Making tacit knowledge visible: Uncovering the knowledge of science and mathematics teachers

Teaching and Teacher Education 86 (2019) 102907

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Making tacit knowledge visible: Uncovering the knowledge of science and mathematics teachers Sharon Fraser a, *, Kim Beswick b, Suzanne Crowley a a b

University or Tasmania, Australia University of New South Wales, Australia

h i g h l i g h t s
A framework was developed which explicates the tacit knowledge of experienced science and mathematics teachers.
The framework provides novice and out-of-field teachers access to expert ways of selecting teaching resources.
The framework was developed and validated iteratively by both experienced and novice teachers.
A process is described which uncovers expert knowledge without using surveys, observations and interviews.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 August 2018 Received in revised form 8 August 2019 Accepted 10 August 2019 Available online xxx

There is a chronic shortage of appropriately qualified science and mathematics teachers particularly in disadvantaged, rural and isolated communities. Less experienced and out-of-field teachers who often teach in these contexts face difficulties in accessing professional learning and mentoring. While increasing their access to quality resources is useful, these teachers need to both decide whether a resource is appropriate in their context and be able to use it confidently. This paper reports on the process used in the STEMCrAfT project to explicate the knowledge that experienced science and mathematics teachers use when selecting and using resources, and the framework that resulted. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Novice teachers Out-of-field Resources Science and mathematics teaching

1. Introduction Throughout Australia there is a chronic shortage of appropriately qualified science and mathematics teachers (Hobbs, 2012); a problem that is especially severe in disadvantaged or isolated communities (McKenzie, Santiage, Sliwka & Hiroyuki, 2005; Weldon, 2016). Teachers in these contexts tend to be less experienced than their metropolitan counterparts and face difficulties in accessing professional learning and mentoring by more experienced and expert colleagues (Beswick and Jones, 2011). These issues are not unique to Australia: for example, an international symposium on rural education held in Australia (Lyons, Choi, & McPhan, 2009) featured presentations about issues related to teacher isolation and professional learning in rural, isolated and

* Corresponding author. School of Education, College of Arts, Law and Education, University of Tasmania, Locked Bag 1307, Launceston, Tasmania 7250, Australia. E-mail address: [email protected] (S. Fraser). https://doi.org/10.1016/j.tate.2019.102907 0742-051X/© 2019 Elsevier Ltd. All rights reserved.

often socioeconomically disadvantaged school communities in the United States, Canada, and South Korea. Others have described similar challenges in British and Scandinavian contexts (e.g., Sigsworth & Solstad, 2008). Increasing the availability of quality resources in the form of instructional materials that are fit for purpose and aligned with the curriculum, to teachers in schools in rural and disadvantaged communities has been posited as a way forward (Sullivan, Perry, & McConney, 2013). For the past decade there has been a focus in Australia on the development of digital curriculum resources for teachers as this has the potential to expose teachers to “innovative curricula, stimulating applets and simulations, and other hands-on resources” (Hanson & Carlson, 2005, Foreword). In recent years there have also been several Australian Government initiatives focussed on developing resources that enable holistic curriculum planning for primary science (see Primary Connections, https:// primaryconnections.org.au/), secondary science (Science by Doing, https://www.sciencebydoing.edu.au/), and mathematics

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(Maths by Inquiry, https://www.science.org.au/learning/schools/ resolve) which are seen to be of particular use to less experienced teachers or those teaching out-of-field.1 Resources for schools that provide inspiring applications of science and mathematics have been developed, but there is often a gap between these resources and teachers' understanding of where to locate them, confidence in using them, and the adequacy of their discipline knowledge. The time required to select a resource and uncertainty about the choices to be made, may limit the uptake of excellent resources or result in lower quality resources being used. Access to people with relevant expertise and experience to assist is sometimes the most needed yet least readily available resource. Digital libraries bring scattered resources together into a coherent and accessible space, but such sites often include an overwhelming volume of resources which makes finding the ‘right’ resource a daunting task, while access itself can be problematic for rural and remote teachers where internet connections are not always available or reliable. Hanson and Carlson (2005) highlighted the additional challenge of teacher reliance on digital resources and the challenge of finding the time to integrate or adapt them for a particular context. A lack of collegial support and appropriate professional learning opportunities (Handel, Watson, Petcock & Maher, 2013; Hobbs, 2013; Luft, Dubois, Nixon, & Campbell, 2015; Lyons, Cooksey, Panizzon, Parnell, & Pegg, 2006), which might assist teachers to make quality decisions about resources can exacerbate these problems. Teachers who are teaching out-of-field, or who have little confidence to teach science and mathematics, place additional strain on lead teachers and school administrators because they require ongoing professional learning and mentoring (Taylor, 2000). For such teachers the lack of resources may not be the issue, rather it is their capability to select and use confidently those that are suitable to their context and student cohort. There is a need for strategies that make explicit the pedagogical content knowledge (PCK) and pedagogical reasoning of experienced and expert teachers, when they make choices about the use of resources in their teaching. To this end, this paper describes the process and outcome of the Science, Technology, Engineering and Mathematics Critical Appraisal for Teachers (STEMCrAfT) project (funded by the Australian Maths Science Partnership Program, Australian Department of Education) which focussed on making this aspect of expert teachers' largely tacit knowledge, explicit and available to the less experienced and out-of-field teachers. The STEMCrAfT framework is the tool that emerged from the project. It supports teachers to reflect critically as they make decisions about teaching and learning resources. The STEMCrAfT framework was developed jointly by teachers, teacher educators and discipline experts as a professional learning tool. Less experienced primary and secondary teachers of science and/or mathematics and those teaching out-of-field or in rural or regional areas, were the cohort of teachers for whom the tool was designed. The aim of the project was not to change participants' assessment of resources or necessarily any aspect of their teaching. Rather the goal was to explicate the tacit knowledge that experienced teachers called upon when choosing resources which aligned with their pedagogies in support of their students' learning. The research questions addressed in the study were: 1. Upon what knowledge do expert teachers of science and mathematics draw when they make decisions about teaching resources?

1 An ‘out-of-field teaching is defined as “a secondary teacher teaching a subject for which they have not studied above first year at university, and for which they have not studied teaching methodology” (Weldon, 2016, p. 1).

2. How can the knowledge of expert teachers of science and mathematics be made explicit and available to less experienced colleagues or colleagues teaching out-of-field? In addressing the first of these questions the study adds to existing understandings of the knowledge needed by teachers of science and mathematics. Our findings in relation to the second question have the potential to inform providers of professional learning for teachers of science and mathematics as well as educators in these fields in initial teacher education. The processes we used to uncover the knowledge of expert science and mathematics teachers could be used to undertake similar work in relation to teachers of other school subjects and hence our findings have relevance to professional learning providers and teacher educators beyond science and mathematics. We begin by outlining the issues faced by teachers in rural and regional areas and the implications of these for student learning before discussing the knowledge needed by teachers of science and mathematics and presenting the study and its findings. 1.1. Science and mathematics teaching in rural and regional areas Issues faced in rural and regional areas include the transient nature of the teacher workforce, professional isolation, lack of time for mentoring and collaboration, as well as poor access to technical, support services, and resources (Lyons et al., 2006). In addition to high rates of teacher turn-over (Handel, Watson, Petcock, & Maher, 2013) in rural schools, a large proportion of the new teachers are beginning teachers, often teaching out of their area of expertise (Hobbs, 2013; Lyons et al., 2006). This is particularly the case in science and mathematics, where more than a third of Australian secondary mathematics teachers and a quarter of science teachers are not trained to teach in that field (Productivity Commission, 2012). In rural and regional areas few of these teachers have access to senior teacher mentors. Teaching positions in rural and regional schools are difficult to fill and in many instances are filled by casual and contract teachers (Handel et al., 2013), few of whom have the opportunity to attend the professional learning activities needed to develop their capacity to teach unfamiliar content (Handel et al., 2013; Tytler, Mousley, Tobias, McMillan, & Marks, 2006). These factors impact negatively on the attraction to and retention of teachers in those schools (Beswick et al., 2006; Kidd, 2014). Consequently, many students are being taught science and mathematics by out-of-field teachers (Harris Jensz & Baldwin, 2005; Office of the Chief Scientist, 2014a; Weldon, 2016). Whitehurst (2002) found that being taught by teachers without qualifications in a teaching area negatively affects student achievement. Teaching out-of-field can also impact a teacher's identity, self-efficacy and sense of wellbeing (Pillay, Goddard, & Wilss, 2005). The confidence of some primary school teachers and their capacity to deliver lessons as a result of their low levels of content knowledge in these areas is also of concern (Marginson, Tytler, Freeman, & Roberts, 2013; Palmer, 2002). In 2011 the proportion of time spent on teaching science in Australian primary school classrooms was just 5.7%; less than that for all but two of the 11 countries for which data were available (Office of the Chief Scientist, 2014b). Primary and lower secondary school teachers' tendency to lack confidence, competence and self-efficacy for teaching mathematics (Beswick et al., 2006; Watson et al., 2006) and science (Hackling, Peers, & Prain, 2007) has also been established. A lack of deep knowledge of the subject area impacts upon primary teachers' confidence and competence to teach these subjects and hence to inspire their students to learn. Dinham (2014) has argued that primary students' attitudes towards mathematics

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and science are relatively good predictors of their ongoing study in secondary school and later achievement in these subjects.

1.2. Developing knowledge for science and mathematics teaching Student learning in science and mathematics relies upon the teacher's ability to engage students in deep learning of content that is comprehensible to them (Ball, Thames, & Phelps, 2008). The knowledge that underpins this ability is referred to as pedagogical content knowledge (PCK) (Ball et al., 2008;Loughran, Berry, & Mulhall, 2012; Magnusson, Krajcik, & Borko, 1999; Shulman, 1986). PCK is more than the sum of a teacher's subject matter/ content knowledge and pedagogical knowledge, rather it is their amalgamation and transformation to create a form of knowledge that is subject specific and unique to teachers (Shulman, 1986). Researchers have identified that for both science teachers (MorineDershimer & Kent, 1999; van Driel, Verloop, & de Voos, 1998) and mathematics teachers (Baumert et al., 2010), a thorough understanding of discipline content is essential to their development of PCK. Summarising the work of Whitehurst (2002), Sheehan and Mosse (2013) noted that science teachers who have a qualification in their area of teaching have higher achieving students when compared with the students of teachers teaching out-of-field, irrespective of the students' socioeconomic background or prior achievement. Similarly, Ponte and Chapman (2008) argued that teachers who do not have strong knowledge of mathematics are likely to be less able to help students develop relational and conceptual understandings. Countries such as Finland, which consistently ranks highly in international studies of science and mathematics achievement, require that their teachers are fully qualified in their discipline and understand how to teach it (Marginson et al., 2013). Teachers do not graduate from teacher education courses as expert teachers, rather they have an emergent PCK which develops over time and through experience in the classroom, as Hoban (as cited in Loughran et al., 2012, p. 1) attests: Upon reflection, I realised that, as a secondary science teacher for 14 years, I knew my science content but very little about how children learn. … Thus began my awakening about understanding the complex relationships between teaching and learning that is still evolving today. … In retrospect … I had such a simplistic conception of teaching during those first 14 years; it is a little embarrassing that I believed I had mastered the job (Hoban, 2002; pp. xvi - xvii).

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development of middle-school mathematics teachers' knowledge, personal numeracy, pedagogical awareness, pedagogical content knowledge awareness, and finally pedagogical content knowledge consolidation. The PCK of expert teachers has become implicit; highly personal and hard to formalise although it can be seen in their actions and is quite difficult to communicate to others e it has become tacit knowledge (Loughran et al., 2012). As Polanyi (1966) suggests, “we can know more than we can tell” (p. 4). For the novice teacher to learn from the expert or subject-specific discourse communities, tacit knowledge must be captured and made explicit. Classroom observation and video-stimulated recall are frequently used means of uncovering teachers' thinking in the act of teaching (e.g., Muir et al., 2010; Patrikainen & Toom, 2004). The power of video-stimulated recall lies in its affordance of the identification of ‘critical incidents’ (Angelides, 2001) that become the € n, 1987). Scho € n's theory of focus of reflection-on-action (Scho reflective practice also offers other ways to think about how the tacit knowledge of practitioners might be made explicit. The theory is underpinned by a constructivist view of learning that posits that rather than uncovering an objective reality, individuals make and remake versions of the world that fit with their experience. Reflective conversations among practitioners can bring the tacit knowledge employed in such ‘worldmaking’ (Goodman, 1978) to € n (1987) described the process as follows: light. Scho Through countless acts of attention and inattention, naming, sensemaking, boundary setting, and control, they make and maintain the worlds matched to their professional knowledge and know-how … When practitioners respond to the indeterminate zones of practice by holding a reflective conversation with the materials of their situations, they remake a part of their practice world and thereby reveal the usually tacit processes of worldmaking that underlie all of their practice. (as cited in Kinsella, 2010, p. 10). Plack and Santasier (2004) described reflective practice as a € n's (1987) notions of reflectioncyclical process incorporating Scho in-action and reflection-on-action as well as Killion and Todnem’s (1991) reflection-for-action. Reflection-for-action is intended to encapsulate the combined purpose of reflection-in and on-action by generating insights that inform future actions (Killion & Todnem, 1991). Working either individually or with colleagues using each of the three types of reflection can allow practitioners to unpack the knowledge on which they draw before, during and after action (e.g., Plack & Santasier, 2004). 2. The STEMCrAfT project

Berliner (1988) stated that developing PCK takes time and suggested that teachers move through five distinct phases as they develop it, moving from novice (rigid in action) through advanced beginner (gaining insight), competent performer (rational), proficient performer (intuitive), to expert. He describes experts as ‘arational’ in that they; … engage in performance in a qualitatively different way than do the novices or the competent performers. Experts are not consciously choosing what to attend to and what to do, they simply flow. They get involved and they just do it. They act effortlessly and fluidly and, in a sense, arationally, because it is not easily described as deductive or analytic (p. 19). Berliner (1988) found that experienced teachers have rich, contextualised stories to tell as they rely on case and episodic knowledge; compared with novice teachers they think and act differently. Beswick et al. (2012) identified four stages of

The STEMCrAfT project aimed to contribute to building the confidence and capacity of rural and regional primary and secondary teachers of science and mathematics through the development of a jointly-developed framework for teacher analysis, critique, and evaluation of teaching resources. In collaboration with rural and regional primary and secondary teachers of science and mathematics, STEM academics, and teacher educators from an Australian university, the main aim of the STEMCrAfT project was to: 1. Provide a framework by which teachers can select science and mathematics and teaching resources (human expertise, online or material) that are best suited to their needs and context. The manner and extent to which the project achieved this aim is the focus of this paper. Two additional aims of the project were to use the STEMCrAfT framework to:

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2. Enhance the confidence and efficacy of teachers in rural and regional schools in relation to mathematics and science knowledge and its application; 3. Assist teachers to inspire rural and regional students and improve their achievements in mathematics and science and their inclination to continue its study at senior secondary and tertiary levels. The project recognised and drew upon the experience of rural and regional teachers, with their understanding of the diverse contexts of their schools, their students', and school needs. Such teachers collaborated with STEM academics who had deep understanding of their disciplines and ways of working, and teacher educators with their understandings of how PCK for science and mathematics teaching can be developed. Teachers (both those participating in the project and those at whom the project was aimed) were intentionally positioned as leaders of their own professional learning. Academics in STEM disciplines and teacher education took on facilitative and consultative roles to support teachers in developing the framework. In this paper, we provide answers to our two research questions and report on the process by which we addressed the first aim, namely the development of a framework useful for teachers of science and mathematics. We describe how the framework explicates the knowledge our expert teachers of science and mathematics draw upon when they make decisions about teaching resources for less experienced colleagues and/or colleagues teaching out-of-field. Teacher participants were recruited from the two Australian states of Tasmania and Western Australia (WA) because these states represent the diversity of rural and regional areas in the country: Tasmania (0.9% of Australia by area), while geographically small, has rugged terrain and a highly dispersed population making isolation a product of topography and distance from a large metropolitan centre. In WA (33% of Australia by area) distances are vast with many small schools serving communities, often mainly indigenous and thousands of kilometres from major population centres. 3. Method Participants. 26 experienced teachers of science and/or mathematics 18 in Tasmania and eight in WA participated along with 11 inexperienced or out-of-field teachers of these subjects (two in Tasmania and nine in WA). All teacher participants were nominated by senior educational system leaders with the experienced teachers being recognised as successful teachers of mathematics and/or science, considered to have well developed PCK inclusive of content knowledge in their discipline area. The teachers were drawn from the government and Catholic education sectors in both states. Of the 20 Tasmanian teachers, 10 indicated that they taught both science and mathematics, eight taught only science, one taught only mathematics, and one did not indicate the subjects that he/she taught. Of the 18 experienced Tasmanian teachers, all but two taught in secondary schools, 12 were female and eight were male. The two out-of-field or inexperienced Tasmania teachers were both male and taught in secondary schools. Of the 17 WA teachers, 11 indicated that they taught both science and mathematics, five taught only science, and one taught only mathematics. Of the eight experienced WA teachers, four taught in secondary schools and four in primary schools with four being female and four male. Five of the nine out-of-field or inexperienced WA teachers taught in secondary schools; seven of these nine were female and two were male. Procedure. The project was undertaken in two phases over an

8-month period. Phase 1 was conducted in Tasmania and Phase 2 in WA. Phase 1: Initial framework development. This Phase comprised a 3-day workshop. The first two days were attended by the experienced teachers, whereas the third day included the out-of-field or less experienced teachers along with three of the experienced teachers who were able to stay for the additional day. During the first two days the experienced teachers:
were introduced to the STEMCrAfT project and the model of reflective practice shown in Table 1;
reflected upon and discussed issues impacting upon the teaching of science and mathematics;
applied the reflective process to critique specific STEM resources2 to produce a draft framework for decision making about science and mathematics teaching resources; and
field tested the draft framework through its implementation using one or more additional resources provided. The theory of reflective practice (Killion & Todnem, 1991; Schon, 1987) was used as a scaffold to make the teachers' thinking visible. For each of the three types of reflection shown in Table 1, the teachers first considered their individual practice in selecting teaching resources and then discussed their thinking in groups before sharing with the whole group. The resulting initial draft of a framework comprised a series of questions grouped under three headings (before, during and after use of the resource). It was applied to three specific resources in order to prompt further reflection on the thinking and knowledge involved in making resource related decisions. The three resources were chosen to be diverse and included a text based mental computation teaching program, a software program, and a Primary Connections (Australian Academy of Science, 2005) unit including student activities and teacher notes. A group of six teachers considered each. The outcome of these two days was a draft framework which was the focus of the third day of the workshop when lessexperienced teachers of science and mathematics (n ¼ 2) joined some of their expert colleagues (n ¼ 3) to critique and further refine it. This group used the framework to appraise a further eight STEM resources, critiquing and honing the framework while doing so. The resources chosen for this task were again diverse and included an interactive presentation on maritime engineering, a program claiming to teach calculus to primary school students, and an integrated K-12 STEM program. By the conclusion of Phase 1, the draft framework was judged by the group to be suitable for use by beginning teachers and those teaching out-of-field. The participating teachers were invited to contribute to the further development of the framework by:
Introducing it to colleagues and asking them to trial it;
Implementing the framework with resources of their choosing; and
Providing feedback to the project team. Phase 2: Further framework development. During Phase 2, three members of the project team and four teachers who participated in Phase 1 travelled to WA for a 1-day workshop. The project team and Tasmanian teachers facilitated the 21 teachers of science, technology and mathematics from regional, rural and isolated parts of WA to further refine the framework using a similar process to

2 For the purposes of the project, a resource was considered to be anything or anybody that could be used to contribute to teaching and learning; for example, a computer application, field trip, textbook, aboriginal elder or community expert.

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Table 1 Three types of reflection. Reflection type

Practitioner focus

1. Reflection for planning 2. Reflection during practice 3. Reflection on practice

What a practitioner does prior to teaching, in this case, searching for and choosing a resource to support their teaching and students' learning What a practitioner does as they are teaching the lesson/unit, in this case, whilst using the resource. What a practitioner does as they reflect back on the lesson/unit of work, in this case, which used the resource.

that employed in Phase 1. The WA teachers worked with the framework to critique STEM resources, providing feedback which was used to further enhance it. They also contributed to the development of supporting materials (STEMCrAfT Guidelines) aimed at assisting teacher mentors to use the framework with their less experienced colleagues. After Phase 2 all participating teachers and their colleagues were asked to:
implement the framework with resources of their choice;
enhance the draft ‘STEMCrAfT framework’ through providing feedback; and
enhance the draft ‘STEMCrAfT guidelines’ through using an online community of practice established for the project or providing feedback directly to the project team. The resulting STEMCrAfT framework and associated guidelines can be accessed online at: (http://www.utas.edu.au/education/ research/research-groups/maths-education/stemcraft-project). Data generation. Throughout each of the workshops, teacher participants were asked to both reflect upon the process undertaken in developing the framework, and to evaluate the usefulness of the framework for critiquing science and mathematics teaching resources. Throughout and at the end of each day, participants were provided with templates for individual written reflection, which asked open-ended questions in relation to these components of the project, providing the project team with rich qualitative data. Table 2 shows the questions used in two of the templates: one designed to prompt reflection on the emerging framework and the other designed to capture teachers' learning from applying the framework to particular resources. In addition, the teachers had opportunities to brainstorm the things that they thought about when deciding whether to use a resource, and to discuss their responses to questions that appeared in the reflective templates (see Table 2 for examples) that were completed throughout each day. Records of these discussions were shared in the form of notes on whiteboards of, for example, aspects of their thinking at each of the planning, implementing and evaluating stages of using a resource, and the knowledge upon which they drew in making these considerations. Subsequent to each of the workshops (Tasmania and WA), participating teachers were able to nominate to participate in a post-project interview, with questions exploring the suitability of the framework (content, design, applicability) and any suggestions

for improvement. Data are reported using pseudonyms in the following section. 4. Results and discussion In keeping with the two research questions that guided the study, the results are presented in two sections. The first concerns the product of the workshops, the STEMCrAfT framework, which encapsulates the knowledge on which expert teachers of science and mathematics draw when they make decisions about teaching resources (Research Question 1), and the second presents data and findings about the process of making this knowledge explicit (Research Question 2). 4.1. The product of the workshops: the STEMCrAfT framework The framework, shown in Table 3, comprises questions in seven categories designed to be worked through sequentially. These categories emerged as the teachers worked with the STEM resources provided them during the workshop and subsequently reflecting upon their practice, both during the workshops and subsequently. The framework is based upon both their completed templates and the outcomes of whole group discussions. For example, drawing from typical comments provided in the template, one respondent shared the steps he undertook when selecting a resource to use in a lesson or unit of work: I look around at what resources are currently available. Are these better than what I have used previously? What direction might this resource take my lesson? Is this resource worth incorporating or should I re-use something that has been good in the past? (Tas expert teacher 1) Another participant communicated how she reflects upon the usefulness of a resource as she was using it during a teaching episode: [While teaching, using the resource] I monitor for understanding of concept; monitor use/student engagement and evaluate students' interest e what questions have students posed in relation to topic? (Tas expert teacher 2) A third summarised his thinking when reflecting back upon the utility of a resource after a teaching event: I ask myself, would I use this again? What should I change? How did the class go e were they engaged? Did they achieve outcomes? Who still needs help? Did I maintain control? Would I share this

Table 2 Questions from two of the reflective templates. Your individual feedback on the draft framework

Capturing your learning and initial thoughts

1. What are the benefits of the framework in its current form 1. How useful was it to consider your thinking against a particular resource? in guiding resource selection? 2. What is missing from the framework? What needs to be 2. What did you learn by undertaking this activity? added, removed or clarified? 3. Are we heading in the right direction? If so, why do you 3. What issues have arisen for you in regard to STEM teaching? think this? 4. What has this activity highlighted for you as being potentially important for teachers teaching out of area, or teachers teaching in regional, rural and remote areas?

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Table 3 Questions that form the STEMCrAfT framework and implicated knowledge. STEMCrAfT framework

Knowledge required

Step 1 - Preparation
Identify the STEM resource you would like to review.
What is its name?
What is it needed for?
How did you find out about it? Was it recommended? By whom?
Does it/How does it relate to the Australian Curriculum requirements you want to address? Step 2 - Planning
Do you understand/have the knowledge and pedagogies that could be used to deliver this outcome?
Does this resource provide accurate, contemporary information?
Will this resource help you and your students understand this topic?
Does this resource suggest pedagogies that will enable you to achieve the outcomes you require?

Knowledge of Curricula:
Science, Mathematics, Design Technologies; Digital Technologies and their integration.

Step 3 - Context
Does the resource connect with your students' prior experience and interests and can it be linked to your students' familiar contexts?
Does your school have the additional resources this resource would need to be effective? (laboratory, funding, Occupational Health and Safety (OHS), material, IT support etc.)
Can the resource be used and or adapted for the diverse learner needs?
Have you got the time to understand how to effectively use this resource? Step 4 - Resource usability
What are the problems you might anticipate when you use this resource?
What are the OHS issues to consider?
How does this resource compare with resources you have used previously?
What are the numeracy and/or literacy demands of this resource [for students]?

Knowledge of:
The topic to be taught [including what is not relevant (Loughran et al., 2012)],
Instructional strategies for teaching the topic,
How understanding of that topic is typically developed (including difficulties that students typically encounter, representations that are likely to be effective in developing students' understanding, how students might demonstrate understanding or lack thereof),
Students' understanding: what the particular students bring in terms of existing understanding or relevant experiences, and
Pedagogies afforded by different types of resources. Knowledge of:
Students' understanding, including prior experiences, interests, and contexts with which they will be familiar,
Resources available at the school,
Areas of student difficulties, with the ideas or with accessing/using the resource,
Appropriate task adaptations/curriculum differentiation for diverse learners, and
Self-knowledge in relation to what needs to be known to use the resource effectively. Knowledge of:
Robustness of the resource in terms of being effective when inexpertly used,
Possible dangers from miss-use (accidental or intentional) and mitigating strategies,
A range of comparable/alternative resources,
Numeracy, and literacy. Knowledge of:
Preparation needed,
Additional supervisory needs, and
Exactly how the resource will be used and its effectiveness optimised. Knowledge of:
The range of affordances of the resource,
Horizon content knowledge beyond the immediate topic,
Assessment of student learning/understanding both during and after a learning episode,
OHS requirements,
Self-knowledge in relation to what needs to be known to use the resource effectively, and
Self-knowledge in relation to content knowledge and pedagogy.

Step 5 - Support considerations
Do you need any support to use this resource?
Is this resource self-contained? Or do you need to order materials (think time, cost and availability etc) Step 6 - Evaluating the implementation
Is this resource a long-term unit resource concept or a short-term unit applicable resource?
Is the resource assisting my students to achieve the intended learning outcome(s)?
Do I have some formative assessment to support this?
Have there been any problems?
If “yes” can you explain?
Were there any unexpected OHS issues?
What have you learned about using this resource for the future? (Did you meet with any unexpected problems?)
What have you learned that would allow you to use this resource better?
What have you learned about your own knowledge and pedagogies? Knowledge of: Step 7 - Feedback to your colleagues teaching STEM
Can you describe how this resource worked and place a post on the STEMCrAfT
Features of the resource and/or its use that made it effective/ineffective, and
How the resource contributed to students' learning. Community of Practice?
What aspects worked well?
Why did it work?
Student feedback e what did they say?
Advice for future users:  I would use this resource again. BI would/would not consider using this resource again.

again? (Tas expert teacher 7) Ultimately teachers' combined reflections were distilled, and the seven overarching categories or steps were identified and agreed upon by the group: preparation, planning, context, resource useability, support considerations (e.g., internet access), evaluating the implementation, feedback to colleagues. In view of the difficulties posed by unreliable internet connection in some rural and regional contexts attested to by the literature (e.g., Hanson & Carlson, 2005) as well as remotely located participants in the project, the framework was designed to be downloadable and hence able to be used offline including in hard copy. By making their way through the framework, teachers are

required to consider their own capabilities in the learning area, the appropriateness of the resource to the curriculum, their teaching context, the diversity and needs of their learners and the support required to use the resource. Answering these questions requires expert teachers of science and mathematics to draw on their PCK and so the questions explicate that knowledge. For example, answering Question 7, “Will this resource help you and your students understand this topic?” requires knowledge of the topic that is to be taught, how understanding of that topic is developed (including difficulties that students typically encounter, representations that are likely to be effective in developing students' understanding, how students might demonstrate understanding or

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lack thereof), and what the particular students bring in terms of existing understanding or relevant experiences. Table 3 also includes the kinds of knowledge implicated by each step of the framework. These knowledge types were derived from an analysis of the questions in the framework undertaken by the authors, and although comprehensive are unlikely to be exhaustive. The knowledge identified in Table 3 includes aspects that would fit in each of the categories of PCK for teaching identified by Magnusson et al. (1999) for science: Knowledge of Science Curricula, Knowledge of Students' Understanding of Science (e.g., knowledge of students' prior experiences, interests, and contexts with which they will be familiar), Knowledge of Instructional Strategies (e.g., knowledge of appropriate pedagogies for teaching the topic) and Knowledge of Assessment of Scientific Literacy (e.g. what science learning to assess and how). The knowledge identified in Table 3 is also comparable with the PCK categories identified by Ball et al. (2008) revealing an equivalent level of alignment for mathematics: Knowledge of Content and Curriculum (e.g., knowledge of the curriculum), Content and Students (e.g., knowledge of students' prior experiences, interests, and contexts with which they will be familiar) and Content and Pedagogy (e.g., knowledge of appropriate pedagogies for teaching the topic). Horizon Content Knowledge (Ball et al., 2008) is also evident in knowledge of the scope of the curriculum beyond the immediate topic. One can also identify at least five of the seven knowledge types posited by Shulman (1987) as required by teachers: namely, content knowledge (e.g., knowledge of the topic to be taught); curriculum knowledge (e.g., knowledge of the curriculum); pedagogical content knowledge (e.g., how understanding of that topic is typically developed); knowledge of learners (e.g., knowledge of students' prior experiences, interests, and contexts with which they will be familiar); and knowledge of educational contexts (e.g., OHS requirements). General pedagogical knowledge and knowledge of educational ends, purposes and values (Shulman, 1987) are not clearly evident in the framework. This is not surprising given the fact that the overall purpose(s) of education provides the intellectual context in which teachers think about detailed aspects of their teaching such as resource selection and can remain implicit. It is often also difficult to distinguish general pedagogy and topic-specific pedagogy (PCK) (Chick, Pham, & Baker, 2006), particularly when teachers from the same discipline are discussing resources, hence such aspects of teacher practice were not highlighted by teachers in the framework. Nevertheless, knowledge at this broad level that encompasses what teachers believe science or mathematics is and what it means to learn these disciplines is important to teaching and shaping the classroom experience of students in subtle but discernible ways (see Beswick, 2012 in relation to mathematics). In contrast to existing conceptualisations of science and mathematics teacher knowledge, the framework suggests the need for self-knowledge, that is, acknowledging the information that an individual draws upon or requires in order to find an answer, make a decision, or to act in the world. This is evident in two places in the framework e in relation to “what needs to be known to use the resource effectively” and “content and pedagogy”. For teachers who are new to teaching or new to teaching a particular subject, knowing what you do not know is a crucial first step to acquiring that knowledge. Fine-grained analyses and listing of expert teacher knowledge such as encapsulated in the framework can serve a useful purpose in drawing less experienced and out-of-field teachers' attention to possible gaps in their knowledge. The length of the framework is consistent with the fact that the knowledge drawn upon by expert teachers is rich (Berliner, 1988) and extensive. A corollary of this is that the framework takes time

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to work through. This would be particularly the case for inexperienced and out-of-field teachers in Berliner's novice phase of PCK development. The time required was highlighted as a problem by some more experienced participants from Tasmania, who suggested that the results of assessments of various resources that teachers do, might be pooled and made available to others. Such an approach would have merit for teachers working in similar contexts, but it neglects the value inherent in the process of thinking through the answers to the questions. Further research would be needed to explore whether making expert teachers' knowledge available to less experienced colleagues using tools such as the STEMCrAfT framework can hasten the process of acquiring expertise, or whether becoming an expert (Berliner, 1988) or reaching PCK consolidation (Beswick et al., 2012) simply takes time. If the latter is the case, then tools like the STEMCrAfT framework can at least militate against key aspects of expert knowledge being overlooked.

4.2. The process of the workshops: Making expert teachers' knowledge explicit The findings provide evidence that the reflective conversations undertaken in the STEMCrAfT project were successful in making the teachers' choice of resources, informed by tacit knowledge, explicit. The following comments from two of the experienced Tasmanian teachers, describe both the tacit nature of the knowledge that they and colleagues routinely use, and the fact that the framework encapsulated that knowledge: … you know, probably more than 80% of the things [in the draft framework], is the stuff that we just do all the time, but we never actually like realised we're doing it. But to put it on paper and to put it in a framework to say, this is what you're actually going through when you're doing it, it was a bit enlightening that way, like I felt, oh yeah, I do this. Actually yes, I do this. (Tas, expert teacher 1) And I think the workshop itself was a real eye opener in terms of making me realise how much my practice becomes embedded. So, when we actually had to pull out all of the things that we do in planning and using and implementing and evaluating the resources … it was amazing … quite amazing how much there is to what we do but that we just become unconscious in doing it. So, it just becomes part of our everyday practice. (Tas, expert teacher 2) As was typical of the responses of other participants during post-project interviews, this latter participant affirmed that the STEMCrAfT methodology enabled his thinking processes to be explicated: I think … the framework that we developed and the ideas behind the workshop hold a lot of promise to helping in that area [assisting out-of-field, new and/or isolated teachers] …. .For me the framework is about making explicit the steps that we go through in selecting a good resource, finding a good resource, selecting it and then putting it into practice and figuring out if it is good (Tas, expert teacher 2). The development of the framework using an iterative process as described could be seen as a modification of the cyclical process described by Plack and Santasier (2004). It differed from their

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approach in that different teachers, both experienced and less so, from diverse locations were involved in the conversations at various stages. Drawing on a range of perspectives in this way is likely to have enriched the extent of the knowledge uncovered by the overall process. A pre-service teacher (novice teacher) who subsequently worked through the framework with his mentor teacher (a participant in the project) while undertaking a practicum placement, stated that the framework encapsulated the sorts of things he needed to think about, and by implication the kinds of things about which he needed to know: I did find it really helpful. Because I don't have much experience sort of as a teacher and selecting resources and planning lessons and things like that, it was quite good just to sort of direct me to the sorts of factors I should be thinking about when choosing a resource. So, it sort of stimulated my thinking in that way … (pre-service teacher 1) Whereas experienced teachers could recognise their own knowledge when they considered the questions in the framework, less experienced and out-of-field teachers such as the pre-service teacher quoted above, appreciated the guidance it provided about the sorts of things that needed to be considered. Although the framework was developed with relatively isolated teachers in mind, working with a colleague in a mentoring role while considering the questions, emerged as a powerful way to assist lessexperienced and out-of-field teachers. Working through the framework enabled novice teachers to understand the importance of “critically looking at resources; not just using it e thinking about why I use it” (WA novice teacher 10). A participant who identified as a novice teacher recognised that both the framework and the process by which the framework was constructed in the STEMCrAfT project, enabled access to expert knowledge, providing a: Reflective practice opportunity e [which] helps evaluate a new resource. It follows your natural thought process & planning process - most teachers would do this informally when planning on using a resource (WA novice teacher 15) Furthermore, the framework was perceived as being useful for gathering evidence in support of requests for further resourcing, as it provided one teacher with “good for evidence to put to board/ school to obtain more of that resource for the school” (WA novice teacher 4). The experience of participating in the project was also seen as an important professional development opportunity, due to its usefulness in connecting novice teachers with other more experienced teachers of science and mathematics, underlining the importance of a community of teachers whom he thought could: …. help with my planning. I was also told on the day about many great resources that can be found online already, as well as numerous text resources that are available as well. I was also offered assistance through emails and phone calls if I required it (Tas novice teacher 4 - reflection). The framework adds to novice teachers' self-knowledge about their own knowledge and understandings and might, therefore, prompt a deeper exploration of relevant issues than might otherwise occur. The framework provided a systematic way to unpack the necessary thinking behind choosing a resource as well as facilitating conversations that could contribute to the development

of expert knowledge in the less-experienced colleague. 5. Conclusion The study makes two major contributions to understandings of teacher knowledge. First, we have described a process by which such knowledge can be uncovered that is not reliant on large scale surveys or intensive classroom observation and interviews. Importantly, the process could be applied to the knowledge needed to teach any subject area. Second, the STEMCrAfT framework demonstrated how the complex and rich knowledge of expert science and mathematics teachers can be made available to less experience or less expert teachers of these subjects. Whereas existing models of teacher knowledge describe various categories of knowledge needed for teaching science or mathematics, the STEMCrAfT framework uses questions to point teachers to the necessary knowledge while engaging in a specific teaching decision-making context. As such it is much more practicefocussed and immediately useful than other teacher knowledge frameworks prominent in science and mathematics education literature. Nevertheless, the STEMCrAfT framework encapsulates most knowledge types identified by Shulman (1987) and each of the aspects that Magnusson et al. (1999) identified for science PCK and Ball et al. (2008) identified in their mathematics specific elaboration of PCK. It makes evident the clear synergies between the knowledge components of PCK identified for science (Magnusson et al.) and mathematics (Ball et al.). Such alignment between science and mathematics PCK models warrants further examination. Authors such as Hauk, Toney, Jackson, Nair, and Tsay (2014) have started the process by looking to extend mathematics PCK to include the interplay among content, beliefs and values, an inclusion that has existed for some years in science PCK models (Magnusson et al., 1999; Park & Chen, 2012). Researching the synergies between science and mathematics PCK models as a simultaneous thread, would assist teachers who commonly teach both of these subjects to make sense or their practice across these related disciplines. In addition, this focus highlights the need for self-knowledge in relation to aspects of knowledge that might be missing or limited. The STEMCrAfT framework articulates the process by which expert teachers of science and mathematics select teaching resources thereby making explicit their tacit knowledge. The less experienced teacher participants in the study were able to replicate the pedagogically sound process for choosing resources and activities best suited to their context, thereby endorsing the potential usefulness of the framework. The question of whether detailed descriptions of the knowledge that comprises expert PCK encapsulated by the STEMCrAfT framework, could be of assistance in hastening the development of PCK was beyond the scope of the project. Nevertheless, the framework provides a tool by which the development of that knowledge can be approached systematically, and that militates against crucial aspects of that knowledge being overlooked. The process of iterative collaborative reflective conversations described by Schon (as cited in Kinsella, 2010) amongst expert and less experienced teachers in developing the STEMCrAfT framework was effective in revealing the knowledge from which expert teachers of science and mathematics draw when selecting teaching resources. This conclusion is affirmed by comparison with models of PCK in the literature (Ball et al., 2008; Shulman, 1987) and by the reactions of the participants both as they discussed the required knowledge and as they used the framework with less experienced colleagues. Unlike other uses of reflective conversations (e.g., Plack & Santasier, 2004) the conversations in this case involved different

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and diverse groups of teachers, a fact that is likely to have strengthened the process as a means of explicating expert knowledge. Engaging in such deeply reflective conversations was illuminating for all participants; it enabled experienced teachers to realise the extent of their tacit knowledge and embedded practice, thereby affirming their professional capability, and provided less experienced teachers access to this professional knowledge. The STEMCrAfT framework is still considered a ‘work in progress’ in that there are likely to be other aspects of the knowledge on which teachers draw in the single aspect of teaching e selecting a resource e that can be nuanced. Exploring the benefits of extending the framework beyond the focus on resource selection, to support teachers to reflect critically upon other aspects their practice (e.g., particular pedagogies suitable for particular topics) may be useful. Education researchers and professional learning facilitators can also learn from the process by which the framework was constructed. The STEMCrAfT guidelines, developed in concert with the framework were developed with professional learning and mentoring activities in mind. The benefits of using the framework collaboratively with colleagues, when planning the school teaching year for example, or when working with less experienced colleagues or in a professional learning community would also benefit from further exploration. While the iterative collaborative reflective conversations that enabled the creation of the framework were deemed beneficial for all participants, such occasions are rare for teachers in general, and even more so for teachers teaching in rural and regional areas. How professional development opportunities such as this can be provided to such dispersed groups of expert and novice teachers remains a challenge but is an issue that demands more research. As does the extent to which the particular needs of teachers from rural and regional areas are recognised and addressed through policy (Luft et al., 2015) and supported in practice. Finally, although the framework was designed by and for teachers of science and mathematics, its applicability to other curriculum areas is yet to be determined. The requirement that teachers critique, select and advocate for particular resources in support of their teaching and student learning is ubiquitous and ongoing. Field testing the framework with expert and novice teachers and teacher educators from other curriculum areas would be useful. A non-discipline specific version of the framework has the potential to enable less experienced teachers in curriculum areas other than science and mathematics, to access the tacit professional knowledge of experienced educators in their discipline. Certainly, the process used to explicate expert teacher knowledge in the STEMCrAfT project would be applicable to teachers in other curriculum areas. Acknowledgement Funding for the project reported here was provided by the Department of Education, Australian Governement, through the Australian Mathematics and Science Partnerships Program (AMSPP) Priority Projects. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.tate.2019.102907. References Angelides, P. (2001). The development of an efficient technique for collecting and analyzing qualitative data: The analysis of critical incidents. Qualitative Studies in Education, 14(3), 429e442.

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