Resources for and from Collaboration: A Conceptual Framework

Abstract

Resources are important for all joint work and learning, and particularly for collaborative professional work and learning among teachers. They provide a means for the design of learning environments, for joint work in pursuit of learning goals, and can support links between teacher collaborative learning and teaching practice. They can also be a focus of analysis for research and explanatory mechanisms that illuminate the complexity of relationships in collaborative work.

1 Introduction

Resources are important for all joint work and learning, and particularly for collaborative professional work and learning among teachers. They provide a means for the design of learning environments, for joint work in pursuit of learning goals, and can support links between teacher collaborative learning and teaching practice. They can also be a focus of analysis for research and explanatory mechanisms that illuminate the complexity of relationships in collaborative work.

In this chapter, we provide a framework for conceptualising different kinds of resources and their functions in supporting productive teacher collaboration. Drawing on our work with teacher collaborative groups in two different contexts, we argue that resources can be conceptualised more broadly than they are currently, and that a broader conceptualisation supports us to see and design for aspects of collaboration previously hidden. In particular, we draw on two sets of questions to guide our work:

What resources are available to support teacher collaboration? With what effects, both on the collaboration and the resources themselves?

What resources are missing for supporting teacher collaboration? How and to what extent can teachers overcome these missing resources?

These questions were an important part of the work of Theme D at the ICMI 25 Study Conference and our discussions there suggested that resources are dynamic and living, that they evolve in relation to the contexts of collaboration and the classroom, and they go beyond material objects to include human, social and cultural resources (Chap. 5, this volume). We discuss our use of the term ‘resources’ in more detail later in this chapter.

In developing a framework of resources somewhat broader than conventionally conceptualised, we hope to draw attention to missing resources, in two senses. First, some resources are missing from current conceptualisations of resources, and this absence might limit our view of what can and does happen in teacher collaboration. Second, some resources that are available in some contexts, for example online resources, may not be available in others, because of the inequitable distribution of resources. We therefore hope that our framework provides ways for designers and researchers of collaboration to focus on inequities among contexts and not to assume that middle-class contexts in the ‘developed’ world are the norm.

We develop the framework in relation to our work with collaborative teacher professional development in two geographic contexts—South Africa and the United States—which are different in many ways and remarkably similar in others. Looking across our similarities and differences has supported us to see how aspects of our framework are sensitive to context and, at the same time, may be applicable in various other contexts—supporting others to describe their current work and to see possibilities for new design and research.

2 Conceptualising Collaboration

The ICME-13 survey on teachers working and learning through collaboration defined collaboration as:

co-working (working together) and can also imply co-learning (learning together). It involves teachers in joint activity, common purpose, critical dialogue and inquiry, and mutual support in addressing issues that challenge them professionally. (Robutti et al., 2016, p. 652)

and teachers working together as:

collaborating for some specific aims, which could be directed towards: improving students’ learning; improving their professional role in the school; learning to use new resources (e.g. technological tools); creating a professional network within the school or region; and discussing institutional reforms and demands around the curriculum, the national evaluations system, etc. (p. 653)

These definitions suggest that joint work produces learning and that collaborative learning requires the intent to work together and a purpose for this work. Collaboration can be organised, as in professional development sessions, or occur spontaneously, as teachers talk to each other about their practice; it can be long-term, as in on-going professional learning communities, or ad hoc, as the need is felt by teachers. Collaboration can take place in face-to-face settings, or virtually, and can be local, taking place within a school or among nearby schools, or more global, among teacher associations or groups constituted online. Organised collaboration is usually designed by professional development providers, by teachers or by teacher educators and teachers working together.

What collaborative groups look like, and how they work, have been described differently by different researchers. Wenger (1998) defines communities of practice (COPs) as groups of people engaged with each other, focused on a joint enterprise, and creating a shared repertoire—a set of resources which support their enagement in relation to the joint enterprise. Communities learn together and are always sociohistorically situated in webs of social relations, as are the resources that support communities and their learning. Gueudet and Trouche (2012a) refer to ‘collectives’ as, “not necessarily implying cohesion or involvement in a common project” (pp. 305–306), thus including a broader range of potential collaborative work.

Brodie and Borko (2016) have defined a professional learning community (PLC) as a special kind of community of practice, with the distinguishing feature of professional learning, where professional learning entails becoming confident with and competent in the knowledge base of the profession, and using it to make and justify professional decisions (see also Chauraya & Brodie, 2017). Professional learning involves regular and sustained inquiry into various aspects of local practice, as they might relate to more global concerns (Jackson & Temperley, 2007; Jaworski, 2008). Louis and Marks (1998) argue that school-based PLCs allow teachers to “coalesce around a shared vision of what counts for high-quality teaching and learning and begin to take collective responsibility for the students they teach” (p. 535).

COPs and PLCs provide opportunities for systematic teacher collaboration and learning, usually facilitated, and it has been argued that thinking and practice develop more powerfully when worked on systematically. The studies reviewed by the ICME-13 survey (Robutti et al., 2016) showed a variety of teacher learning from collaborations, including teacher learning of mathematics, mathematics teaching practices, attending to student thinking, supporting student articulation of their thinking and an increased valuing of collaborative work. Stronger professional collaboration can also be an outcome of COPs and PLCs, i.e. professional collaboration itself is both a means for and and an outcome of teacher learning.

However, the ICME-13 survey found that only about 20% of the studies they looked at explicitly considered whether, how and why collaborations were effective, that “very few studies have revealed unsuccessful collaborations” (p. 680), and that barriers to successful collaboration were largely attributed to teachers’ ownership of the process, to time and to institutional constraints. In addition, it has been shown that the focus of teachers’ interactions—broad enough to allow for disagreement, but focused enough to develop shared understandings—and how teachers interact with each other—with respect, challenge and trust—is important for successful collaboration (Brodie & Shalem, 2011; Katz et al., 2009). While many communities develop these attributes and support growth among their members, others may become unproductive, if some of the important processes break down (Maloney & Konza, 2011; Schaap et al., 2019).

In this chapter, we focus on the critical role that resources play in teacher professional collaboration, noting that which resources are available and how they are used may play an important role in the success of collaborations and teacher learning from them. We focus on collaborations in which the purpose is to engage in extended inquiry into teaching and learning, but suggest that our framework can be used more broadly to think about other forms of collectives and collaborative work.

3 Conceptualising Resources in Teacher Collaboration

The nature of resources that support teacher professional collaboration is an important theoretical and practical concern for designing and researching teacher collaboration. A number of different theoretical perspectives have been used to research teacher learning through professional collaborations, each with associated terms and concepts for resources (Theme D, Chap. 5, this volume). Terms such as ‘tool’, ‘artifact’, ‘instrument’, ‘document’ and ‘resource’ are all used and point to particular theoretical positions. In this section, we review some of the important theoretical perspectives that have informed our work and argue for our use of the term ‘resource’. We also look at the extent to which the ‘materiality’ of resources is important.

Vygotsky initially conceptualised tools as mediating between subject and object, or between the learner and what is to be learned. Tools act externally on the object to be learned, and/or internally on the subject, with a tool acting internally called a psychological tool or a sign (Vygotsky, 1978). For him, the notion of tool comes from material tools, which we use to achieve material ends and gain control over our physical environment. However, as people, especially when learning, we both imbue material tools with symbolic meaning and create symbolic tools, which mediate the objects of our learning semiotically (Bartolini Bussi & Mariotti, 2008). Tools that mediate and support learning have a psychological function, i.e. they change cognitive functioning, and tools that look similar can nonetheless function differently, depending on how they are used. The most powerful tool, which acts both internally on our minds and externally on other people, is language. So, for Vygotsky, tools both are material and go beyond the material—what is important is where and how they act. Crucially, objects and tools do not exist outside of social relations and meaning-making.

Building on Vygotsky’s germinal work, Activity Theory broadened the notion of tool use to include artifacts which draw their meaning from and contribute to activity, mediating between subject and object in the context of a community (Engeström, 1999). Activity Theory also broadens our understanding of social contexts, by considering the division of labour and the rules, or norms, of practice in the community, as important interactors with the semiotic mediation between subject and object using tools or artifacts. In this way, Activity Theory supports an institutional focus, necessary for understanding learning in schools. It distinguishes between object and outcome, where object is the focus of or motivation for the activity, while outcome is a product of the activity. In the case of learning, focusing on the same object of learning with different artifacts can produce different outcomes for different learners. Researchers working with Activity Theory use the terms tool, artifact and instrument somewhat interchangeably, and these are both produced in and organise various aspects of activity systems and how different activity systems work together to produce learning (Akkerman & Bakker, 2011; Perks & Prestage, 2008).

Vygotsky and Activity Theory provide us with strongly elaborated theoretical perspectives on which to base our understanding of the use of tools in collaborative teacher learning. Some important principles underlie these perspectives:

• 1. we need to distinguish between the tool/artifact and the object of learning it mediates, and to see distinctions and relations among tools, objects and outcomes;

• 2. as learning happens, objects and outcomes of learning shift and new tools are employed to mediate new objects;

• 3. prior objects and outcomes can become tools for further learning and so we talk about the evolving use of tools as lived and living supports for learning;

• 4. the use of tools and artifacts to mediate learning relies on people assigning meaning to them—they only function in relation to their meanings and salience for the learner—and these meanings are shaped by the broader contexts in which tools and artifacts are used;

• 5. tools and artifacts mediate learning because they support us to see both the objects of learning and ourselves in new ways.

There are two important additional points. First, the distinction among task, object and outcome is not always realised in mathematics teaching, nor in mathematics teacher collaboration. Many teachers and learners see the completion of the task as the outcome of the activity itself, rather than as an object mediating the outcome which is, for example, developing mathematics concepts (in mathematics classrooms) or deepening the practice of inquiry (in teacher collaboration). Success is often seen as the completion of the task, which might constrain the depth of learning in collaboration (Prediger, 2020). Second, we note a further elaboration of the notion of mediation, into three kinds: mediation of the object of the activity, aimed at getting to know the object and also acting upon it; interpersonal mediation, oriented toward others and aimed at both knowing others and acting in interaction with them; and reflexive mediation, through which the subject’s relation to themself is mediated by the instrument (Theme D, Chap. 5, this volume).

Vygotsky and Activity Theory illuminate the use of tools and artifacts in learning, from the perspective of learning. A more recent theorisation—the documentational approach to didactics (DAD)—starts with the notion of tool or instrument, and presents a framework for understanding how teachers use resources, individually and collectively (Gueudet, 2019; Gueudet & Trouche, 2012a, b). Focusing on online resources, they argue that resources made available to teachers are combined and transformed by teachers as they use them. These transformed resources are called documents, which bear teachers’ schema of use, including their intentions and inferences. The range of documents developed by teachers are organised into document systems. Two key processes are studied: instrumentation—how resources shape teachers’ activity—and instrumentalism—how teachers shape resources—in document systems. So resources are living documents that act in various ways in relation to those who use them, and support and extend meaning-making, making this approach consistent with Vygotsky and Activity Theory. What DAD adds is the idea that resources act as systems, although Gueudet (2019) notes that these systems are difficult to identify and suggests a focus on ‘pivotal’ resources.

Drawing from the discussion above, we are ready to clarify our use of the term ‘resources’. Writing about resources in the context of school instruction, Cohen et al. (2003) argue that research has shown weak links between the presence of material resources and student outcomes. They argue for the study of resources to be embedded in the study of instruction, taking into account a broader range of attributes of classroom instruction, including the knowledge and orientations to learning and teaching that teachers and students bring to the classroom. So, together with them and Adler (2000), we prefer the term ‘resources’ to ‘tools’ or ‘artifacts’, because resources go beyond material resources, as tools and artifacts have often been thought of, to include social and human resources. We believe that we use resources in similar ways to how the DAD uses documents, in that resources both shape and are shaped by teachers as they use them. We consider this meaning of resources as central for designing and researching teacher professional collaboration and have gone further in our framework to talk about knowledge, affective and institutional resources, including time and space, as key resources for teacher professional collaboration. We work with the notion of lived resources shaping and shaped by their users in practice.

We do not distinguish between material and non-material resources, because the materiality of resources refers to their form, rather than their function, and most material resources, as well as many non-material resources, serve to represent practice in various ways, so we refer to these as representational resources which can be supported in different formats. We do not distinguish between online and other resources, again because it is the function of the resource that is important for us. However, we note that assumptions about access to digital and online resources may perpetuate inequalities. As noted in Theme D (Chap. 5, this volume), when working globally, we cannot assume universal access to digital resources, particularly in the two contexts of the authors of this chapter: South Africa and the United States.

Our final theoretical perspective brings together how we use resources in relation to teacher collaboration. Wenger’s (1998) theory of situated learning defines learning as participation in communities of practice, producing and constituted by meaning and identity. Wenger’s work requires understanding of the use of resources in communities of practice, through mutual engagement in relation to a joint enterprise and creating a shared repertoire—a set of resources which support enagement in relation to the joint enterprise. Communities and their resources are socially and politically situated.

Wenger introduces the notions of participation and reification. Participation refers to the active, living aspect of interactions and collaborations, as people engage with each other and learn. Reification denotes the products of such participation, which might be ideas, language, processes or material products, which then inform future participation. Participation and reification continuously revivify each other and therefore create living and evolving resources and learning practices. For Wenger, identity is key to learning: learning is as much a becoming as a coming-to-know, and teachers’ identities are key in how they shape and are shaped by different resources and how they learn through professional collaboration.

A situative view of professional learning (Putnam & Borko, 2000) is informed by: how resources move and change across the different sites of professional learning—predominantly the community and the classroom (Akkerman & Bakker, 2011; Kazemi & Hubbard, 2008), i.e. how they are used for collaboration and from collaboration; and how they function for teachers in particular contexts because of the meanings ascribed to them (Cobb & Jackson, 2012). For example, if teachers tend to review student work to determine whether students have ‘correct’ or ‘incorrect’ understanding, they are likely to orient similarly to student work that is introduced in a collaboration context. So, if a goal of collaboration is to orient differently to student work, for example to gain insight into how students are thinking rather than simply evaluate their thinking as correct or incorrect, then careful attention needs to be given to the different orientations that teachers bring to the collaboration and how to work with them.

4 A Framework for Resources in Collaboration

Drawing on the above, the following principles underlie our framework: resources are socially and historically situated; they mediate the object of inquiry and therefore lead to learning to produce different outcomes; their meaning and functioning depend on the contexts of their use; they emerge from and support activity systems and practice; they are shaped by and shape participation in practice, and support reifications as products of learning; and prior reifications can become resources for further collaborations, learning and practice.

In line with these principles, we distinguish five kinds of resources that support teacher professional collaboration: representational resources; knowledge resources; affective resources; human resources; and institutional resources. These resources support teachers’ interactions and learning with each other. We describe these in more detail below, but we note here that some have argued that our conceptualising of resources may be somewhat broad (L. Trouche, personal communication, February 4, 2020), with institutions providing affordances and constraints, rather than resources, and knowledge being an outcome of collaboration, rather than a resource.

The designation of people as resources also may not sit comfortably with some, as people interacting with each other are seen to use, rather than be, resources (Trouche, 2020). We prefer the broader use, together with Adler (2000), who indicates both knowledge and human resources as important. Given the stark inequalities across contexts, we argue that what institutions provide should be seen as resources—indeed, they are resources. Access to other people, for example teacher educators or researchers, may be constrained in some contexts and these people bring resources to, and are themselves resources for, teacher development. We also argue that affective resources are crucially important in learning, and have been under-theorised in prior research on teacher collaboration, so we want to put this squarely on the map here.

4.1 Five Kinds of Resources

4.1.1 Representational Resources

This category refers to what are usually thought of when referring to resources for collaboration, namely various representations of practice, which support teachers to inquire into teaching and learning, for example: learners’ work; lesson plans; textbooks; assessment items; learners’ errors; classroom scenarios or actual lessons. These may come from actual classrooms, including teachers’ own classrooms, or be designed specifically for teacher collaborative work. They may come in different formats, such as print and digital. Specially designed digital forums for teacher collaboration are included here. Existing online platforms, such as Moodle, Google Docs or Facebook, are included if used for collaborative purposes (e.g. Anderson, 2020). Chapter 5 in this volume, representing the work of Theme D at the Study Conference (see also papers from Theme D in Borko & Potari, 2020), has many creative and inspiring representational resources, and the authors discuss how these have and might work to support teacher collaboration, learning and practice.

A key resource often used in collaboration, different from the others in this category, is protocols that guide the collaboration. These were not discussed in Theme D in the conference. We discuss them briefly later, in relation to how they were used by facilitators as to human resources, but we do believe they are deserving of more study as representations of the collaboration itself (Andrews-Larson et al., 2017; Segal et al., 2015).

4.1.2 Knowledge Resources

The knowledge resources for mathematics teachers include mathematical knowledge and pedagogical content knowledge (Ball et al., 2008), as well knowledge of their and their learners’ families and communities. We also include teachers’ orientations to teaching and learning, and their visions of high-quality instruction as part of their professional knowledge (Munter, 2014).

Kazemi and Hubbard (2008) distinguish between knowledge and knowing, where knowing is seen as knowledge-in-use, namely how our actions and practices are related to what and how we know. Teachers come to their collaborations with knowledge and ways of knowing developed in practice, further develop these through working with representional resources in collaboration, and their knowledge and knowing further inform future practice and collaboration. Knowledge resources shape and transform representational resources, which in turn shape and transform knowledge resources. Developing professional knowledge requires on-going, sustained inquiry, with a shared object of learning.

4.1.3 Affective Resources

All learning involves emotions. For teachers to teach well, they need emotional sensitivity to themselves and their learners. For teachers to work together productively, they need to be able to challenge each other’s thinking and practices in generative ways, going beyond “contrived collegiality” (Hargreaves, 1991). Safety and trust are important to be able to learn with others, and emotions such as fear and anxiety might work against collaborative learning, while emotions such as empathy might support it.

4.1.4 Human Resources

These include all the people involved in collaborative groups and supporting professional learning. People form an overarching category, since they make meaning of and draw together the other key resources. Teachers often interact with facilitators in their collaboration. School principals and district advisors can also be included here, as they support collaboration, linking human and institutional resources. We include learners in this group and will elaborate further below. Teachers’ identities and dispositions are key to their learning and collaboration, and are included in this category, as is their ownership of the process of collaboration (Robutti et al., 2016). While this key resource is the focus of Theme C (Chap. 4, this volume), it is also central to our framework.

4.1.5 Institutional Resources

Here we refer to the resources that schools and districts make available to teachers to collaborate. These include the provision of time and space for professional collaboration, whether and how the time is scheduled into teachers’ work, whether appropriate space is (made) available and whether the importance of collaborative teacher work is acknowledged and valued. Institutional resources include the expectations of school and district leaders for such work, the extent to which collaborative work is seen a priority for teachers and the hierarchies that exist among teachers in schools and in the collaborative context. Institutional resources also refer to how teachers perceive their obligations to the institution (Chazan et al., 2016) and how their views play out in their collaborations. Institutional resources refer both to the very real material resource constraints experienced in many contexts, and to the ways in which limited or adequate resources are made available for collaborative teacher work. This category draws attention to the deeply cultural, political and historical contexts in which teachers’ collaboration occurs across different contexts, and the many inequalities that still pervade our school systems.

In summary, institutional resources frame the work that happens in collaborative contexts and the relationships among actors and resources. All of this work is situated in social, cultural and political contexts, mediated through the institutional contexts, and these contexts are fundamental to which resources can be and are used and how they are used. The human resources that we are directly concerned with in the collaborative context are the teachers and facilitators, but other human resources such as school and district leaders are key and, as noted earlier, their values, priorities and expectations contribute to the institutional context of the collaboration.

Representational, knowledge and affective resources form the core of the actual collaboration among teachers, facilitators and the content. While many of Theme D papers discussed at the ICMI 25 Study Conference (Borko & Potari, 2020) do relate the use of representational resources to knowledge resources, there is little focus on institutional and affective resources. We discuss each of the resources categories further below, with examples from our two research contexts.

4.2 Resources in Collaboration and Practice

We now develop our framework in more detail, noting two key points made earlier. First, resources travel between teacher collaborative groups and classroom practice and, as they travel, they are transformed for use in the different contexts. This is particularly the case for representational and knowledge resources but, we will argue, it is also the case for the other resources in our framework. The processes of adopting, adapting or redesigning resources across contexts are not simple, and are deserving of our attention and study. Second, in many cases, missing resources, particularly but not only institutional and representational resources, contribute to unequal opportunities for teacher development and for classroom learning and, ultimately, to inequities in society. This is most often observed in lack of access to online and material resources, but may apply to some of the other resources as well, as we will show below.

Kazemi and Hubbard (2008) make a distinction between unidirectional and multidirectional analyses of teacher learning across professional development and classroom settings. From a unidirectional perspective, researchers assume that the intent of professional learning is to ‘learn’, i.e. accrue knowledge, within the professional learning setting, and to then ‘apply’ this learning in the classroom. Current design and research takes less account of how teachers bring their ideas and ways of knowing from the classroom to professional development. From a multi-directional perspective, this direction is equally important—it is assumed that teachers’ participation both in the professional learning and in the classroom settings is transformed, as they are “engaged in knowing in both contexts” (p. 432) and bring their knowledge and knowing across contexts.

A multi-directional perspective does not mean that all participants orient and learn in the same way in professional learning. Rather, teachers participate differently in the different contexts, for good reasons. In our terms, the varied resources that teachers bring to bear on their participation, and the resources associated with the professional learning and classrooms settings, shape participation.

As Kazemi and Hubbard argue, a key challenge both for professional learning facilitators and for researchers is to learn about the meanings that teachers generate in relation to representational resources, like lesson plans, student work or curriculum materials, in and across contexts. We expand this to take account of all the resources in our framework, so that we can leverage what is known about teachers’ sense-making across contexts, as they design new resources and forms of activity.

5 Our Research Projects and Contexts

We develop our framework further by drawing on specific projects that we have each worked in, Karin in South Africa and Kara in the United States. The two contexts enable us to highlight important contextual similarities and differences in teachers’ use of resources for collaboration. In what follows, we first briefly introduce each of the projects, and then elaborate as we apply the framework to each of the contexts.

5.1 Data-Informed Practice Improvement Project (DIPIP), South Africa

The Data-Informed Practice Improvement project (DIPIP) (2011-2014) was located in Johannesburg, the major urban area in South Africa. South Africa is the most unequal country in the world, as measured by the GINI coefficient, and our education system reflects this inequality, with the vast majority of learners located in schools that struggle to support their learning (Motala et al., 2012). Poor achievement in mathematics is widespread and strongly correlated with race and socio-economic status (Spaull & Kotze, 2015). The teaching profession is not well respected, teachers are not well paid and there is substantial ‘teacher-bashing’ in the press. Teachers, particularly those in low socio-economic status schools, where the DIPIP project worked, often have high teaching loads and teach large classes, and teacher morale is low. There are often strong hierarchies and little trust among various levels of the system, with government, principals, teachers and parents often blaming and judging each other for the widespread low achievement of learners. As with many other countries, there is little tradition of collaborative teacher work in South Africa.

One of the aims of the DIPIP project was to understand what is possible for mathematics teachers’ professional learning in PLCs in such a context. A key characteristic for successful collaboration is a focus, or object of inquiry, that is both narrow and broad enough to allow for substantive discussion and sustained learning (Katz et al., 2009). In the DIPIP project, we chose the object of inquiry to be the reasoning underlying learners’ mathematical errors. The assumption, based on the substantial errors and misconceptions research, was that systematic errors are built on partially valid mathematical reasoning and that making that reasoning explicit for teachers and learners can help both to value learners’ current mathematical thinking and to develop more robust mathematical thinking (Smith et al., 1993). The focus on errors was a mechanism to access three important dimensions of teaching and learning mathematics: learners’ thinking, which makes sense to them and can be worked with, even (and especially) when partially correct; teaching practice, which can work with learners’ errors and thinking; and teachers’ own knowledge, both content and pedagogical content knowledge. Errors can be seen as absences, as they often are viewed by many teachers, or as presences, as a resource for future learning—and in this way they can become a knowledge resource for teachers.

Teachers were supported by facilitators to work on a set of developmental activities to develop their knowledge of the reasoning behind learner errors in the various sites of teaching. Although the activities were set up before the project started, we built in areas of choice and flexibility for PLCs. A key area of flexibility built in from the start was to choose the mathematics content they would work with, based on analyses of their learners’ errors. As they became more familiar with the project, they chose to repeat some activities, to leave out some or to change the order, in consultation with the project team. The project can therefore be seen as somewhat adaptive (Koellner & Jacobs, 2015), since the model specified some key parameters, but also allowed for flexibility in relation to local contexts.

Teachers analysed tests, which provided an overview of strengths and weaknesses in learners’ mathematical knowledge in a particular school, grade or class. Based on the test analysis, they chose learners who had made interesting errors that they wanted to understand more deeply, and interviewed them. They then took the results of these two analyses and mapped them against the curriculum, working out when and how the key concepts were taught and what curricular issues might have contributed to the errors.

Based on these three activities, teachers chose a leverage concept, which is a concept that underlies many of the errors that learners make in a topic, for example: the meaning and use of the equal sign. Once a concept was chosen, the DIPIP project facilitator found literature on that concept, including learner errors on it. The PLCs read and discussed these papers and drew on these discussions to plan lessons together. The lessons aimed to surface learner errors in regard to the concept and to find ways to engage the errors, rather than avoid them. These lessons were taught and videotaped and the community then reflected on episodes in each teacher’s lessons, in order to understand their strengths and challenges in dealing with learner errors in class.

Our research team, consisting of graduate students and post-doctoral fellows, researched the teachers’ collaborations by analysing their conversations in the communities and their teaching practices across the four years of the project. We will draw on the various analyses and what we have learned to exemplify parts of the framework (Brodie, 2013b, 2014, 2021; Brodie & Chimhande, 2020; Brodie et al., 2018; Chauraya & Brodie, 2017).

5.2 Middle-School Mathematics and the Institutional Setting of Teaching (MIST) Project, United States

The Middle-School Mathematics and the Institutional Setting of Teaching (MIST) project was a design-based research project (2007–2015) in which mathematics education and education leadership and policy researchers partnered with leaders in each of four, large educational jurisdictions (‘districts’) located in US cities, with the goal of investigating and supporting instructional improvement in middle-grades mathematics at scale (Cobb et al., 2018).

As described in detail elsewhere (Cobb et al., 2013), the team purposefully recruited districts which were typical of large, urban US districts in many respects; they faced a number of challenges including limited funding, high rates of teacher turnover, high numbers of novice teachers in any given year and significant numbers of students identified as ‘low-performing’. However, the partner districts were atypical in one important respect—their response to high-stakes accountability pressures to increase the performance of students, especially students from historically under-served communities (e.g. students of colour, students living in poverty, students receiving special education services or students for whom English is not their native language), on standardised assessments.

Rather than ‘teach to the test’, which targeted low-level understandings, these leaders aspired to support all students to develop conceptual understanding of key mathematical ideas, procedural fluency and proficiency in problem solving. And they recognised that supporting students to meet rigorous learning goals would require both high-quality curriculum materials and professional learning for most teachers. District leaders provided a number of professional learning supports for teachers, including one-on-one coaching sessions and district-wide professional development sessions, while—especially relevant to the focus of this ICMI study—in all schools and districts, teachers were provided with regular time to collaborate. The amount and regularity of the time to collaborate varied across schools and districts. For example, in one district, grade-level teachers were expected to collaborate each day for 45–60 min, while, in others, teams were provided 45–60 min to meet on a weekly basis. In some schools whole departments met, while in most schools teams met in grade-levels.

The MIST research team engaged in annual cycles of data collection, analysis and feedback. At the beginning of each school year, the team interviewed central office leaders to document their intended strategies for the year. They then collected and analysed data on how the various strategies were playing out in schools. Between 30 and 60 teachers in each district were interviewed each year, as well as coaches and principals, while video-recordings of classroom instruction and audio- and/or video-recordings of professional learning, including teacher collaborative time, were collected. At the end of each academic year, the team shared findings with the district leaders and made recommendations regarding how to improve the strategies for the coming year.

Different from the DIPIP project described above, members of the research team did not directly facilitate teacher collaboration, although in the second half of the project, team members did co-design and co-lead professional development for facilitators. Within the MIST project, mathematics educator Ilana Horn led the study of teacher collaborative time across districts. In what follows, we especially draw on findings that she, postdoctoral fellows and graduate students produced (e.g. Andrews-Larson et al., 2017; Horn et al., 2017, 2015, 2018).

6 The Resource Framework

We now indicate how the five kinds of resources supported or constrained the teachers’ collaborative work in the two projects. We show how the different resources work in concert with each other and, where applicable, their co-evolution across classroom and collaborative contexts (Kazemi & Hubbard, 2008), and we suggest how this framework may inform design and research more generally.

6.1 Representational Resources

Although collaborating with colleagues about teaching has become more common in recent years, by-and-large classroom instruction remains a private endeavour. Representations of practice, for instance, accounts of teaching such as verbal ‘replays’ of what transpired in a given lesson (Horn, 2010), student work (Kazemi & Franke, 2004), lesson plans (Ball & Cohen, 1999; Lampert, 2001) and/or video-recordings of teaching (Borko et al., 2008; van Es & Sherin, 2008), are therefore a critical resource for teacher professional collaboration. Representations of teaching comprise the shared text of collaborative inquiry (Grossman et al., 2009). As Grossman and colleagues argue, representations of practice “can vary significantly, both in terms of comprehensiveness and authenticity” (p. 2065)—and the nature of the representations shapes community members’ opportunities to learn.

Engaging with a representation of practice is an interpretive, meaning-making act, and is influenced by the other resources we discuss in this chapter. For example, what particular members see, or notice, in a representation of practice is shaped by their current mathematical knowledge for teaching, as well as their perspectives on teaching and learning (Jackson et al., 2019). And whether community members treat a representation of practice (for example, student work) as an opportunity to investigate students’ sense-making, as opposed to an opportunity to triage students for further tutoring, may be shaped by principals’ expectations and broader institutional discourses (Rigby et al., 2020).

Not surprisingly, all of the papers at the ICMI 25 Study Conference in Theme D (Borko & Potari, 2020) provide some form of representational resources. Many of these used some form of digital and online forums. Of the 18 papers presented, only five had no digital input (not counting classroom videotapes as digital). The benefits of digital formats are that they more easily support the collaborative design and redesign of resources by teachers, and may support access to resources not possible in other ways (Karima, 2020). However, Chap. 5 (this volume) argues that access to digital resources cannot be taken for granted in many contexts and, if we are not able to support access for all teachers and learners, inequities may be exacerbated.

In the South African project, the teachers analysed tests, learners’ responses to tests, interviews with learners and videotapes of their own lessons, and created tasks and lesson plans, which were also subsequently analysed and improved upon. Taken together, these resources focused teachers on the key representation of practice that we used in our project, learners’ errors and the reasoning underlying them. Conversations in the communities varied in content and depth (Brodie & Chimhande, 2020), and teachers’ use of learner errors as a resource for teaching also varied (Chauraya & Brodie, 2017). The focus on errors was useful for some teachers and not so for others (Brodie, 2021), as can be seen in the following quotations.

Being able to get the reasons behind learners’ answers, I can now at least try to ask them […] to keep on probing the learners until they realise their mistakes.

We analysed question by question, concept by concept, that’s where I saw that maybe, somehow, we are short-changing our learners. That was quite a rude awakening, ja, and I hope that I could use that even in the other subjects that I teach. Because I think it would have a far-reaching positive impact.

Where, what, how do I benefit from this [...] it was nice arguing, identifying some of those errors made by learners, trying to think why they made these mistakes, how, why, you know, those different views from learners, people justifying those wrong answers. It was fun, it was fun, but you know, in as much as it was fun […] I couldn’t link what we were doing with what we are doing in the classrooms.

The first two quotations suggest that the focus on errors supported teachers to see their learners differently and possibly become more responsive to them. The third quotation suggests that, for this teacher, a focus on more immediately applicable resources for teaching may have been more useful than our plans for a longer-term developmental sequence of activities.

In the US project, the focus of the groups varied somewhat. Common foci included lesson planning and analysing student data, and a small number of groups focused on investigating and developing specific forms of teaching practice, e.g. how to introduce rigorous mathematical tasks. As such, representational resources tended to include lesson plans and curricular materials, as well as students’ responses to interim district- and school-based assessments. Whereas these representations were common across groups, how teachers engaged with these resources varied in crucial ways.

In productive teacher collaboration, as Horn et al. (2017) argue, teacher groups engaged in conversation about the ‘how’ and ‘why’ of instruction, in relation to the representational resources. For example, when discussing student assessment data, they examined the details of how students responded, like noticing patterns in students’ incorrect responses. And, crucially, they then engaged in an analysis of why those patterns might exist. They connected an analysis of the patterns of student thinking with an analysis of what was emphasised, or not, in instruction. These connections laid the groundwork for discussions of future work; that is, what teachers might do differently in future instruction to support students to develop desired understandings.

Similarly, when discussing curricular materials in light of lesson planning, in productive collaborations, teachers identified the key mathematical ideas and practices they wanted to target in a given lesson, and they anticipated student responses. They dug into how particular instructional decisions might shape what students would learn, and they made public their whys, that is, their rationales for why they might choose to make a particular decision. This airing of rationales supported teachers to weigh alternatives, and to make principled choices about what they would do in the future.

Unfortunately, conversations in which teachers examined the ‘how’ and ‘why’ of instruction were rare. Horn et al. (2017) studied the conversations of 24 work groups across 16 schools (a total of 77 meetings). Instructional leaders nominated these work groups as ‘best-case scenarios’, yet still Horn and colleagues documented rich learning opportunities in only about one-third of the meetings. When analysing standardised assessment data, by-and-large conversations tended to focus on determining if students ‘got it’ or not, as well as identifying students for tutoring or remediation, apart from an inquiry into why students might not have ‘gotten it’ to begin with (Horn et al., 2015). And conversations about lesson planning tended to focus on pacing or logistics, rather than discussion of mathematical content or students’ ideas.

The findings from the two projects suggest that the focus and quality of representational resources shape teachers’ learning opportunities within collaborative contexts. Across both contexts, we see the importance of representations that have the potential to support teachers’ conversations about learners’ reasoning, and to connect insight into learners’ reasoning to instructional decisions. In the DIPIP project case, the specific representations of learners’ errors (assessment data paired with interviews about students’ thinking) provided teachers with access to learners’ reasoning; and video-records of instruction and lesson plans supported teachers to connect learners’ reasoning to specific instructional decisions they made. Similarly, in the MIST case, teachers identified patterns in students’ responses and then conjectured what about instruction might have contributed to those patterns.

The design of both projects supported multi-directional movement of resources between classroom and collaboration. In the DIPIP project, teachers engaged in cycles of work in which they planned lessons in the collaboration, tried them out in their classrooms, returned to collaboration with resources and, on the basis of their analyses, planned future lessons. Similarly, in the productive examples in the MIST project, teachers engaged in cycles of inquiry, in which analyses of records of practice in collaboration informed their future lessons. While the two cases illustrate the centrality of representational resources in teacher collaboration, how teachers engaged with representational resources was very much shaped by the other categories of resources discussed below.

6.2 Knowledge Resources

Professional learning builds on, challenges and produces knowledge. This knowledge can be local, such as data or experiences from practice and knowledge of learners and their communities, and global, as in research findings and ideas for best practice. Successful professional learning relates local and global knowledge (Jackson & Temperley, 2007; Katz et al., 2009). Mathematics teachers’ knowledge is a key resource in collaborative learning—what teachers bring to their collaborations will inform the collaboration and its outcomes, and knowledge is obviously a key outcome of collaborative learning. Thus, knowledge can be both resource and object, depending on the situation. Teachers’ mathematical knowledge for teaching is best described as a combination of mathematical content knowledge (CK) and pedagogical content knowledge (PCK) (Ball et al., 2008).

In addition to mathematical knowledge for teaching, we also include in this category teachers’ professional visions (Hammerness, 2001; Munter, 2014), including what they aspire to accomplish in their practice, and their views of their students’ current capabilities (Jackson et al., 2017). Both shape teachers’ instructional choices (Horn, 2007), including how they select and interpret representational resources, and how they enact instruction (Wilhelm, 2014; Wilhelm et al., 2017). Moreover, teacher collaboration is often intended to support teachers to develop a shared instructional vision—one that is attuned to broadening access to all learners, especially in the context of a reform effort. Thus, just as with mathematical knowledge for teaching, teachers’ instructional visions and views of their students travel between class and collaboration, and may be transformed through this travel.

The DIPIP project design took a particular view of the development of teacher knowledge and practice. The assumption was that teachers tend to be most focused on what they do every day in their classrooms, i.e. their practice and their PCK. Therefore, the best way to draw on and develop teachers’ knowledge in an integrated way is to start with their practice and PCK, and to develop CK in relation to them (Brodie & Sanni, 2014). This is different from many PD programmes that start with CK and then move on to related PCK. One of our key principles was that, in coming to understand learner needs, teachers can come to understand their own learning needs: what mathematics they need to learn and how to use this new knowledge to improve their practice (Brodie, 2014). All teachers notice learner errors; however, very few teachers see them as based on valid reasoning and as opportunities for deepening mathematical knowledge. We explicitly positioned teachers both as experts and as learners. As experts, they contributed their knowledge of teaching mathematics, their contexts and their learners, while, as learners, they deepened this knowledge.

We have some evidence that the focus on PCK supported conversations both about PCK and about CK. In one community, we found that 34% of conversations were on CK and 66% on PCK, depending on the particular activity (Brodie et al., 2018). Of the 58 CK conversations across the 17 meetings, 30 (52%) were triggered by PCK conversations. Of the 161 PCK conversations, 23 (14%) were triggered by CK conversations. Thus, PCK conversations did lead to CK conversations, while the converse was less visible (Brodie, 2014; Marchant & Brodie, 2016).

We also found that the knowledge content of the conversations in the PLCs varied in relation to the different activities. For example, the lesson planning sessions supported conversations on mathematical content, as teachers tried out the tasks, and the videotaped reflections supported conversations on practice as teachers discussed responses to learners’ errors (Chimhande & Brodie, 2016; Marchant & Brodie, 2016). Taken together, the different activities supported conversations on mathematics (CK), as well as on learner thinking and teacher practice (PCK).

In the MIST project, similarly to the DIPIP project, there was evidence that, while rare, teachers did occasionally deeply engage with the underlying mathematics, thereby providing opportunities to develop mathematical content knowledge. For example, Horn et al. (2018) describe how a sixth-grade team at Magnolia Middle School engaged in a three-week assessment cycle. In week one, teachers used interim student assessment data to identify ideas with which students were struggling, and then investigated the underlying mathematics, and developed a common formative assessment to give to students. In week two, the team analysed the resulting student work. Aided by a coach and assistant principal, both of whom had substantial mathematics teaching expertise, they investigated students’ ideas deeply and designed instructional responses. In one case, the workgroup identified that students were having difficulty making sense of the concept of a unit rate.

In light of student thinking, the facilitators “introduced a new instructional strategy—in this case, a double number line—that teachers might use to support students in making sense of the difference between additive and multiplicative problems” (p. 102). In week three, teachers reported on the enactment of their instructional responses, and again reviewed student work to note progress and to identify next steps. Throughout, the facilitators supported and pressed teachers to position students as sense-makers, to treat mathematics as a sense-making activity and to deepen their mathematical knowledge for teaching.

Describing work groups like the Magnolia sixth-grade team, Horn et al. (2020) write, “As teachers identified, elaborated, and addressed instructional challenges, their understandings of students’ learning difficulties and students’ mathematical thinking [their views of their students’ capabilities and mathematical knowledge for teaching] were conveyed to colleagues” (p. 11). In fact, they quantitatively investigated relationships between engagement in meetings like those in Magnolia (which they called ‘high-depth’ meetings) and teachers’ mathematical knowledge for teaching and views of their students’ capabilities. They found that teachers developed more productive views and deepend their mathematical knowledge for teaching through high-depth meetings. However, as noted earlier, high-depth meetings were unusual, even in the best-case sampling of teacher workgroup meetings in the MIST project.

Across both projects, we see that knowledge is a key resource in teacher collaboration. Teachers come to their collaborations with professional knowledge and this knowledge is transformed during the collaboration to produce new knowledge. Professional learning activities can support teachers to talk about their knowledge with each other, to build explicitly on their own and others’ knowledge, to develop ways of seeing differently and more deeply, and to develop different relationships between different forms of knowledge and between knowledge and practice. In both the DIPIP and MIST project examples, the activity of examining students’ thinking and reasoning on its own, and in relation to instruction, supported the deepening of pedagogical content knowledge and content knowledge.

In both cases, making visible the ‘hows’ and ‘whys’ of their teaching with colleagues also supported teachers’ deepening of professional vision; that is, of what it is that teachers were aspiring and attending to in their own instruction, and in coming to view more of their students as capable of making sense of mathematics. As with all resources, how knowledge is transformed in collaborative conversations depends on how it is appropriated and developed in the collaboration, as well as how it is shaped by and shapes the collaborators. It is possible for conversations to become unproductive, when current knowledge, visions of practice and views of learners do not support growth and become solidified in the community, rather than flexible and open to change.

6.3 Affective Resources

While it may seem strange to think of emotions as resources, they are an important resource for collaborative learning. There is a strong history of research on emotions associated with learning mathematics (e.g. Black et al., 2009; Hannula, 2012), but a definite absence of the role of emotions in mathematics teacher learning (Breen, 2009; Vedder-Weiss et al., 2020). There are no emotion words in the frequency cloud of words in the titles of the survey sources in the ICME survey on mathematics teachers’ collaboration (Fig. 9.1) (Robutti et al., 2016, p. 662), and a look through the volume Tools and processes in mathematics teacher education (Tirosh & Wood, 2008) does not show a focus on emotions. So emotions are a missing resource in the research, and may be important when thinking about building equitable participation in collaborative learning.

Fig. 9.1

Wordcloud from ICME survey. (Robutti et al., 2016, p. 662)

A supportive environment for collaborative learning requires space for professional disagreement and conflict among ideas, so that there can be generative conversations and space for growth (Katz et al., 2009). At the same time, if conflict becomes personal, possibilities for collaboration and learning are reduced. So two key features for collaboration to be productive are safety and trust. Safety to challenge and be challenged, to agree and disagree, and trust that the process will support everyone’s learning, and that contributions can both be given and received. Research suggests that, where there are strong hierarchical relationships within schools and where teacher morale is low, it is difficult to sustain engagement in PLCs (Schechter, 2012; Wong, 2010). The following quotations from the DIPIP project show a range of trust that teachers experienced in their PLCs.

We can talk to the other community members freely without, how can I say, stage-fright. We are confident because we are talking with colleagues, knowing that no-one is judging you.

I don’t know about videorising [sic]. I think we’re coming from an era where people were critical about you, they were looking at all the bad things that you were doing [...] Now, we understand you’re videorising¹ it so that we can see ourselves developing. But, somehow, at the back of our minds, it’s like, is it true? Are they not hiding something from us?

Because, at the end of the day, we would see it as a research which benefits someone and not us really.

A real fear about working with others is being judged, explicitly or without your knowledge. In some school systems, ‘poor’ performance can affect job security, and so being judged can have material consequences for teachers. However, it can also have emotional consequences, creating or reproducing doubts about not being good enough. Trusting that teachers and learners are the ultimate beneficiaries of the work may also be difficult for teachers working in schools and systems where their needs are not always taken seriously.

At the same time, communities that work well can support positive emotions associated with learning. A key role for faciliators of collaborative learning groups is to create and support safety and trust. In the DIPIP project, we articulated the following facilitator moves for building community: validate all ideas as useful contributions to the conversation; articulate positive aspects of negative situations; identify with teachers’ issues and concerns; notice and counter disengagement and exclusion (Brodie, 2016).

One reason that we chose a focus on learner errors in the DIPIP project is that we wanted to support teachers to see learners as mathematical thinkers, to hear and interact with their thinking. As teachers began to interpret and explain learners’ errors, and to see errors as reasoned and reasonable, they began to blame themselves, or other teachers, for learners’ errors, finding the reasons for learners’ errors in how they were taught previously. The PLC facilitators worked hard to counter this tendency to blame, but we saw it recurring in our data and believe that it is difficult to work against, given the widespread blame of everyone by everyone in our system, and the emotions associated with not suceeding in mathematics, which are made even more salient when focusing on errors. As one teacher told us:

Because now it was somehow it was a bit painful. If you find that learners who were doing grade eleven, and learners who were doing grade eight, they were given almost the same test. But now, when you check the errors that were done by grade-eleven learners, they were the same as the errors that were done by grade eight.

Many of the teachers expressed similar pain when confronted by the fact that learners made the same errors as they progressed in their school careers. One teacher told us (half-jokingly) that, when you see learners making errors in grade eight, you can blame it on the primary school teachers, but when the errors persist when taught by herself and her colleagues, it becomes difficult to decide where to apportion blame. For some teachers, this was a learning and growth point—they realised that there is no blame for errors; they are a normal part of learning mathematics and we can develop strategies for working with them to develop learners’ mathematical thinking. But, for other teachers, the explicit focus on learner errors was demoralising and contributed to their feeling overwhelmed. At the same time, many teachers talked about positive emotions that supported their engagement in the project. The first teacher quoted above declared how she felt confident in sharing ideas without being judged. Many teachers enjoyed that their communities provided safe spaces for sharing ideas and gaining new insights.

So, emotions have both positive and negative consequences for collaboration and learning. Emotions are also both a resource for and an object of inquiry, because an important part of teacher learning must be to focus on their own and their learners’ emotions, particularly when dealing with errors. Emotions are transformed through collaboration and learning—understanding why and how is an important task for researchers.

Emotions travel everywhere with human beings, so they will manifest both in collaboration and in classrooms. In thinking about emotions as a resource, it may be important to focus on them more explicitly in the design of collaboration. For example, teachers’ fears about being judged in the collaboration can be used as a resource for them to think about how learners fear being judged in the classroom. They may then be able to develop some classroom scenarios, based on classroom events, where they identify and respond to learners’ emotions. They can also bring actual cases from their classrooms for discussion in the groups.

6.4 Human Resources

People are both actors and resources in teacher collaborative work and, as they bring together the other sets of resources, they function at an overarching level. As ICMI 25 Theme C notes, there can be a number of participants in collaborative teacher learning: teachers, facilitators, researchers and principals, among others, and they bring different strengths to the collaboration. From the perspective of Theme D, how people revivify resources for learning is important, as well as how they may become key resources for and from collaborative learning. We focus on teachers and facilitators, and also on students, as a potentially missing resource.

How teachers orient towards their collaborations is important in how they work and learn together, particularly given their customary privatised practice (Little, 1990). In the DIPIP project, Chauraya (2016) showed how teachers’ views of collaboration shifted over time in a community. Initially, teachers saw collaboration as asking other teachers for help, particularly more ‘senior’ colleagues, reflecting the hierarchies in the schools. After some time in the community, the teachers began to see it as a forum for joint development, with everyone able both to give and to receive support, and, as this happened, they came to see themselves in new ways. A related finding occured when some project teachers wanted to know why the better-resourced school down the road did not come to share their knowledge in the community. While this can be interpreted as teachers assuming that better material resources means better knowledge resources, it can also be seen as understanding that extending the community beyond one school can be helpful, and that other teachers would bring in different resources (Brodie, 2013a).

Robutti et al. (2016) refer to teachers’ ownership of their collaborations, where teachers feel that the leadership and responsibility of the collaboration lies with them, and that their needs and interests are being served. In collaborative groups initiated and guided by teachers themselves, such ownership might be easier to achieve, although it may be seen differently by different participants. In collaborations guided by teacher educators, we have to work carefully to develop and support teacher ownership of the process, the resources and their learning. Related to ownership is voice (Robutti et al., 2016), where teachers feel that they have the space to articulate their ideas and are confident that they will be heard and engaged with. For teachers to experience ownership and voice in communities, there needs to be some level of trust, among teachers and among teachers, facilitators and the project team. Trust is an important affective resource as discussed above. In the DIPIP project, some teachers did feel trust, and thus ownership and voice, while others did not, and withdrew from the project (Brodie, 2021).

Not all collaborative groups include a person tasked with being a facilitator. However, there is research to suggest that such leadership is important, particularly for systematic, regular inquiry (Katz & Dack, 2013). Across our two contexts, we found that a facilitator can be an especially important resource in teacher collaboration. In the MIST project, most teacher groups were allocated a facilitator. The faciliator was sometimes a ‘teacher leader’, e.g. a teacher who was assigned specific responsibilities by the school administration; a ‘coach’, e.g. a person designated to support teachers’ learning, either by the school or district; or an administrator. The faciliator’s expertise in teaching mathematics and in supporting teachers’ learning, as well as their relationship with the teachers, mattered greatly for how they were perceived by the teachers.

The MIST project analyses of teacher collaboration indicated that a facilator could shape opportunities for teachers’ learning in important ways. For example, Andrews-Larson et al. (2017) analysed audio-recordings of grade-level collaboration meetings in two schools, in which there was evidence that teachers exhibited growth in instructional quality. They observed that, especially in the context of co-planning for instruction, facilitators routinely pressed teachers to elaborate their verbal representations of their classrooms, to articulate evidence or reasoning behind their claims about students, to treat students as sense-makers and to surface the instructional principles behind their decisions.

Importantly, Andrews-Larson and colleagues found that, while protocols for organising a meeting appeared helpful in structuring the questions a facilitator might ask in collaborative time, a protocol did not guarantee that a facilitator would press teachers to elaborate their rationales and principles. As another example, in the Magnolia sixth-grade team example described above (Horn et al., 2018), we see the important role that the facilators—in that instance, a coach and an assistant principal, both with extensive expertise in mathematics teaching—played in supporting teachers to engage deeply with mathematics content and the ideas of their students.

While much of the research focuses on teachers and facilitators, and their use of resources, learners might be thought of as a missing resource in teachers’ collaborative learning. Although learners are often represented in teacher collaboration through their work, in videotaped lessons and other representations of practice, teachers often do not see learners’ perspectives when thinking about learner work. The DIPIP project focused on learner errors and, as we have discussed above, this supported some teachers to see learners differently, although with some pain and blame. But we did not find out about learners’ views of their errors or about emotions that are evoked among learners when teachers work with learners’ errors.

There are some examples of work with learner perspectives in relation to teacher learning. Vogler and Prediger (2017) captured students’ views of a teaching situation on videotape and then showed them to the teachers, reporting how seeing students’ perspectives helped the teachers to think about the consequences of their interactions with students and proposing how they might interact differently in future. In work subsequent to the DIPIP project, we have shown that different ways of valuing and working with learner errors are important for learners’ mathematical identities (Gardee, 2019). Also interesting is a study by Sherman and Catapano (2011), where students participated in a mathematics club and in-service and pre-service teachers participated as mentors in the club. From interacting with their own students in a different context, the teachers came to see them as productive mathematical thinkers. So introducing actual learners as real people, with thoughts and feelings about their learning, may be an important missing resource for teacher collaboration and might support stronger collaborations and learning.

6.5 Institutional Resources

Institutions are key mediators of social and power relations and frame much of what happens in collaborative learning for teachers. How resources are allocated, the nature of school hierarchies, the extent to which collaboration is valued in the school and district, and school leaders’ expectations for collaboration all form part of this framing. In arguing for a view of mathematics teaching that takes relationships between teacher agency and social and institutional structure seriously, Chazan et al. (2016) argue:

It has been customary in our field’s literature to look at resource use as an individual issue only, one that depends on individual teachers’ access to resources or personal knowledge or beliefs about the use of resources. We contend that, in our efforts to consider the institutional context of the work of the teacher, we should also consider that the use of resources in a teacher’s work also depends on the role that those resources play in framing the position of the mathematics teacher in its institutional context. (p. 1078)

Here, we focus especially on the institutional resources of time and space to collaborate, and school leaders’ values and expectations.

6.5.1 Time and Space

Time is probably the scarcest resource for busy professionals. In the MIST project, time to collaborate was built into teachers’ contracts. However, in the DIPIP project, this was not possible and all the teachers we interviewed stated that time was a key challenge to participation: finding time to meet as a group and finding time to do the work of the project outside of meetings, for example the project readings or personal reflections on videotaped lessons (Brodie, 2021). Given the high teaching loads in the schools, there was no time during the school day for teachers to meet. All of the communities met after school, which often clashed with teachers’ personal commitments, such as picking up their own children from school. Some teachers spoke about making time for their collaborative work, for example:

Because what I’ve also learnt is that here on earth there’s no time, but one has to make time for anything after all.

But as for me I consider it as pressure that I can’t do anything about, other than finding a better way to deal with […] I must just find myself time.

However, a number of teachers said that they could not find time and, when there was a clash between school commitments and project commitments, they had to prioritise their school commitments. For teachers with many, big classes, there was little time for other activities.

You really find no time to give to this other project, because you know I have at least to give also my time to this because it’s my contractual obligation […] with the workload that we had, it’s overwhelming, you know really, really it’s overwhelming.

Teachers at wealthier schools are more likely to have smaller and fewer classes, and therefore more time for joint work and professional development. At some wealthier schools, time can be found within the school timetable for collaborative work, but in most schools in South Africa, teachers have to make use of their own time and personally prioritise their own development above other commitments.

Space is also related to resource inequalities. Most government schools in South Africa have little space that can be dedicated to teacher collaboration. Classrooms, libraries, staffrooms, laboratories and small offices were variously used as spaces in the DIPIP project, which meant that records of past meetings were difficult to display and all equipment had to be brought in for each meeting (equipment was also vulnerable to theft).

Not all collaborative groups need to meet face-to-face and online collaborations allow for teachers from different schools to meet and learn together. However, there are also inequalities between rich and poor in relation to access to the internet, for example data is very expensive in South Africa. It is not yet known whether virtual collaboration can support the kind of systematic learning that PLCs do, particularly when trying to design resources for multidirectional influences between classroom and collaboration. Supporting on-going, sustained inquiry among teachers in the same school, who can then make strong collective changes to their practices, and bring their issues from practice into the collaboration, is central to PLC work and requires appropriate spaces in which to work.

6.5.2 School Leaders’ Values and Expectations

Another critical institutional resource concerns whether and how school leaders value collaboration and their expectations for what happens in collaboration. We saw a range of leadership support and consequences of this support in the DIPIP project (Brodie, 2021). Some principals actively supported the project while others spoke about trying to encourage their colleagues to participate, but they did not know much about the details of the project. For the most part in South Africa, principals’ roles are conceived of in terms of management rather than academic leadership, leaving many principals themselves with few resources to support academic learning among their colleagues.

A key element of how leadership support played out was in the relationships between teachers and school leadership. Some teachers said that while the school leadership supported the project because it reflected well on the school, the teachers experienced challenges. The comments below suggest some conflict with the school administration.

As an administrator, the picture you are giving, whether it’s nice or not nice, you would want things to work for your school. So you would say, let’s try it. But the people on the ground who were supposed to do it, they said, we can’t. Because I still remember we had a meeting and it was a push and pull.

Because, really, we were overwhelmed we were coming up with reasons, you know, sometimes you don’t have to give your real reason, you try to look and source a polite way of saying.

These comments reflect the hierarchical nature of South African schools. Teachers are unlikely to express critical views, to explain their needs or to ask for explicit support from principals; rather, they might accept requests on the surface, but then reject and refuse them in other ways. Relationships between teachers and school leadership also relate stongly to trust and other affective resources as discussed above.

In the MIST project, the school leader’s expectations for what happened in teacher collaborative time very much shaped the nature of conversations, and thus teachers’ opportunities to learn (Horn, 2018; Horn et al., 2018; Rigby et al., 2020). Recall that time to meet was built into teachers’ contracts in these districts. This meant that school leaders had some influence over the focus of teacher collaboration. And, especially given the context of high-stakes accountability, it was common for school leaders to press for teachers to use collaborative time to identify students in need of tutoring or remediation, with the hope that if those students received auxiliary support, they would perform better on standardised assessments. Futher, in light of the skills-oriented nature of the assessments at the time, a focus on improving student performance did not call for deep investigation of mathematics or student thinking.

In a case study of one school, Rigby et al. (2020) found that, over the course of three years, teachers’ discussions across the three grade-level groups dramatically shifted; whereas 60% of their initial conversations focused on unpacking mathematical concepts and procedures, by the third year, 60% of their discussions focused on naming topics and standards to be targeted. Concurrently, researchers documented that teachers shifted from initially framing their work as about helping students learn mathematics to focusing on helping students to pass tests. And, not surprisingly, whereas in the first year, the majority of their conversations focused on how they might adjust their instruction to support students, by the third year, it was common to hear teachers attribute students’ performance to factors that they perceived to be not in their purview (e.g. students’ behaviour). Notably, the researchers explain these shifts through a focus on the role of the school leader. Administrators attended teacher collaborations frequently in the second and third year, as compared with the first one. Regardless of whether admistrators were the official facilitators, they consistently shaped the focus of the meetings when they attended, directing the conversation to focus on what standards students were ‘low’ in and identifying students for remediation in those standards.

There were exceptions. Recall the assistant principal at Magnolia Middle School described above, who, along with an expert coach, supported and pressed teachers to focus on the ‘how’ and ‘why’ of instruction. Summarising findings about school leaders’ influence on teacher collaboration in the MIST project study, Horn et al. (2018) identified two critical roles that school leaders played in support of productive collaboration. One key role concerns furnishing teacher teams with facilitators with instructional expertise, as well as expertise in supporting teachers to collaborate. In some cases, this required leaders to seek a faciliator outside of the school community. A second key role concerns “protecting teachers’ time during appointed meetings” (p. 106). In productive communities, school leaders ensured teachers were able to use collaborative time to inquire into instruction and plan for future instruction, as opposed to fulfilling administrative tasks.

7 Conclusion

Teacher collaboration holds great promise for supporting teachers’ professional learning, as well as their intellectual and emotional well-being, and, in turn, students’ learning and well-being. However, as has been elaborated in this ICMI Study, realising positive outcomes in the context of teacher collaboration is non-trivial. In this chapter, we have elaborated a framework that centres the resources that both shape and are shaped through teacher collaboration. We have intentionally taken a broad perspective on resources—considering representational, knowledge, affective, human and institutional resources—in an effort to support others to design, prospectively, for productive forms of collaboration, and to account for, retrospectively, what might have supported and/or constrained the possibilities of a particular collaboration.

As we have illustrated above, how representational resources are used productively (or not) in the context of collaboration is shaped by knowledge, affective, human and institutional resources. Thus, as we have argued, a limited focus on representational resources is likely to fall short in supporting design of good teacher collaboration, as well as in explaining why teacher collaboration resulted in particular outcomes.

We elaborated the framework in relation to two contexts, the DIPIP project in South Africa and the MIST project in the United States. As we argue above, collaborative efforts are necessarily socio-culturally situated. Representational resources are given meaning by people in communities, and they will be used differently in different contexts and will support different kinds of learning. Similarly, what counts as a knowledge resource in a given setting, or the kinds of human and institutional resources that are available, will vary across contexts. However, while the nuances and details of each of the categories of resources that we elaborate may vary across contexts, we argue that the categories, writ large, are important to consider when designing for or researching structured teacher collaboration across contexts. Here, we step back to consider key takeaways.

These two cases suggest the importance of ensuring that representational resources include representations of teaching, and that those representations of teaching provide access to learners’ thinking and/or experiences, as well as to the ability to connect learner outcomes to the specifics of instruction. Representations of students’ learning need to be textured enough (e.g. to include not just learners’ answers, but also learners’ reasoning) such that they can support teachers to generate and investigate conjectures about why learners might be thinking in particular ways and may have developed more or less useful forms of reasoning. And representations of instruction need to be detailed enough such that teachers can investigate together how instructional decisions may have shaped learner outcomes.

However, well-designed representations of teaching do not ensure productive collaboration. Teachers’ current forms of knowledge and perspectives on teaching and learning matter for the kinds of questions they surface and explore in relation to their instruction. In designing for teacher collaboration, it is critical to attend to the forms of expertise that exist in the community, to consider carefully the role of a facilitator both in pressing and in supporting teachers to deepen the kinds of questions they are asking of their instruction, and to deepen their content knowledge and pedagogical content knowledge. It may be that an insider can take on the role of facilitator, but, especially in communities early in their development, an outside faciliator may be needed. As suggested above, protocols can support facilitation, but they cannot substitute for the judgment of a facilitator, the know-how of when and how to encourage new voices, when to press teachers to elaborate their reasoning, and when to insert new ideas. Although not discussed in depth here, learning to facilitate teacher collaboration is a key consideration in the establishment of generative teacher communities.

What we have termed ‘affective resources’ are central both in designing for and in researching teacher collaboration. Creating a setting in which teachers lay bare their instructional challenges and genuinely collaborate in making sense of them and in proposing alternatives, requires that they trust and value one another. Unfortunately, as was true in both of these cases, teaching often takes place in contexts that are marked by scrutiny and mistrust. Therefore, there has to be intentional work done to establish and sustain a community that explicitly works towards ways of relating with one another that are likely counter-cultural.

The extent to which it is possible to realise sustained, productive collaboration depends largely on institutional resources, including time and space, and instructional leaders’ expectations for what happens in collaboration. As much as is possible, attention to these resources at the start of a project is adviseable, and consideration of the institutional resources is crucial in researching collaboration, in order for others to consider the applicability of findings in new contexts.

The DIPIP and MIST projects were both focused on formal teacher collaboration, and much if not all of the literature on which we drew focused on formal teacher collaboration as well. Teachers’ joint work, or collaboration, can happen in a number of ways: from informal conversations to asking for help, to marking or planning together, through various forms of systematic learning in groups or PLCs, like those described in this chapter. In each of these learning contexts, resources will work differently and mediate the work and learning in different ways. How this framework may apply or need to be adjusted, in less structured forms of collaboration, is an open question.

Lastly, we return to the issue of resources ‘for’ and ‘from’ collaboration. Resources are explicitly designed for teacher collaboration, for example protocols to guide the work of a group, specific representations of teaching that the group might analyse, the appointment and training of a facilitator, and the allocation of time and space for the group to meet. And teachers transform and construct resources as a product from collaboration, for example new lesson plans and assessments, knowledge of student thinking and of mathematics, an elaboration of an instructional vision, a sense of affinity and purpose among math teachers, and so forth. Drawing on Kazemi and Hubbard’s (2008) call for multidirectional analyses of teachers’ participation in professional learning and in classrooms, we have identified attention to the travel and transformation of resources ‘back-and-forth’ between teacher collaboration and classroom as one area for future research.

This seems especially important in studies of teacher collaboration, given that the shared text of the group is typically a representation of classroom practice. How do the resources (e.g. knowledge and ways of knowing, emotions, understanding of institutional norms and expectations) that figure in classroom teaching relate to the resources prioritised in the collaboration? How can collaboration be designed to take teachers’ classroom-based resources and lived realities into account, while also supporting the transformation of those resources? Careful attention to this back-and-forth would help in elaborating the relations between teacher collaboration and classroom practices, both of which are embedded in political contexts, and in which teachers are often asked, implicitly or explicitly, to reconcile competing expectations.