Is there any book or names that you could give me?Sophie: No. It's sort of a combination of how I was teaching anyway and then experience with [name of another teacher] usingtechnology …. (0828Q12)

(Note: non-italicized words in square brackets are our editorial insertions, intended to clarify Sophie's meaning and/or topreserve anonymity.)

4.1.4. Local coherence versus the difficulty of forging more distant connectionsIn most of her answers about single tasks or the class, Sophie explained her teaching choices coherently and integrated

different frames. However, her explanations were less coherent when our question caused her to refer to teaching decisions in




different contexts. For example, asked to explain the pedagogical approach she used to teach the software for systems modelling(STELLA), Sophie coherently explained:

Table 2Exampl

Sourc

S1. AuKno

S2. ExKnoexp

S3. PeKnoteacof)

S4. CrKnothe

S5. CoKnominand

S6. MKnominexpcou

S7. ReKnominin t

S8. HyKnoin tknorefl

PleasInsig

It's their own work, not in groups, and that's deliberate for this task because I want them as individuals to know how to dothis. I don't want them to figure it out in a group. It's really detailed instructions. They do a lot of group work later on wherepeople who do enjoy doing this take over and that's fine, that's their job, but I want every single student to specifically

es of sources of mental resources.

es and means of validation Description Examples

thoritative external sourceswledge validated by culture and others

Ideas come from the culture and literature ofthe subject, existing teaching resources,published research, administrative authorities,etc.

• “It's common in every book that you're going toread on system dynamics model” (0821Q15)• “ … and the large team task is what was decidedfor the unit” (0821Q19)

plicit evidencewledge validated personally by directerience and explicit evidence

Ideas based on feedback, inquiry into teachingpractice, observation and other empiricalevidence

• “But both years I've had feedback that they didn'trealize how good an assignment it would be untilthey started doing it” (1011Q10)• “ … this particular task we did last year and we dida lot of in depth research into whether the studentslearned what they were supposed to” (1011Q9)

rsonal experiencewledge validated, mainly intuitively, byher's experience outside (or in the contextthe course, or directly in action

Ideas come from experience as a learner,apprentice, teacher, tutor, subject expert, etc.and from direct interaction with the context ofaction

• “Because that's how I learned it” (0828Q10)• “The chat was probably because I watched[Colleague] in the first year” (0821Q19)• “The causal loop diagram, that's something I juststarted last year and it seemed to work quite well”(0904Q11)

eativity and intuitionwledge created and validated intuitively byteacher.

Ideas originated in the mind of the teacher • “The way of doing causal loop diagrams, it justmade sense to me” (0828Q20)• “The causal loop diagram I definitely came up withmyself” (0904Q13)

gnitive mindwledge created and validated in the teacher'sd by using knowledge structures, processesheuristics of the discipline

Ideas abstracted from the teacher's engagementwith subject knowledge

• “The first one, that the loop that goes from thecustomer base to the customer loss rate, that canhave a number of ways of interpreting and it's goodto bring up a number of things about how modelsare just simplified versions of a real system…”

(0828Q32)• “They spend the rest of the time in my part usingthe software to build or to interact with systemdynamics models so it's really an integral part ofknowing how to use the software, knowing whatthese diagrams mean, really understanding whatlies behind them, of course they've had to buildthem” (0904Q03)

etacognitive mindwledge created and validated in the teacher'sd by reflecting on cognitive phenomenaerienced outside (or in the context of) therse, or directly in action

Ideas abstracted from experienced cognitivephenomena within the mind of the teacher

• “I always get questions that I don't necessarilyknow the answers to and I have to figure out what itis that my brain does and try and explain that tosomeone else” (0904Q22)• “Then I was really trying to understand why theywanted to put it as plus when my book said it was aminus and I was trying to figure out whether therewas something I could pick out of their explana-tion…” (0828Q40)

flective mindwledge created and validated in the teacher'sd by reflecting on the experience of teachinghe context of the course

Ideas abstracted from interactions andexperienced pedagogical phenomena within themind of the teacher

• “But I thought it was a good thing that they werethinking about it that deeply” (0828Q40)• “… I decided that I wouldn't do that for the rest ofthem [examples], because it was taking too long andthey weren't getting out of it what I wanted them toget out of it ….” (0926Q26)

pothetical mindwledge created and validated hypotheticallyhe teacher's mind, usually by blendingwledge of context with other sources andecting on projected experiences

Knowledge rooted in the perceived context ofaction, including perceptions of students' needs,abilities, constraints, tools, interactions, etc.

• “For people in business school certain features areimportant for them to know in depth which isn'trelevant for these people because most of themdon't have an economics background, they don'tneed to understand the maths behind it ….”(0828Q4)• “I'm not under any misconception that everyonewould be able to do it, would be interested in doingit, should be interested in doing it, but to be able toat least understand the language and be able tocommunicate with it with other people I think isimportant” (0926Q21)




PleasInsig

experience doing this. It's definitely an individual task, it's definitely not a figure-it-out yourself type of task, it's very structured.The instructions are very specific so it's not throw them into the deep end and see if they can figure-it-out. (0904Q19)

Asked “Is there, in your teaching, any other topic where you use a similar approach?” she replied:

No. I really see this particular activity as they're learning to use a piece of software. It's not the conceptual thing behind it,it's not anything else, and I don't teach that in any other subject so I think it's a good way to teach software use, thisparticular skill. (0904Q19)

As Sophie taught an ‘Information Technology in Education’ course that also focused on skills needed to use software, we thenprompted her to compare the two. Sophie answered:

So in some ways it [the Information Technology in Education course] is similar but the instructions are a lot less intense,the software is more familiar, it's easier, and they can do similar things in Word as in Power Point so there's a lot morecrossover during the weeks that we're doing it. It's also face to face, so if someone has a problem I can go straight to theirscreen. The problems that they have are a lot less intricate. The problems students have with STELLA sometimes have todo with the concepts behind it, like ‘what does this equation mean?’. Even though the equation is written out for them,they still have trouble figuring out that that means these two particular bits in the equation together. The problems thatthey have with PowerPoint is ‘I can't remember how to get toMaster Slide’, and I go: View, Master, Master Slide, and that'sit. So it's a different level. No one has conceptual misunderstandings with PowerPoint. (0904Q24)

While Sophie appeared to perceive some similarities and differences between the two approaches, it was difficult for her toarticulate these. In response to further probing, Sophie shifted in her explanations of whether her teaching of system dynamicssoftware also included conceptual aspects and complexities or just technical skills. The materials she used for teaching thesoftware included both technical skills and some conceptual questions. For example, one of her instructions said:

With the Selector double click on Lifespan. Define it to be 76. Click OK. Question: What does the value ‘76’ represent in yourown words? (0903R1)

The two learning situations shared one feature (the use of software), but also differed (e.g. one course included an explicitconceptual component, while the other did not). From a normative perspective, integrating three generic frames of reference –

disciplinary knowledge, how people learn and how to teach (GF1–GF3 in Table 1) – Sophie's explanations look inconsistent.Surprisingly, the task design was better aligned with the nature of the knowledge than were Sophie's answers. Nevertheless, itseems Sophie did not assign much importance to the conceptual matters here; she focused on technical skills in that particularclass. From her situated phenomenological perspective, integrating three contextual frames of reference – course aims, knowledgeof students and her own teaching experiences (CF4, CF6 and CF7 in Table 1) – the conceptual questions in the task description didnot carry much pedagogical significance. Furthermore, generic instructional principles common to teaching students to usesoftware in each of the two contexts were deeply bound up with considerations derived from the other diverse frames ofreference, and these differed for these two situations (e.g. different course goals; one online course and one face to face; somestudents had software experience, others did not). Also, Sophie learned to use these software tools herself in different contextsand in different ways: her personal intuitive knowledge of how to learn to use themwas different in each case. This leads neatly toa consideration of the sources of Sophie's working knowledge.

4.2. Main sources of working knowledge

In the interviews, particularly in answers to epistemic questions like “Where does this (idea) come from?”, “How do you knowthis?”, “Why is it so?”, Sophie typically responded by referring to the origins of her mental resources for teaching and how herpedagogical ideas were validated. Our exploration showed that many of Sophie's mental resources originated in eight broadsources: (S1) external authoritative sources; (S2) explicit evidence; (S3) personal experience; (S4) creativity and intuition; (S5)cognitive mind; (S6) metacognitive mind; (S7) reflective mind; and (S8) hypothetical mind. These pedagogical ideas werevalidated in a variety of ways. Some were accepted as true or validated by reference to epistemic culture. Some others werejustified by reference to research-based knowledge or explicit evidence, while others manifested themselves as intuitive,subconsciously validated decisions. Table 2 gives descriptions and examples of each key category.

Sophie's mental resources had diverse origins – ‘ready’ knowledge generated by others, process and context of action andinteraction – and were validated in multiple ways. For example, her ideas about the nature of the subject, how people learn andhow to teach, came from authoritative sources (S1), but were also validated by her personal experience of learning this type ofknowledge (S3) and by deep reflection on both her own cognitive processes and those of her learners (S6 & S7).

Three findingswere particularly striking: (1) how Sophie used authoritative sources and integrated themwith a range of personalexperiences (and, conversely, the difficulties she felt when authoritative knowledge and experience were contradictory); (2) howSophie used her ‘metacognitive’ and ‘hypothetical’ mind for generating and validating pedagogical ideas and adapting them to thecontext; and (3) ways she reconciled new situated experiences, emerging from her interactions with students, with past knowledge,and how she gradually refined her pedagogical ideas. We discuss each of these in turn in the next three subsections.




4.2.1. Integrating authority, evidence and personal experienceSophie often attributed her teaching ideas, in some cases for entire tasks, to external authoritative sources, typically systems

dynamics books and websites. Her answers often emphasised the importance of the quality and clarity of subject knowledgecontent and tasks; this was a common theme when explaining the choices she made (see S1 in Table 2).

PleasInsig

It's important because she [a more experienced teacher and author known to Sophie] has been doing this for a very longtime. I did meet her at the conference and I liked her work anyway. She's a teacher and she's been incorporating this unitinto her classes for 15 years. (0821Q12)Something like the population one [a population model], they've been tested and used for so long that I know it's a goodexample. (0904Q39)

Most of Sophie's judgements about ‘task clarity’ and ‘content quality’ were based on her realist epistemological stance, inwhich knowledge claims validated by others, and empirical evidence she had collected, played important roles in justifying herdecisions (see S1 and S2 in Table 2). However, this validated knowledge was not stable or unchangeable. For example, during thesemester, she encountered several situations when a task did not work as expected. She recounted one such situation:

There was a lot of discussion about positive and negative feedback. Some of it was because they were disagreeing with theexample that I provided. I don't think thatwas a bad thing. I think both them and the exampleswere providing good reasons forthe choices they made so that was fine, it provided a good reason for them to really expand their ideas. (0828Q17)

However, making sense of this episode again, in another context, she answered:

This year I thought because the last couple of years I've thought them [the examples] upmyself and there's been an issue becauseI haven't thought something through all the way, this year I decided to use some causal loop diagrams from Sterman [Sterman'sbook] but therewere still issueswith one of his. So I think if I'm teaching it [next] year I'll go back to doingmy own, because thenat least it will be something really relevant for them and I won't worry so much if there's discussion or not. (0828Q35)

Probing further about this in other contexts, it became apparent that she sometimes regarded this experience as beneficial forstudents, but sometimes expressed dissatisfaction:

I don't know that that was the best example so I think I'll keep looking for something. (0828Q30)

Two pedagogical ideas coming from two sources – an authoritative book (S1) and personal experience (S3) – contradictedeach other. On one hand, Sophie sought to provide students with ‘clean’ and ‘tested’ examples (typically, trusted tasks fromauthoritative sources). On the other hand, her direct experience showed that this contradictory example, while not matching herquality criteria, resulted in valuable student experiences coherent with her pedagogical philosophy that “… a little bit of chaos isfine” (0828Q12). (We show how Sophie reconciled this contradiction later.)

This initial, quite intuitive, personal experience of ‘how things work’ played an important role in refining her understanding.Many other pedagogical ideas, validated mainly intuitively throughout her teaching and learning experiences, were noticeable inSophie's sense-making (S3, Table 2). These experiences were productive resources for making decisions about pedagogicalapproaches that ‘simply work,’ as well as for refining her decisions. For example, in describing her teaching decisions, Sophie oftenreferred to her experience from previous years — teaching the course both with colleagues and by herself. This was a commonsource of reasons for changing or not changing tasks she had adapted or designed. She commented:

That's what we did last year and it worked very well. They did it really quickly, were really into it, were able to relate it, butit was not working for this group. (0926Q27)Last year they had a lot of trouble with that. We'll see how they do this year with more time spent on it. (0926Q46)

Overall, Sophie's personal experiences also provided strikingly richmental resources formaking and explaining teaching decisions.She referred to her own and others' experiences – as teachers as well as learners – as a natural source (S3) for teaching decisions.

4.2.2. The teacher's mind as a source for generating, validating and adapting pedagogical ideasIn many situations the main source of pedagogical ideas was not only experience, but also Sophie's mind. This included intuitive

creative design decisions with respect to new tasks (S4), decisions that drew upon cognitive strategies from the discipline (S5), higherlevel strategies for examining experienced cognitive and pedagogical phenomena (S6 andS7, respectively) and the anticipated contextof action (S8).

Sophie sometimes attributed the origins of her pedagogical ideas to her creative mind, saying that she came up with these designdecisions herself and justifying this as ‘commonsense’ — “it just made sense to me” (0828Q20) (S4). Sophie's experience of cognitivephenomena and of her metacognitive mind – her experience of her own cognitive and metacognitive activity – also emerged asstrikingly important sources of ideas about how studentsmight come to understand, and how shemight teach, systemdynamics (S5 &S6). For example, Sophie commented on her metacognitive strategies (S6) in making decisions about pedagogical approach:

… if they don't understand it and it's not coming out in the discussion then I need to try and figure out how I understandthat and explain it to them in a different way. (0828Q12)




In situations where her personal experience with systems modelling differed from the pedagogical approaches described inthe literature (S1 Authoritative sources), she consciously reflected on and chose her own approach — validated by her mind andpersonal experience (S6 & S7; S3):

PleasInsig

I don't agree with [name of an expert in the field]'s work on why students don't understand system dynamics models andwhy they can't make the predictions they make. b…N I think that there are better ways of using it, explaining it, supportingpeople's learning. So I don't spend as much time as he does on the maths and the calculus …. (0828Q09)… the way in which I construct the systems in my head, the way that I understand them, I understand the maths behind itbut the way that I'm visualizing is the language they use. So the stocks and the flows and the way a system is put together. Idon't visualize the numbers or equations behind it even though I understand it …. (0926Q06)

In situations where neither evidence nor personal experience was adequate to meet her pedagogical needs, Sophie applied herknowledge about the context, coupled with hypothetical projection of students' imagined experiences, to make appropriatedecisions (S8). For example, perceived students' needs were one of the sources for making judgments about appropriate kinds ofteaching materials and tasks. She commented:

I have looked at the open university resources at MIT but it's at a very different level to what we need it for, training peopleto become system dynamic modelers, it's usually training engineers at MIT which is very different to half a course ineducation so I haven't found much there that's relevant. (0821Q13)

4.2.3. Combining multiple sources and refining pedagogical ideasIn more complex situations, Sophie combined mental resources from a range of diverse sources. For instance, when asked

about the contradictory example given in Section 4.2.1 above, Sophie responded:

Yes, it was.When I looked at it in the book [S1 Authoritative source] it looked like a good example [S8Hypothetical mind] becauseit had a reinforcing loop on one side, bouncing loop on the other, it was about spreading things by word of mouth [S5 Cognitivemind], that's an easy thing to understand [S6 Metacognitive mind] and I didn't look too closely at the balancing one [S6Metacognitive mind] until we got into the class [S2 Explicit evidence]. Then I was really trying to understand [S6 Metacognitivemind] why they wanted to put it as plus [S2 Explicit evidence] when my book said it was a minus [S1 Authoritative source] and Iwas trying to figure out whether there was something I could pick out of [S5 Cognitive mind] their explanation [S2 Explicitevidence] but I couldn't see that therewas toomuch fault [S5 Cognitive mind] in how theywere justifying it [S2 Explicit evidence],so I decided that that would be fine [S6 Metacognitive mind]. Because the other answer in the book [S1 Authoritative source] as apositive alsomade sense [S5 Cognitivemind]. If youweren't thinking about it as deeply [S8Hypothetical mind] as these guyswere[S2 Explicit evidence], it was straightforward [S6 Metacognitive mind]. But I thought it was a good thing [S7 Reflective mind] thatthey were thinking about it that deeply [S2 Explicit evidence]. (0828Q40)

Sophie's experience, and the contradictions she encountered, seemed to stimulate her to refine her pedagogical ideas. Reconcilingexperiences related to the episode above, she commented:

The first one, that the loop that goes from the customer base to the customer loss rate [variables in the model], that canhave a number of ways of interpreting and it's good to bring up a number of things about how models are just simplifiedversions of a real system b….N Just be a bit flexible. There are a number of correct answers. (0828Q32)

In short, Sophie's pedagogical ideas and decisions were not static. She flexibly moved from the objectivist view of knowledgeand pedagogical principles in which tasks should be validated and clear, to the intersubjectivist view, emphasising students'critical thinking and ability to see the limits of ‘objective’ knowledge.

Her direct experience of how her pedagogical decisions work in practice – including experience supported by ‘hard’ data –

supplemented her knowledge about ‘what works’ and ‘why it works’ and was an essential source for her improvements in taskdesigns. Sophie directly commented:

The two previous years I used existing models so I didn't have to develop anything, but now I have enough experience to beable to develop something. (0821Q8)Definitely I use it [data about students' learning] in the design of the tasks. That's why a lot of the tasks have changed thisyear because we had the opportunity to do a lot of analysis and we have the knowledge so I was able to change the tasks intime. I also use it to predict what questions students will ask so I can change how I explain tasks a little bit. I can changehow I answer question because even if I'm aware that they'll ask this question, I know why they're asking it now. I can tryand tailor it a little bit more that way. (1016Q28)

Interviews showed that Sophie confidently found experiential mental resources for explaining tactical decisions, but rarelyarticulated theoretical principles that underpinned her teaching. Explicitly articulated ‘conceptual pedagogical knowledge’wasalmost invisible in her explanations. Even questions about more abstract pedagogical principles were usually answered byproviding more concrete descriptions, connected back to personal experience. For example, asked how teaching systems




dynamics is different from teaching sciences, Sophie reflected on her experience and extracted from it complex pedagogicalprinciples:

PleasInsig

It's probably similar in a lot of ways. There's theory and practical application, so if I'm thinking of learning physics andthere's equations that go with velocity b….N If I'm thinking about like uni science where it was much more learning thetheory and then you do experiments rather than applying a specific skill you could think of needing a certain level of skillbefore you start performing experiments b….N So say in chemistry we'd be doing an experiment that would be applyingsome sort of theory, but in doing that we would be learning how to do a titration …. (0926Q12)

Mental resources rooted in direct experience and deeply personal ways of knowing were continually activated and refined inher working knowledge.

5. Discussion: a case for knowledge-in-pieces and intuitive pedagogy

In the Introduction we alluded to an orthodox view of a teacher's pedagogical knowledge as a coherent system of concepts andbeliefs – a personal theory of teaching – from which a teacher can deduce appropriate courses of action. That is, we would expectpedagogical ideas to be (prospectively or retrospectively) articulated and applied consistently in different contexts. On this view,weaknesses in a teacher's ability to teach effectively may result from (a) gaps in the knowledge base and/or (b) difficulties inapplying what is known. As a novice teacher moves towards becoming an expert, the development of pedagogical knowledgeentails substantial (non-monotonic) changes in the conceptual framework and/or belief system. We have presented someempirical and practical limitations of this view and propose that it is more helpful to view teachers' knowledge as contextualised,more fragmented and dynamic. Sophie's interviews have illustrated our argument.

The interviews suggest that the mental resources she deployed in explaining her teaching decisions combined multiple framesof reference and had multifarious genealogical roots. Some of her mental resources have roots in authoritative sources about goodcontent and effective pedagogy; others come from direct experience of learning, teaching, model-building and using software.The evidence suggests that Sophie's ideas could not all be connected into one coherent personal pedagogical theory. Rather hermental resources are rooted in diverse experiences and have a family resemblance to diSessa's (1993) p-prims.

The p-prims of physics originate in the implicit learning that takes place as people interact with, and make sense of, thephysical world around them. Likewise, many of the pedagogical ideas constituting Sophie's working knowledge originated as shemade personal sense of her own teaching and learning experiences. Some of these mental resources, we suggest, emerge fromone's early experiences of coming to understand why other people behave as they do, and are related to ‘action explanations’(diSessa, 2000; Heyes, 2009; Hutto, 2008; Malle, 2006). Others emerge from later experiences of teaching and learning (Buitink,2009; Kettle & Sellars, 1996). These experiential pedagogical resources might be regarded as a specialised class of resourcescombining social p-prims (diSessa, 2000) rooted in personal experiences of social interaction (including teaching and learning),and epistemic p-prims (Hammer & Elby, 2002) rooted in personal experiences of coming to know.

We do not argue that experience and unreflected intuitive ideas alone could provide a sufficient base for teaching expertise.Rather we suggest that they can provide productive, and perhaps necessary, experiential resources for understanding howteaching and learning phenomena work: on which one could build expert-like tacit and explicit understanding. As Sophie argued“now I have enough experience to be able to develop something.” (0821Q8). This view of knowledge links mind, immediatesituational contributions, action and one's past cultural, social and material experiences. It reflects what Billett (2006) called “therelational interdependence between social and individual agency” that guides professional learning throughout working life.

In the interviews, we noticed that Sophie's earlier experiences provided initial mental resources for making sense ofpedagogical phenomena, while more recent teaching experiences helped her refine this knowledge. Most interestingly, Sophiemoved flexibly from the objectivist view of knowledge and pedagogical principles, emphasising accuracy of taught knowledge, tothe intersubjectivist view, emphasising the subjective nature of knowledge and students' critical thinking. These two views,which Torff (1999) regarded as distinct features of ‘folk pedagogy’ and ‘expert pedagogy,’ appeared to be similarly experiential,equally valued and, generally, compatible pedagogical approaches. In short, what is often regarded as ‘folk pedagogy’ and ‘experttacit knowledge’ could be viewed as a constitutive mesh of diverse experiential resources, rather than two incompatible kinds ofintuitive knowledge.

Our interviews with Sophie also echo Sfard's (1998) warning about the dangers of choosing just one pedagogical perspective andthen looking for coherence in teachers' theories and actions across contexts and situations. Disciplines and professions are notcoherent packages of one specific kind of knowledge, but comprise of concepts, skills, strategic knowledge, epistemologicalunderstandings, values and beliefs. Sophie's interviews illustrate this diversity — she wanted students to grasp the basic concepts,develop skills in usingmodelling tools, learn to create their ownmodels, and understand “that models are just simplified versions of areal system” and “there are a number of correct answers”. Different kinds of knowledge and different learning goals – as when Sophietalked about teaching students to use modelling software and teaching more conceptual knowledge – could be reached effectivelyusing different pedagogies that might appear to be contradictory. It could be more important for teacher expertise to recognise thisdiversity of knowledges, choose themost important goal and dynamically combine it with an effective pedagogical strategy and othersituational aspects, rather than to maintain static conceptual coherence across goals and situations (Goodyear, 1992).

Wagner (2006), describing transfer of physics knowledge, noted:




PleasInsig

Different contexts or different aspects of a single situation might be interpreted via different combinations of p-prims or otherknowledge resources, so their lack of systematicity can prevent people from noticing contradictions, and their contextsensitivity can prevent people from seeing similarities. Learning physics, then, involves organizing (or reorganizing) andsupplementing useful intuitive knowledge in ways that restructure interpretive schemata and more uniformly systematizecausal and explanatory understandings (p. 7).

We believe similar remarks could be made about pedagogical knowledge. In many situations, Sophie activated, switchedbetween, and combined several mental resources — some of them general and some linked to a specific context; some validatedby Sophie's real-world experience, and some validated by her mind. These blends were complex and sometimes involvedsimultaneous work with several conceptual ideas and contextual frames. Sophie did not have difficulties working simultaneouslywith, and integrating, non-conflicting mental resources. However, she found that reconciling conflicting experiences, pedagogicalideas and sources was challenging. Sophie's case indicates that abstracting general principles from specific experiences might beless complicated than reconciling contradicting pedagogical principles or recognising conceptual similarities and differencesbetween two distant contexts (as in the example where she taught students to use software in two different contexts).

We do not claim we have identified all possible frames of reference (Table 1) and all sources of mental resources (Table 2).This was not our goal. However, we suggest that a teacher's ability to recognise key frames of reference and to frame problemsfrom different perspectives could be a central element of their pedagogical expertise. Awareness of different frames could providea focus for what are often vaguely-structured deliberative teacher learning strategies. Such awareness could also subsequentlyhelp teachers integrate the intuitive understanding emerging from direct experience into more organised and articulated workingknowledge structures.

Further, we note how Sophie, in her explanations, drew not only on intuitive mental resources for making decisions about‘What’ and ‘How’ that emerge from direct interactions with material, social, emotional and cognitive worlds (S1–S5, Table 2), butalso on a rich array of mental resources about ‘Why’ and ‘When’ that emerge from her metacognitive experiences, projections andother reflective interactions with her mind (S6–S8, Table 2). Professional knowledge and learning theories that focus on thereflective nature of professional growth usually emphasise deliberative practice and articulated reflective thought (Schön, 1987).In contrast, such theories rarely acknowledge that teachers may already have a range of epistemic resources, developed as a resultof their personal experiences, for engaging productively in reflective interactions and everyday reflective work.

6. Conclusions

The importance of frameworks for theorising knowledge in ways that link ‘formal’ conceptual constructs and explicit ways ofknowing with informal ‘functional’ constructs and ways of thinking has been increasingly emphasised in socio-cultural studies(e.g. Greeno, 2012). While we do not make empirical generalisations from our n = 1 study, we believe our analysis also provides aprima facie case for the value of, and need for, exploring different ‘functional’ mental resources and ways of knowing that teachersemploy in their everyday pedagogical sense-making: such as pedagogical p-prims (Kali, Goodyear, & Markauskaite, 2011;Markauskaite & Goodyear, 2011). The examination of a teacher's working knowledge at a more fine-grained ontological level, andfrom a more flexible epistemic perspective, makes it possible to avoid imposing an a priori division between ‘naïve’ and ‘expert-like’teacher conceptions, and to see how everyday experiences and intuitions can gradually grow into a more systematic, yet context-sensitive, understanding of pedagogical phenomena.

Studies from adjacent areas show that this view of knowledge could also offer generative insights into how productivelearning unfolds in interaction and how it could be supported by teachers and mentors (Elby & Hammer, 2010; Philip, 2011). Aswith physics education (Elby & Hammer, 2010) or ideological change (Philip, 2011), some further research on teachers' expertise,using larger numbers of teachers, might benefit from focussing on specific pedagogically challenging situations, and aim to detectthose mental resources, and their configurations, which prove to be generative (or limiting and unproductive) when teachers arecoming to understand how students learn, and how to teach. These results could then be used to help teachers integrate theircontext-specific experiences into a more systematic pedagogical understanding that could guide their professional sense-makingacross diverse situations and contexts.

Acknowledgements

The authors acknowledge the financial support of the Australian Research Council through grant DP0988307. We also extendour thanks to ‘Sophie’ for sharing so much of her thinking about teaching with us. We also acknowledge feedback and editorialassistance of our colleagues and research students Agnieszka Bachfischer, Yael Kali, David Ashe, and Pippa Yeoman.

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Lina Markauskaite is a Senior Lecturer in the Faculty of Education and Social Work and a member of the CoCo Research Centre at the University of Sydney. Lina'sresearch includes investigations into students' and pre-service teachers' ICT literacy, personal epistemology and epistemic fluency; ICT-enhanced researchmethods in the social sciences; and national strategies and policies for ICT in education. Her background is in mathematics (MSc, Vilnius, Lithuania), informatics(PhD, Vilnius, Lithuania) and communications management (MCM, Strathclyde, UK). She has published more than 50 refereed papers. Before moving fromEurope to Australia in 2004, she conducted research in schools and wrote extensively for educational practitioners and children. Her latest edited book is“Methodological choice and design: Scholarship, policy and practice in social and educational research” (Springer, 2011, with Peter Freebody and Jude Irwin).

Peter Goodyear is a Professor of Education and co-director of the CoCo Research Centre at the University of Sydney in Australia. He is a Senior Fellow of theAustralian Learning and Teaching Council and the first Australian Research Council Laureate Fellow in the field of Education. His research focuses on networkedlearning; learning and teaching with technology in higher education; the nature of professionals' “working knowledge”; and complexity in educational design.From 1995 to 2003 he was Professor of Educational Research at Lancaster University in the UK. He is editor-in-chief of the journal Instructional Science. He haspublished over 100 research articles and book chapters. His latest books are “Students' experiences of e-learning in higher education: The ecology of sustainableinnovation” (RoutledgeFalmer, 2010, with Rob Ellis) and “Technology-enhanced learning: Design patterns and pattern languages” (Sense Publishers, 2010, co-editedwith Symeon Retalis).



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