1 The Need for the Study

Across education systems and at all educational levels, mathematics teachers work and learn together through various forms of collaboration. Teachers collaborate both in face-to-face and virtual settings, and in a diverse set of formal and informal groupings, including teams, communities, schools, teacher education programs, professional development courses, and local and national networks. Their collaborations may also include people who support their learning such as coaches, mentors and professional development facilitators.

Teachers’ collaborative work has a long tradition in mathematics education as an important way of bringing educational innovation into the everyday practice of teaching. The idea of mathematics teachers working and learning through collaboration has been gaining increasing attention in mathematics education research, particularly since the report on Lesson Study in Japan from the TIMSS classroom video study (Stigler et al., 1999; Hiebert et al., 2003). In 2014, ZDM: The International Journal on Mathematics Education published a special issue focused on collaboration entitled, “Interactive practices in promoting professional development of didacticians and teachers of mathematics: An international perspective”. As Jaworski and Huang (2014) noted in their introduction to this special issue, “we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development” (p. 173).

This attention to teachers learning through collaboration is especially relevant as countries around the world strive to improve educational experiences for all children, and to see these improvements reflected in scores on international assessments such as PISA and TIMSS (Schliecher, 2015). Indeed, Schliecher’s OECD report includes a policy recommendation: “Encourage collaboration among teachers, either through professional development activities or classroom practices” (p. 56). It cites research indicating that collaborative professional development is related to a positive impact on: teachers’ instructional strategies; their self-esteem and self-efficacy; student learning processes, motivation and outcomes.

Efforts to understand what teachers do as they work in collaborative groups, and how these experiences lead to improvement in their practice and expertise, have led to a growing interest in examining the different activities, processes, contexts and outcomes for teacher collaboration around the world. The work completed by the ICME-13 Survey Team on this theme is further evidence of the considerable international interest in research on teachers working and learning through collaboration (Jaworski et al., 2017; Robutti et al., 2016). Similar to Schliecher’s OECD report, the ICME-13 Survey, which was presented at the ICME Congress in 2016, showed that across education systems mathematics teachers work and learn through numerous forms of collaboration, involving different groups of people in a variety of roles. These diverse forms of collaboration and varying combinations of people contribute to learning and development in a variety of ways.

The project also identified several gaps and limitations, not only in the existing research base, but also in the survey’s coverage of relevant topics within the theme. For example, Jaworski et al. (2017) reported that their research questions about learning outcomes were the most difficult to address. They did not have consistent clarity on the specific mathematics knowledge and pedagogy that was learned, the ways in which learning occurred or the relationship between collaboration and learning. As they also noted, the survey predominantly reported from the perspective of researchers. In addition, there were issues for which the survey showed that research is not extensive and further studies are needed, such as sustainability and scalability, the role of digital technology in teachers’ collaborative learning, working with teachers of different educational levels and making teachers’ voices more evident.

ICMI Study 25 aims to build on previous findings about mathematics teacher collaboration and to address the gaps and limitations identified in the ICME-13 Survey. Specifically, as was stated in the Discussion Document (IPC, 2019) that solicited contributions to the Study, it aims: to reflect the diversity of settings and groupings in which mathematics teacher collaboration occurs; to explore the tools and resources that support mathematics teacher collaboration; to address the breadth of outcomes of such collaboration; to represent teachers’ experiences and learning through their own voices, as well as the voices of researchers. Because there are different ways of understanding the nature of teacher collaboration and its consequences, the Study includes contributions representing multiple theoretical perspectives and a variety of methodological approaches. (The Discussion Document is included in this Study volume as an appendix.)

2 The Scope and Aims of the Study

The scope and the aims of the study were established and developed through the meetings of the International Program Committee (IPC), the Study Conference and preparation of the Study volume. The Study volume was the outcome of the collaboration between the members of the Committee, the participants in the working groups at the conference, and the plenary speakers and panellists. We discuss below the scope and the initial aims of the study as they are stated in the Discussion Document.

The primary aims of the Study as they are phrased in the Discussion Document are:

to report the state of the art in the area of mathematics teacher collaboration with respect to theory, research, practice, and policy; and to suggest new directions of research that take into account contextual, cultural, national and political dimensions. (p. 3)

To address these aims, we had to define the meaning of teacher collaboration. We discussed possible definitions in the first meeting of the IPC. The distinction between ‘co-operation’ and ‘collaboration’ that has been addressed earlier in our field (Peter-Koop et al., 2003) was also considered in our discussions. For Peter-Koop et al., co-operation is usually set up externally and the participants contribute to various aspects of a task. On the other hand, collaboration is initiated by the participants, and it involves the sharing of leadership and control to achieve a goal worthwhile to all participants.

Our conceptualisation of mathematics teacher collaboration adopts a similar perspective. It goes beyond the gathering of teachers in the context of a professional development program or even in everyday school meetings or online networks. Collaboration is characterised by the formation of communities where teachers are involved in joint reflection aiming to develop teaching. We also acknowledge that the form, the goals and the outcomes of collaboration depend on the conditions in which it takes place, as well as on the experiences of the participants and the availability of resources. The ICME-13 survey showed that, although teachers are the central actors in collaborative contexts, their ‘voices’ typically are not heard outside the context of collaboration. A central goal of the Study is to provide the opportunity for teachers to share their collaborative experiences in the Study Conference and in the Study volume. To this end, we organised a plenary teacher panel at the conference, and one of the chapters of this Study volume is based on the work of this panel.

The research areas and the set of questions that this Study investigates are organised into four themes: A. Theoretical perspectives on studying mathematics teacher collaboration; B. Contexts, forms and outcomes of mathematics teacher collaboration; C. Roles, identities and interactions of various participants in mathematics teacher collaboration; D. Tools and resources used/designed for teacher collaboration and resulting from teacher collaboration.

The IPC formulated several questions for each theme to be addressed in the Study. The questions of Theme A concern the different theoretical perspectives that can enhance our understanding of the processes and the outcomes of teacher collaboration, their strengths and weaknesses, as well as methodological issues related to the study of teacher collaboration. In Theme B, the questions are about the different models of teacher collaboration, their effectiveness in relation to the desired outcomes and the different contexts and conditions for teacher collaboration. Online teacher collaboration, and its benefits and challenges, are also considered in this theme.

The questions of Theme C address the roles and identities of the different stakeholders in the context of teacher collaboration. They also aim to investigate what types of learning environments support professional learning of teachers and of other participants. The Theme D questions refer both to the resources that are available to support teacher collaboration and their impact on the collaboration, and to the design of resources in the context of collaboration. Moreover, issues of scaling-up collaboration and the opportunities for digital environments and resources are also addressed in this theme.

The themes and the questions are reported in the Discussion Document. They were the basis of the submitted papers and of the work of the Working Groups in the Study Conference, and they are reflected in the structure of this volume.

3 The Study Conference: Its Program, Structure and Outcomes

The themes and questions identified by the IPC and described in the Discussion Document provided the basis for the Call for Contributions to ICMI Study 25. The call invited submissions of several types including: reports of research studies; syntheses and meta-analyses of empirical studies; discussions of theoretical and methodological issues; examinations of the ways that teacher collaboration has taken place in local or national contexts. To address the complexity of mathematics teacher collaboration, it also encouraged papers reflecting different cultural, political and educational contexts and submissions by researchers, teachers and policy-makers.

We received more than 100 submissions in response to the call. These papers were reviewed by the IPC, which provided feedback and, in many cases, requested revisions. 80 papers were accepted for the Study Conference and were included in the Conference Proceedings. The countries represented include: Algeria, Argentina, Australia, Austria, Brazil, Canada, China, Colombia, Cyprus, Denmark, France, Germany, Greece, India, Iran, Ireland, Israel, Italy, Japan, Malawi, Malta, Mexico, Netherlands, New Zealand, Norway, Portugal, Slovakia, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Turkey, United Kingdom, United States and the US Virgin Islands.

The ICMI Study 25 Conference was hosted by the Instituto de Educação, Universidade de Lisboa in Lisbon, Portugal, on February 3–7, 2020. As is the case for all ICMI Study Conferences, most of the time was spent in Working Groups organised around the themes and led by IPC members. During the Working Group sessions, brief presentations by the participants, based on their papers, served as a springboard for in-depth exploration of the themes and associated questions. These intense discussions were directed toward the preparation of this Study volume. In preparation for the Working Group discussions, a draft of the Conference Proceedings was distributed to participants prior to the conference, so that they would have time to read the papers for their theme’s Working Group in advance.

We also invited four renowned scholars to present plenary lectures related to each theme at the Study Conference, and four others to respond to their lectures. The plenary lectures were included in the Conference Proceedings. The lecturers and reactors were:

  • Theme A: Susanne Prediger, lecturer; Boris Koichu, reactor;

  • Theme B: Masami Isoda, lecturer; Alf Coles, reactor;

  • Theme C: Konrad Krainer and Carina Spreitzer, lecturers; Bettina Roesken-Winter, reactor;

  • Theme D: Karin Brodie, lecturer; Kara Jackson, reactor.

In addition, to ensure that teachers’ voices were well-represented at the Study Conference, we invited four practitioners actively involved in very different collaborative experiences to participate in a plenary panel moderated by a renowned scholar. The panelists’ papers and the moderator’s introduction and synthesis were also included in the Conference Proceedings. The panelists were: Yiyi Chen, China; Christelle Fitamant, France; Lameck Dition Sandram, Malawi; Shelli Temple, USA. The moderator, whose career includes multiple collaborative projects with teachers, was Hilary Hollingsworth, Australia.

The Study Conference was held after the beginning of the COVID-19 pandemic, before the world was aware of its nature and the rapidity with which it would spread. Several countries, including China, had already begun to implement travel restrictions. To enable participants’ attendance, our conference hosts at the Instituto de Educação, Universidade de Lisboa were able to arrange their virtual participation. This experience, although not what we envisioned or would have preferred, presented the opportunity for our group to reflect upon and learn from an additional form of collaboration. We share some of those reflections throughout this Study volume.

4 Structure of the Study Volume

The chapters in this book are organised in four parts. The first Part consists of this introductory editorial chapter. Part 2 includes the four chapters that reflect the four organising Theme Working Groups of the ICMI Study Conference:

  • Theme A: Theoretical Perspectives on Studying Mathematics Teacher Collaboration (lead authors: João Pedro da Ponte and Takeshi Miyakawa);

  • Theme B: Contexts, Forms and Outcomes of Mathematics Teacher Collaboration (lead authors: Cristina Esteley and Rongjin Huang);

  • Theme C: Roles, Identities and Interactions of Various Participants in Mathematics Teacher Collaboration (lead authors: Ronnie Karsenty and Shelley Dole);

  • Theme D: Tools and Resources Used/Designed for Teacher Collaboration and Resulting from Teacher Collaboration (lead authors: Ornella Robutti and Luc Trouche).

The lead authors for each chapter are the IPC members who led both the working groups during the Study Conference and the writing of the chapters. Working groups members had different levels of collaboration during the writing process; these are reflected in the lists of co-authors and contributors.

Part 3 includes chapters related to the plenary addresses and the plenary panel. There are two chapters related to Theme A, one by the plenary speaker and one by the reactor. Chapters related to Themes C and D were written collaboratively by the plenary speakers and their reactors. The chapter related to the plenary panel was authored by the moderator and the four speakers, under the leadership of the moderator. (Due to unexpected circumstances, there is no chapter for the plenary address for Theme B.) Thus, the five chapters are:

  • Theme A (plenary): Using and Developing Content-Related Theory Elements for Explaining and Promoting Teachers’ Professional Growth in Collaborative Groups;

  • Theme A (reaction): The Art of Being Specific while Theorising for and from Practice of Mathematics Teachers’ Collaboration;

  • Theme C: Capturing Collaboration in Mathematics Teacher Education, in Terms of Relevant Actors, Targets and Environments;

  • Theme D: Resources for and from Collaboration: A Conceptual Framework;

  • Plenary Panel: Working and Learning in Collaborative Groups: What’s Key to Mathematics Teachers?

The final part (Part IV) of this volume consists of two commentaries, one by Dario Fiorentini and Ana Losano, and one by Rina Zazkis. We invited these distinguished scholars, who have extensive experience with teachers’ collaborative work, to comment on the Study themes and chapters in this Volume.

5 Editorial Overview of Thematic Working Groups Chapters and Plenary Chapters

5.1 Thematic Working Group Chapters

5.1.1 Theme A

Chapter 2 reports the outcomes from the working group on theme A (Theoretical perspectives on studying mathematics teacher collaboration) and the presented papers (18) pointing out theories and theoretical frameworks used to study mathematics teacher collaboration. Its aim is to address the four questions stated in the discussion document to indicate the role of the theories in understanding the processes, as well as the outcomes of teacher collaboration, and to illuminate different theoretical perspectives that have been currently developed. The chapter is written by the leaders of the group, da Ponte and Miyakawa, as well as three co-authors and it is structured in five sections.

In Sect. 2.1, the authors discuss the background of Theme A and in particular the ICME-13 research survey and the discussion document. Through this review, they identify theories and theoretical frameworks that originated both outside and inside the mathematics education research that had been used to study mathematics teacher collaboration. Examples of the dominant theories in the first category are Communities of Practice/Inquiry and Activity Theory, while in the second is Meta-Didactical Transposition, Documentational Approach to Didactics.

Epistemological issues about what is theory in general, and in mathematics education in particular, are addressed in Sect. 2.2. The authors point out different interpretations that exist about the nature of theory and argue that, to bring to the fore, these conceptualisations will generate discussions that will advance our field. They support their argument by referring to the dynamic relationship between theory and research, to the implicit and explicit theories, and, in general, to the role of theory in understanding phenomena of practice.

The variety of theories used to study mathematics teacher collaboration, their origins and role, as well as their interrelationships, are discussed in Sect. 2.3. The authors list 22 theories/theoretical perspectives mentioned in the papers presented in this working group, indicating a great diversity in comparison to those reported in the ICME-13 survey. These theories fulfil two main roles: understanding the phenomenon of teacher collaboration and designing the work of a collaborative group according to the context. The authors illustrate these different roles of the theories through specific examples from the presented papers. Moreover, in this section, the origins of the theories are discussed in terms of their specificity to mathematics teaching and learning or to social and cultural aspects that are also central in the context of mathematics teacher collaboration. Examples of the different relationships between the origins of the theories and their contributions to understanding teacher collaboration are also provided.

Finally, the authors report that most studies focus upon the development of theoretical constructs to address specific aspects of mathematics teacher collaboration, while few papers discuss and compare theoretical perspectives. They provide three examples of studies to illustrate ways that the theories have been used: adapting theories mainly outside mathematics education research and used to theorise aspects of mathematics teacher collaboration; studying the networking of theories to understand mathematics teacher collaboration by combining different aspects of it; comparing theoretical models used to design teachers’ collaborative work.

In Sect. 2.4, an emphasis is given to the role of theories in understanding the process and the outcomes of mathematics teacher collaboration. Two main forms of collaboration are distinguished in terms of the object of the collaboration. One form concerns the aim to solve a specific problem of practice, where it is initiated mainly from the teachers, and the second form aims to professional development activities that are supported mainly by an ‘expert’. Through the analysis of the presented papers these forms are exemplified, and specific issues related to the process of collaboration are identified. Although the theories and perspectives seem to address some of these issues or mathematics teacher collaboration at a generic level, there is the need to enrich them with concepts that allow the study of the complexity of mathematics teacher collaboration as it is addressed also in the other theme chapters.

In Sect. 2.5, the issues addressed in the previous sections are summarised in relation to the questions addressed in the Discussion Document. The study conference presentations of Theme A indicate a diversity of theories and perspectives that generally are not very specific to mathematics teacher collaboration, the different origins and uses of the theories to address aspects of mathematics teacher collaboration and the need to enrich dominant theories (e.g. Activity Theory or Communities of Practice), with theoretical constructs that allow mathematics specific aspects of teacher collaboration, but also affective, cultural and political ones.

5.1.2 Theme B

Contexts, forms, and outcomes of mathematics teacher collaboration are the focus of Chap. 3. Esteley, Huang and several co-authors and contributors from the working group examine different forms of mathematics teacher collaboration, the contexts in which collaboration is enacted and outcomes of the collaborative process. Their analysis of the Theme B papers is guided by the five questions posed in the Discussion Document: (a) What models of teacher collaboration have been developed? What are the design features, goals, and outcomes of the different models? (b) How effective are various models for promoting different outcomes? (c) Which forms of collaboration are appropriate in different contexts? (d) What are the affordances and limitations of each form of teacher collaboration? (e) What are the benefits and the challenges that online teacher collaboration poses to the teachers?

Section 3.1 introduces the chapter. It begins with a brief review of the literature on teacher learning through collaboration and the guiding questions that were identified in the Discussion Document. The authors then describe the three levels in their framework for understanding teachers’ collaborative work: micro (classroom), meso (institution) and macro (education system), and the approach they used to analyse the Theme B conference papers with respect to the contexts and goals, forms, outcomes and mathematical content of teacher collaboration.

Section 3.2 analyses the goals of the mathematics teacher collaboration projects represented in the Theme B papers using the three-tiered model. Looking across the papers, the authors note that national or multiple-site programs typically address national needs and concerns such as curriculum reform, while programs at the institutional level typically focus on developing teachers’ knowledge or teaching practice. In the few programs at the classroom level, teachers’ collaboration focuses primarily on improving specific teaching strategies.

The authors organise their discussion of forms of mathematics teacher collaboration in Sect. 3.3 according to four categories or models: adaptations of Lesson Study (LS); researchers–teachers partnerships; networks; forms related to specific purposes. LS adaptations typically focus on the institutional level, and involve a community of researchers and teachers who create original resources and design lessons for teaching specific mathematical content. In researchers–teachers partnerships, the professional learning community, as a collective, decides on goals and processes of inquiry, and engages in activities such as the design of teaching resources. The network model involves collaboration among communities or institutions, for example between communities of researchers from one or more institutions and communities of teachers or preservice teachers. The objectives and processes of the joint work are varied. In models of collaboration connected to specific purposes, specificity of purpose is the focal point of the joint work. In all four models, collaboration may be long-term or short-term and the joint work may focus on the classroom, school or educational system level.

Section 3.4 addresses the outcomes achieved in mathematics teacher collaborations. The authors focus first on products developed through collaborative work, noting that most products are at the classroom level and include resources such as lesson plans and mathematical activities. Next, they consider outcomes related to teacher learning, providing examples of projects that reported changes such as teachers’ greater understanding of the curriculum content and better support for all students’ learning of algebra. They also present some results that were considered unsuccessful and describe obstacles that hinder collaborative work, such as teachers’ lack of time and unforeseen changes in institutional routines and requirements. They then consider sustainability and dissemination of the outcomes of collaborations. With respect to sustainability, they observe that most collaborations that lasted 5 years or more were government initiatives or received sustained funding. The most common forms of dissemination were conferences and digital media. They conclude this section by highlighting the large number of long-term collaborations that exist across the world, and suggesting that nationwide programs seem to be based on the idea that the collaborations themselves are the most relevant outcomes, rather than results that can be disseminated beyond the collaboration.

The authors reflect on the role of mathematics content in teacher collaborations in Sect. 3.5. They observe that mathematical content both catalyses and supports teacher change, and is an outcome of the collaborative process. Mathematics-related content was central to many of the collaborative projects discussed in the Theme B working group. The nature of the mathematics content varied including, for example, mathematical tasks, mathematical practices and learners’ mathematical thinking. Topics related to the knowledge required for teaching mathematics included Mathematical Knowledge for Teaching, curricular knowledge and horizon content knowledge (Ball et al., 2008) and pedagogical content knowledge (Shulman, 1986). Mathematics-related activities in teacher collaborations that were addressed included doing mathematics, talking about mathematics and investigating representations of mathematics teaching and learning. In concluding this section, the authors suggest that more research is needed on how mathematics content mediates teacher learning outcomes.

In Sect. 3.6, the authors draw from the analyses presented in Sects. 3.2–3.5 to answer the five questions that guided the work of the Theme B working group. They conclude with suggestions for further research.

5.1.3 Theme C

Chapter 4 addresses Theme C: Roles, identities and interactions of various participants in mathematics teacher collaboration. Karsenty, Dole and several co-authors and contributors from the working group explore the roles and identities of the actors in collaborative groups such as teachers, mathematicians and researchers; and the nature of interactions between them. Section 4.1 introduces the chapter, noting that it presents a comprehensive overview of scholarship in this field, while paying particular attention to the emergent literature on the role of facilitator—the professional who manages the activities of the group, and whose responsibilities may include setting norms for interactions, supporting teachers’ exchange of experiences and new insights, and monitoring the discussion. Throughout, the authors consider both themes and issues related to various aspects of the roles, identities and interactions of participants in collaborative groups, as well as unanswered questions and directions for future research.

Section 4.2 focuses on methodological issues. It begins with a discussion of the methods and theoretical perspectives represented in the Theme C papers, and an analysis of the relevant actors, targets and environments addressed in a sample of these papers. Then, attending more specifically to the role of facilitator, the authors consider several methodological issues and challenges that have surfaced in research on the profession of facilitators, or mathematics teacher educators more broadly.

Section 4.3 reviews contemporary research that addresses the facilitator’s role in designing, maintaining and supporting collaborative activities for mathematics teachers. The authors examine several frameworks and models used in studying the role of the facilitator, the knowledge and skills central to the role, and the practices of successful facilitators. They then consider several situational challenges associated with promoting productive collaborative work: starting and managing a discussion; establishing and maintaining norms; sharing responsibility while keeping the discussion on track.

Section 4.4 focuses on the preparation of facilitators. The topics it addresses include: the trajectory of becoming a facilitator; principles of facilitator preparation; preparation programs for facilitators. The authors examine facilitators’ development over time, including changes in their knowledge, beliefs, identity, and practices, based on an analysis of six papers focused on projects to develop and support mathematics professional development facilitators. The section concludes with a discussion of means and models for supporting facilitators.

In Sect. 4.5, the authors examine the environment or setting in which teacher collaboration takes place. The section begins with a discussion of several models of teacher collaboration that address the environment of collaboration. They next focus on the internal environment created by participants within a collaborative community, exploring the roles of various participants and the nature of interactions that support the development of these communities. The concepts of communities of practice (Wenger, 1998) and communities of inquiry (Jaworski, 2006) frame their discussion. They then consider cultural and contextual aspects of the external environments in which collaborative communities exist, and institutionally imposed factors such as the time allocated for teacher collaboration. Here, they consider teacher collaboration both with and without facilitators.

In the final section of the chapter, the authors briefly summarise the foci of the previous sections and offer several suggestions for further research, including research on the impact of different actors in the environment on teacher collaboration and on facilitators, issues related to scaling up programs of teacher collaboration, and institutional factors that impact the sustainability of mathematics teacher collaboration. They conclude by acknowledging, “While there is still much work to be done, we recognise the progress made in recent years in studying different roles in mathematics teacher collaboration, reflected in the considerable body of research that we have drawn upon here to address this important issue” (Chap. 4, p. 192).

5.1.4 Theme D

Chapter 5 refers to Theme D: Tools and resources used/designed for teacher collaboration and resulting from teacher collaboration. It aims to illuminate the role of tools and resources designed and used in mathematics teacher collaboration, as well as those developed from mathematics teacher collaboration. It is written by the two group leaders (Robutti and Trouche), four co-authors and 15 contributors, participants in the Theme D Working Group. It is the outcome of the 18 papers presented in this group and discussed in the Working Group sessions. What is particular in the Theme D Working Group in comparison to the other groups was the use of virtual collaboration of the participants and the production of a shared discussion document during and after the conference. The chapter is structured in seven sections.

In Sect. 5.2, the authors present the background on Theme D and the five questions that are stated in the discussion document, the way that the group operated in the conference and their definitions of central concepts and constructs relevant to the theme. Distinctions between tools, resources, instruments and documents are discussed, as well as concepts and theories related to teacher collaboration such as community of practice, community of inquiry, boundary crossing, teacher knowledge and professional learning.

Theme D papers focusing on the design of resources through the collaboration of teachers with researchers and knowledgeable others are discussed in Sect. 5.2. Initially, the authors discuss the different conceptualisations and uses of curriculum resources in designing and enacting mathematics lessons, pointing out the role of language, the balance of prior and new resources, the critical role of the availability of digital resources, as well as the important role of teacher collaborative actions. Next, they address the design of resources for promoting students’ understanding of mathematical concepts. Finally, relationships between practices developed in the context of mathematics teacher collaboration and those in the school classroom are elaborated.

In Sect. 5.3, the emphasis is on tools and resources that teacher educators and researchers use to support teachers to enact collaborative inquiry into designing, enacting and redesigning mathematics teaching. The authors note that support was facilitated through the promotion of shared reflections concerning the evolutions of the designed resources and the classroom enactments, the use of theoretical and methodological tools in facilitating teachers’ inquiry into teaching, the analysis of teachers’ own and other teachers’ teaching in real classroom situations and by using representations of practice (e.g. hypothetical lessons).

In Sect. 5.4, the emphasis is given to the role of resources and tools in the process of teacher collaboration. Α categorisation of the tools and resources is offered in terms of their purpose to facilitate teacher collaboration (e.g. category 1—those planned for facilitating collaboration, and category 2—those that are not planned but were adapted through the work of the teachers as environments for teacher collaboration). In this categorisation, digital resources seem to be central (e.g. platforms, social-media, video-streaming). The authors elaborate on the use of the tools and resources focusing on their affordances in promoting teacher collaboration.

Section 5.5 addresses the theoretical frameworks and methods currently used to study the impact of teacher collaboration on the participants and the interactions within the teacher collaboration. The impact is studied directly using different sources of data (e.g. recordings of the collaboration, documents, recordings from classroom) or indirectly from teachers’ reflections on their experiences through interviews, questionnaires or focus groups. Dominant theoretical frameworks adopted to study the interactions include boundary crossing, existing frameworks of categorising learning opportunities, Documentational Approach to Didactics (DAD), Cultural–Historical Activity Theory (CHAT) and Anthropological Theory of the Didactic (ATD). Finally, the authors stress the need to develop infrastructures that are based on technology that facilitate teacher collaboration, and research agendas that generate rich data, allow its storage and are associated with metadata for future use.

In Sect. 5.6, the threads and perspectives of current research on the role of tools and resources for and from teacher collaboration as well as the future orientations of research are discussed. Some main results indicate that: (a) the resources for and from collaboration are not distinct but influence each other; (b) the resources that are open and dynamic give opportunities for reflection; (c) tools and resources for fostering teacher collaboration are appropriate when they allow teachers to develop teaching materials while they share their ideas and reflections; (d) the necessity of the development and the use of certain tools and resources to research teacher collaboration. Finally, in Sect. 5.7, the authors report findings from a survey during the COVID pandemic to address the importance of contextual and equity issues in the way that the tools and resources mediate the process and the outcomes of teacher collaboration.

5.2 Plenary Chapters

5.2.1 Theme A

Chapter 6 addresses Theme A, “Theoretical perspectives on studying mathematics teacher collaboration”. As Susanne Prediger explains in the first section, the intent of the chapter is “to elaborate a theoretical foundation for explaining and promoting teachers’ professional growth in collaborative groups” (p. 2, Chap. 6). The chapter argues that the theoretical foundations should integrate content-specific theory elements at both the classroom and PD levels.

Section 6.2 introduces generic models of professional development in collaborative groups (PDCG) and characterises professional growth as changes in teaching practices and practices of inquiry, underlying orientations, and shared categories for noticing and thinking. Section 6.3 presents a vignette from the first meeting of a researcher facilitator and a community of mathematics teachers and special education teachers who are working on differentiating instruction for at-risk students. The vignette, in which the teachers are discussing one student’s approach to multi-digit subtraction, is analysed using a generic framework for PDCG to illustrate limitations of that framework. It is then revisited throughout the chapter and analysed using the content-specific theory elements that Prediger introduces.

In Sect. 6.4, she introduces four content-specific theory elements at the classroom level that are necessary for the design of classroom learning environments, and four parallel theory elements that are lifted from the classroom level to the teacher PD level. At the PD level, for example, the four content-related theory elements are content (elements for specifying and structuring the PD content), growth (elements for explaining mechanisms of teachers’ professional growth), facilitating (elements for explaining the nature and background of facilitating PD) and environment (elements for designing and enacting PD environments).

The first part of Sect. 6.5 introduces the four classroom-level theory elements specific to the vignette—Content: multi-digit subtraction; Learning: mathematics content trajectories; Teaching: differentiated instruction, at-risk students; Learning environment: design principles for creating a learning environment for mathematics—and then analyses the vignette with respect to these theory elements. In the second part, Prediger conducts similar analyses at the PD level. She next offers a theoretical framework for explaining teachers’ professional growth and providing external resources to support professional growth, first for the specific set of vignettes and then for teachers’ communities of inquiry in general. She then offers three “lessons learned” for PDCG in general.

In Sect. 6.6, Prediger provides “meta-theoretical reflections” about the theoretical foundations necessary for explaining and promoting teachers’ professional growth in collaborative groups. For example, she emphasises the importance of the four PD-level theory elements and reminds us that PD content includes both classroom mathematics content and teaching practices. Finally, she suggests that whereas general theoretical frameworks such as communities of inquiry and models of professional growth provide a “generic search space”, they must be elaborated in content-related ways for specific areas of PD content.

5.2.2 Theme A Reaction

Boris Koichu (Chap. 7) begins his reaction to Prediger’s Theme A plenary chapter by noting that her chapter makes an important contribution to debates about the role of theorising in mathematics education research and practice. At the same time, he comments that her central suggestion—that more content-specific theorising is needed—is not obvious. He suggests that, in addition to Prediger’s vignette, episodes in different situations of mathematics teacher collaboration should be analysed using her model of content-specific theorising. The majority of the Commentary is an analysis of an episode in one of Koichu’s PD projects as it addresses three issues: (a) characteristics of Prediger’s research strategy that affords and includes content-specific theorising; (b) the application of the content-specific theory elements to a situation of teacher collaboration that differs from Prediger’s vignette; (c) how to connect content-specificity and generality of theorising in future research on teacher collaboration.

Reflecting on his analysis, Koichu observes that Prediger’s conception of content is multifaceted, including, for example, mathematical, epistemological and PD components. Her theorising about content-specificity aligns with the principles of design research. He analyses an episode in his Raising the Bar in Mathematics Classrooms (RBMC) project using her content-specific theory elements, and concludes that he is able to apply classroom-level and PD-level elements of the framework to the episode and, by doing so, deepened his understanding of both the RBMC episode and Prediger’s ideas. Koichu identifies two features of her ideas that make them transferable to different contexts—the functionally-oriented scheme of analysis and the bottom-up approach that begins by engaging deeply with the mathematical content and then theorises about learning, teaching and PD-facilitating. He concludes that the connection between the content-specific and the general is achieved by considering the particular content as a case of something more general.

5.2.3 Theme C

In this chapter (Chap. 8), the plenary speakers, Konrad Krainer and Carina Spreitzer, in collaboration with the reactor Bettina Roesken-Winter, propose a framework for analysing mathematics teacher collaboration, focusing on the relevant actors, the relevant targets and the relevant environments (RATE). The authors argue that the diversity of participants, goals of collaboration and settings where the collaboration takes place makes the study of collaboration too difficult to go deeply into the process and to compare different initiatives promoted in the collaboration.

The authors discuss the dimensions to the RATE framework and operationalise it in the form of a triangle with vertices, Teachers, Knowledgeable others and Environment, to analyse seven papers published in mathematics education reporting initiatives from four continents. Seven dimensions/codes were used to describe these papers: relevant actors; relevant targets; relevant environments; authors; types of initiative specificity of collaboration; research results.

By comparing the seven cases, the authors come to similar conclusions with other surveys that: (a) small-scale studies predominate; (b) most teacher education research is conducted and reported by teacher educators/researchers studying the teachers with whom they are working. Other observations and directions for future research are also reported, such as the need to: focus more systematically on teacher educators’ learning; make better links between teacher learning and the process of collaboration; emphasise the particularities of the contexts where the collaboration takes place and compare to other similar cases, as well as to stress the importance of sharing reflections.

5.2.4 Theme D

Chapter 9, co-authored by Karin Brodie and Kara Jackson, focuses on resources for collaborative professional work and their role in teacher collaboration and learning. They define resources broadly to include representational, knowledge, affective, human and institutional resources. Brodie and Jackson present a framework for conceptualising these resources and their functions in supporting teacher professional collaboration. In describing the framework, they make two key points about the nature of resources: (a) resources travel between teacher collaborative groups and classroom practice and are transformed or redesigned across contexts; (b) missing resources can contribute to unequal opportunities for teacher development, classroom learning and, ultimately, inequities in society.

After describing the framework, Brodie and Jackson apply it to projects they have worked in, the Data-Informed Practice Improvement project (DIPIP) in South Africa and the Middle-School Mathematics and the Institutional Setting of Teaching (MIST) project in the United States. They show how each type of resource supported or constrained teachers’ collaborative work in the two projects, and they consider how the resources both shaped and were shaped through teacher collaboration. For example, representations of teaching such as lesson plans, video-recordings of classroom lessons, student work and student assessment data often comprise the shared text of collaborative inquiry; and they were a key resource for teacher collaboration in both projects.

The DIPIP project focused on teachers’ use of learner errors as a resource for teaching. Representational resources included tests, learners’ responses to tests and video records of the teachers’ lessons. In an effort to improve their teaching, teachers’ collaborative inquiry communities analysed these representational resources to understand learner errors and the reasons underlying them. In productive teacher collaboration in the MIST project, teachers used representational resources such as lesson plans, curricular materials and student assessment data to engage in conversations about the ‘how’ and ‘why’ of instruction.

The design of both projects supported the movement of representational resources between classroom and collaboration, and these resources were often modified as they moved between contexts. Findings from the two projects suggested that the focus and quality of representational resources shape teachers’ learning opportunities within collaborative contexts. Brodie and Jackson conclude the chapter by highlighting ‘how’ and ‘why’ each plays an important role in productive teacher collaboration and suggesting areas for future research.

5.2.5 Plenary Panel

In the panel, the voices of four teachers from different countries and settings were heard about their experiences collaborating with other teachers. Hilary Hollingsworth and the four teachers—Yivi Chen, Christelle Fitamant, Lameck Dition Sandram and Shelli Temple—were the authors of this chapter (Chap. 10). The aim of the chapter is to understand the learning opportunities offered to teachers in collaborative settings, and to identify conditions that support or constrain teachers’ professional learning. The collaborative groups had been established in projects taking place in China, England, France, Africa and the US, and included mainly planning, teaching and analysing Lesson Study lessons. All except the US group were face-to-face and small-group collaboration. In the US context, thousands of mathematics teachers from different countries collaborated online. Comparing teachers’ experiences, common points are addressed and discussed in the chapter. Improving the quality of mathematics teaching and as a result students’ learning was the focus of all the groups. These goals were formed in the context of the collaboration, and the expertise of other teachers and researchers played an important role in fulfilling their goals and developing professional learning.

Then, the reports of the four teachers are presented providing information about: (a) the context, purpose and design of the collaboration; (b) the collaboration outcomes; (c) what is learned—factors supporting or limiting the collaboration, as well as challenges encountered, and professional learning. Synthesising these reports especially related to lessons learned, the chapter reports several cultural, social, environmental and physical factors that support collaboration, such as a culture for life-long learning of teachers, teachers’ motivation, available resources and connections with other teachers.

Among the factors limiting the collaboration are unwillingness to participate, resource constraints, difficulties to lead new ideas and approaches, and that communication protocols and tools require time. To sustain collaboration and professional learning involves joint reflection about the lessons, analysis of selected lessons and online opportunities. The chapter ends with the use of the Interconnected Model of Professional Growth to identify growth paths of the four teachers and the formulation of a set of questions related to mathematics teacher collaboration, and the four study themes addressed in this volume.

5.3 Commentary Chapters

Dario Fiorentini and Ana Losano organise their Commentary on ICMI Study 25 around four issues: forms and meanings of collaboration; the nature of collaboration and how it is investigated; the relations between collaborative groups and classroom practice; possibilities for scaling up collaborative PD. For each one, they draw upon the earlier chapters in this Study 25 volume and their own experiences of collaboration with teachers in Brazil, in order to reflect on advances and possibilities and to identify challenges related to collaborative PD. With respect to the first issue, they note the diverse meanings of collaboration that were addressed in the Study volume and suggest that effective collaboration requires time, support by participants’ institutions and shared negotiation of goals and action.

In their discussion of the second issue, Fiorentini and Losano suggest that narratives written by participants in collaborative groups both enhance the collaborative work and provide rich material for analysing teachers’ learning. And they make a case for conducting collaborative research with teachers in addition to the more typical research about teachers. They stress the importance of studying the complex relations between collaborative groups and classroom practice, and suggest two promising directions for research: (a) how resources are transformed as they travel between the collaborative groups and the classroom setting; (b) teachers’ developing professional identity and agency as they regularly cross the boundaries between the collaborative group and classroom practice. They highlight the potential of blended and online approaches for scaling up collaborative PD and emphasise that building trust and ensuring that members feel safe are essential for the success of these approaches. Their commentary concludes with the suggestion that collaboration is “a fertile and still little explored field that demands continuity of studies and socialisation, discussion and systematisation in events” (p. 13, Chap. 11).

Rina Zazkis describes her commentary as a reflection on her noticing and wonderings, and what drew her attention when reading the Study volume chapters. Her reflection focuses on five issues that she labels: teachers’ work; broad applicability; mathematics; content-related theorising; effects or products of collaboration. Zazkis points out, for example, that the Study volume chapters consider teachers’ work very broadly to include learning and professional development, as well as planning and assessing student work. She suggests that many ideas about collaboration in the chapters are broadly applicable beyond mathematics. Focusing specifically on mathematics, she identifies an extensive list of possible outcomes of teacher collaboration, which she describes as different forms of professional growth. In the final section of her commentary, Zazkis shares a personal reflection on the value of teacher professional collaboration, explaining how and why building professional community became the central goal of her “foundations of Mathematics” course—the first course in a two-year, cohort-based Secondary Mathematics Education master’s program for practicing mathematics teachers.

6 Reflections on the Study and the Study Volume

Producing this Study volume has been a rather long process. It involved close collaboration among many people, especially the IPC members and leaders of the working groups, and the ICMI president and secretary who initiated the Study. This collaboration took place in multiple physical and virtual spaces in the various phases of the Study—the writing of the Discussion Document, the planning of the conference and the editing of the proceedings and Study volume. Because of the COVID pandemic, a virtual way of collaborating among participants was initiated during the conference, where colleagues from China shared their work online. This virtual form of collaboration was evident in all the working groups and happened before, during and after the conference. Online collaborative meetings are now a part of our everyday realities both as researchers and practitioners. Virtual collaboration was a research topic in the Theme D chapter, where tools and resources are the central focus. It is an area that needs to be researched further in relation to collaboration both during and after the COVID pandemic.

A goal that was promoted in the conference, and to some extent was achieved, was to hear the teachers’ voices from their experiences participating in collaborative activities working with other teachers and researchers. The teacher panel in the conference and in Chap. 10 in this Study volume brought these voices to our study and indicate the gains, but also the challenges that the teachers face. The panel brought to the fore the role of contextual and cultural aspects that frame the collaboration and its outcomes.

Emerging issues from each theme chapter and across the chapters indicate the state of the art in our understanding of teachers working and learning together, as well as future directions. Here, we highlight key learnings and areas for future research for each of the four themes that guided ICMI Study 25. With respect to theory, there is a diversity of theories and theoretical frameworks used for studying mathematics teacher collaboration. However, we need to develop theoretical constructs that allow mathematics specific aspects of teacher collaboration to be addressed, as well as affective, cultural and political ones. Focusing on the process of collaboration, there are obstacles that relate to unforeseen changes in institutional routines and requirements, and teachers’ lack of time that must be managed in long-term collaborations. Most products of teacher collaboration are at the classroom level, and include resources such as lesson plans and mathematical activities. Long-term collaborations continue to be a challenge for the educational community.

To address this challenge, it is important to identify features of successful, long-term collaborations that are generalisable across contexts. We also need to continue developing and improving models of online and blended collaboration, and to identify the features of these models that make them effective. Facilitators play an important role in the processes and outcomes of teacher collaboration. Professional development programs for facilitators, and their role in developing facilitators’ academic knowledge, and social and interpersonal skills, is an important direction for research. The settings in which teacher collaboration takes place, and participants in those settings other than the teachers and facilitators, also impact the outcome of the collaboration. Future research needs to address the impact of facilitators and other actors in collaboration, as well as the role of institutional factors that support the sustainability of mathematics teacher collaboration.

A diverse set of resources for and from teacher collaboration have been identified. The roles of these resources vary, depending on the settings in which the collaboration takes place, as well as the different participants that are involved. Digital tools and resources that offer wide and flexible uses and opportunities for teachers to experience innovative representations of mathematics teaching foster teacher collaboration. Issues that remain open for future research include the quality of resources, the sustainability of tools, the use of resources in scaling up of teacher collaboration and the role of digital tools and resources in mathematics teacher collaboration.

The plenary chapters and the two commentaries on the volume add to the above points, offering directions for future research. Different aspects of mathematics teacher collaboration are discussed in these chapters, such as:

the content-specific character of teacher collaboration;

the need to link teacher collaboration with classroom teaching both as a way of theorising it and for supporting its sustainability;

the emphasis on the quality and the focus of the resources to shape mathematics teacher collaboration;

the need for more research with teachers rather than about teachers, and for encouraging teachers to become co-authors with researchers;

the development of theoretical and methodological perspectives to consider the complexity of mathematics teacher collaboration by focusing on the role of context and on the different agents;

approaches for scaling up mathematics teacher collaboration.

In conclusion, this ICMI-25 Study volume shows that mathematics teacher collaboration is an area that has attracted much research attention during the last several years. Yet, there are still open questions to be addressed at the theoretical, empirical and practical levels. Moreover, there are areas that have not been addressed (or addressed only minimally) in the Study volume, such as the collaboration between teachers of different subjects, the collaboration of teachers at the university level and the collaboration among mathematicians and mathematics educators.

Research in these areas, as well as others not represented in ICMI Study 25, will extend our understanding of teacher collaboration, for example by giving more attention to the characteristics of mathematics (in comparison to other disciplines), collaborative groups that include participants other than K–12 mathematics teachers and additional contextual factors that frame these collaborations. Our understanding and appreciation of the value of teachers working and learning in collaborative groups has grown tremendously in the process of leading ICMI Study 25. We hope that this Study volume encourages additional programs of, and research on, teacher collaboration and looks forward to learning from future projects.