Mathematics Teacher Education and Development

Connecting Algebraic Structures and Solving Equations: Fostering Mathematical Knowledge for Teaching

Verónica Molfino — Mon, 14 Sep 2026 00:00:00 +1000

Whilst in theory, the connections between advanced mathematics and secondary-level mathematics are widely acknowledged as significant by the entire community of mathematics teacher educators, mathematics teachers and student teachers, there remains considerable scope for research concerning the specific nature, types, and mechanisms of these connections. Further investigation is needed into how both practising and prospective teachers may be supported in articulating and applying these links within their classroom practice. This article endeavours to contribute to this area by presenting findings from a study in which mathematics teacher educators participated in workshops, designed learning sequences for prospective teachers, and implemented them. A detailed analysis of one mathematics educator’s process focused on algebraic structures and their relationship to equation solving was carried out. The findings suggest that the experience was beneficial in enabling the integration of diverse connections into practice, thereby fostering his Mathematical Knowledge for Teaching (MKT) as well as that of his students, the prospective teachers. The article elaborates on the connections rendered visible through the Mathematics Teacher Educator’s (MTEs) practice and examines the influence on the development of the MKT among the prospective teachers.

Mathematics Teacher Educators Teaching to Teach: Tasks and Formative Purposes in Initial Teacher Education

Cristina Ochoviet — Mon, 14 Sep 2026 00:00:00 +1000

The study reported in this article examined mathematics teacher educators who teach didactics of mathematics in Uruguay. It analysed the tasks they selected and the purposes for which these were used in initial teacher education. The study involved twelve mathematics teacher educators from three teacher-education institutes and employed an in-depth qualitative case-study design. Data were collected through semi-structured interviews, classroom observations, and task exemplars used by the teacher educators. The findings indicate a wide range of tasks aligned with categories proposed in the literature—including reflecting on similarities and differences, designing and solving problems, learning through the study of practice, selecting resources, and identifying barriers to learning—yet with a low prevalence of tasks that address the beliefs of prospective mathematics teachers. The tasks served diverse formative purposes, including task design and redesign, reflection on students’ thinking, lesson planning, managing interactions, resource analysis, types of proofs, and the languages present in the mathematics classroom. While most tasks aligned with established categories, some did not fit adequately—for example, tasks oriented towards the construction of the object to be taught. Additionally, broader purposes emerged that transcend immediate practice, viewing teacher education as a space for preparing prospective mathematics teachers to become critical practitioners.

Alternative Assessment in a Relational Constructivist Mathematics Methods Course: An Illustration of Mathematics Teacher Educator Practice

Alyson Lischka — Mon, 14 Sep 2026 00:00:00 +1000

For mathematics teacher educators to learn from others’ practice, avenues for sharing those practices are needed. In this Illustration of Practice article, an alternative assessment model implemented with prospective teachers in a relational constructivist secondary mathematics methods course is presented. The article provides one answer to the question of how mathematics teacher educators connect theory and research to their teaching practice. Background is provided to establish the context within which an alternative grading system was implemented and examples from one strand of learning in the course are provided to demonstrate the use of the alternative assessment system. The overall grading rubric and objectives that guide the course are described and cases recounting prospective teachers' experiences with this assessment system are included. This illustration of practice contributes one example of the connection between theoretical foundations and mathematics teacher educator practices. It will support other mathematics teacher educators to consider the ways in which theoretical perspectives inform teaching practices implemented in their courses.

Tools for MathematicsTeacher Educators’ Professional Growth: Conceptualising Inquiry Opportunities for Representations of Teacher Education Practice

Gil Schwarts, Hannah Nieman — Wed, 16 Sep 2026 00:00:00 +1000

Ongoing professional growth is central to Mathematics Teacher Educators’ (MTEs) work, yet they often lack tools to systematically inquire into and learn from their own practice. This multiple case study investigates how two distinct representations of practice — a video-based Video Stimulated Recall Conversation (VSRC) and a survey-based Collaborative Professional Development Survey (CPDS)—support MTEs in inquiring into their own professional practice. Drawing on the semiotic infrastructure for practice framework, we examined how MTEs reflected on practice across two contexts involving prospective teachers: a video-club in Israel, using the VSRC, and an academic course in the United States (U.S.), using the CPDS. Findings show that both tools surfaced common problems of practice, such as time management and balancing facilitator input, while highlighting different dimensions. The VSRC, by foregrounding temporality and the visibility of specific interactions, illuminated real-time decision-making, specific linguistic choices, and gestures. The CPDS, in contrast, revealed teachers’ perspectives and patterns of change over time, offering candid feedback through anonymity. Notably, both tools did not provide artefacts of teacher learning. The study contributes considerations for selecting and designing representations for MTEs' professional growth, underscoring the value of combining multiple, complementary tools that highlight different facets of practice.

Enactivism as a Theory and Methodology for Mathematics Teacher Educators’ Learning as Teachers and Researchers

Tracy Helliwell, Laurinda Celia Brown, Alf Coles, David Reid — Fri, 16 Oct 2026 00:00:00 +1000

This article proposes a methodology for becoming mathematics teacher educators (MTEs), in addressing the question, “How is enactivist learning done?" This methodology draws on enactivism, tying together methodological and theorising work done 25 years apart by two of the authors. The methodology has five dimensions—Using dissonance; Staying with the detail; Finding conviction; Making it real; Going meta—and operates as a methodology for MTE teaching, learning and researching. We offer three illustrations of these methodological dimensions, showing how they cross the three aspects of MTE practice. Towards the end of the article, we share the outcomes of a four-way discussion, using narrative interviewing protocols, consistent with the methodology dimensions. We exemplify how new awarenesses linked to action, enactivist learning, arise for one member of the group when being interviewed by the others. We show how the methodological dimensions are relevant to levels of MTE teaching, MTE learning, and MTE researching practice.

Mathematics Teacher Educator Use of Structured Learning Routines and Curriculum Materials to Support Teacher Learning

Lynsey Gibbons, Kelly McKie, James Hiebert — Thu, 17 Sep 2026 00:00:00 +1000

This article explores how Mathematics Teacher Educators (MTEs) can effectively engage classroom teachers in professional learning. Rooted in empirical data, we hypothesise that MTEs can foster productive teacher conversations by leveraging ambitious and educative curriculum materials in conjunction with a structured set of professional learning routines. The study details the implementation of a "lesson analysis cycle”, which includes collective planning, lesson enactment, and reflection. Analysing interactions between MTEs and groups of same-grade level teachers, the findings reveal that this approach facilitates conversations characterised by their integration of student thinking, mathematical content, and pedagogy. These discussions delve into deep instructional issues with high levels of specificity, evident in instances of negotiating learning goals, identifying critical lesson moments, and debriefing teaching enactments. We interpret the findings as confirming our hypothesis and propose that the curriculum materials plus the structured learning routines offer a replicable model for MTEs to cultivate rich professional learning.

Promoting Content-related Facilitator Expertise: Facilitator Professional Development Approach in the QuaMath Program

Thu, 24 Sep 2026 00:00:00 +1000

In scaled-up professional development programs for teachers, the sessions are mainly conducted by facilitators who were not part of the original design team. The quality of teacher professional development (TPD), therefore, relies on facilitator preparation and ongoing support, enabling them to develop expertise with respect to the content and concepts included. Whereas relevant components of facilitator expertise have been unpacked theoretically and empirically from different perspectives, reports on the designs of facilitator professional development (FPD) programs aimed at promoting such expertise are still rare. In this article, we report on one FPD program which was designed and enacted within the nationwide ten-year implementation program QuaMath (Developing Quality of Mathematics Classrooms and Teacher PD) for 515 mathematics facilitators in different age groups (K–1, 1–4, 5–10, 11–13). We present the FPD approach, including its overall goals for mathematics content-related facilitator expertise, its macro design in terms of structural and institutional characteristics, and its micro design through typical FPD activities. We take this program as a case to argue that fostering pedagogical content knowledge for professional development requires a systematic combination of work at both levels: the classroom and the TPD level.

Learning Through Collaboration: Mathematics Teacher Educators and Mentor Teachers in Teacher Education

Verónica Scorza, Daniela Pages, Sebastián Parodi — Thu, 08 Oct 2026 00:00:00 +1000

Teaching to teach mathematics in a mathematics methods course integrating a school-based practicum experience often involves limited coordination between mathematics teacher educators (MTEs) and mentor teachers (MTs), leading to fragmented supervision and conflicting approaches. This study examines how collaboration between MTEs and MTs in Uruguay supports the professional learning of both groups of teacher educators. Grounded in the framework of boundary learning, we conceptualised their interactions as boundary encounters and analysed five recorded meetings in which MTEs and MTs discussed how to accompany two prospective teachers (PTs) during their practicum. Using a qualitative, exploratory case study design, we traced how the learning mechanisms of identification, coordination, reflection, and transformation emerged in their discussions. Findings show that initial tensions were reframed through the identification of sociocultural differences and pedagogical roles, while coordination developed around boundary objects such as lesson plans and observation tools. Reflection occurred when participants problematised assumptions and adopted others’ perspectives, and transformation was evident in proposals for hybrid practices such as joint planning, co-teaching, and shared examination panels. The study demonstrates that collaboration transforms tensions into opportunities and highlights the importance of creating structured spaces for dialogue as well as formally recognising MTs as co-educators in mathematics teacher education.

Mathematics Teacher Educators’ Orientations Towards Academic and School Mathematics

Jonei Cerqueira Barbosa — Mon, 14 Sep 2026 00:00:00 +1000

The study reported in this article examines how mathematics teacher educators (MTEs) mobilise and articulate reference practices in their pedagogical communication with teachers. Reference practices designate the constellations of norms, epistemic values, artefacts, and validation criteria that MTEs invoke in their professional work. Pedagogical communication refers to the processes by which MTEs anticipate, select, sequence, and legitimate educational messages. Using a qualitative approach, data were generated through classroom observations (recorded through field notes and video recordings), and course documents in two Brazilian settings: a Professional Master's programme for in-service teachers and a prospective mathematics teacher education programme. Selected video-recorded segments were transcribed, and the field notes and transcripts were coded line by line through thematic analysis procedures. Two contrasting orientations were identified. In the first, academic mathematics functioned as the reference practice: objects, sequences, and validity criteria followed formal definitions and proofs. In the second, school mathematics served as the reference: curriculum prescriptions, textbooks, and evidence of student reasoning organised the formative experience. Three analytical dimensions characterise these orientations: the source of objects and tasks, the prevailing epistemic values, and the validation criteria invoked. Drawing on these findings and prior literature, a slider representation that maps the range of positions MTEs may assume along a continuum between academic and school mathematics is proposed. The slider offers a tool for the analysis of professional practice and promotion of teacher reflection.

Keeping Mathematics Alive in Teacher Education: Mathematics Teacher Educators Navigating Tensions

Ami Mamolo, Rina Zazkis — Mon, 14 Sep 2026 00:00:00 +1000

This article reports on three cases of mathematics teacher educators (MTEs) who experienced tensions when aiming their teaching at extending and strengthening the mathematical knowledge of prospective teachers. Of particular interest in this study are tensions related to MTEs attempts to keep learners’ attention on the intended mathematical ideas of lessons and activities, in addition to important emerging issues related to social justice, technology, and pedagogy. We build on literature that has considered tensions that transpire when teaching mathematics in the K–12 setting, extending the discussion to the case of mathematics teacher educators. This article contributes new and refined understanding about the interplay of tensions impacting mathematics teacher educators who, in their attempt to strengthen teachers’ mathematical knowledge, are pulled away from mathematics in different directions.

Becoming a Lesson Study Facilitator: A Case Study

Paula Gomes, João Pedro da Ponte, Marisa Quaresma, Micaela Martins — Sat, 03 Oct 2026 00:00:00 +1000

This article reports on the initial experience of a knowledgeable mathematics teacher, Vanda, as she assumed the role of a novice lesson study facilitator. With two prior experiences of participating in lesson study, Vanda was challenged to facilitate a lesson study with the support of a more experienced facilitator, who worked with her to prepare the sessions. Drawing on a qualitative case study, data collection included participant observation (with audio recordings of preparation and lesson study sessions, logbook and document collection), and audio recorded semi-structured interviews before and after the lesson study. The results show how the dimensions of resources, orientations, goals and identity (ROGI framework) interact in framing Vanda’s decisions, and the complex identity negotiation involved in this transition, as her prior teacher identity both supported and constrained her emerging facilitator identity. Believing that teachers learn from practice, she encouraged exploring simulated classroom scenarios and fostered peer collaboration. Over time, Vanda evolved from a hesitant guide into a confident facilitator, underscoring that facilitation competence is a situated process requiring strong knowledge of lesson study. Her journey also highlights the pivotal role of collaborative planning, and hands-on experience to her development as a lesson study facilitator and the dynamic nature of lesson study, where facilitators continually learn, adapt and grow.

Mathematics Teacher Educators Learning at the Boundary Between Classroom Practice and Educational Research

Margaret Marshman, Kelli Anson — Wed, 16 Sep 2026 00:00:00 +1000

Education departments provide support for teachers of mathematics, particularly out-of-field teachers, to improve their mathematics teaching. In this article, we explore the insights and learnings of mathematics teacher educators (MTEs) working as critical friends outside the formal structures of research or professional learning leadership. As part of the Queensland Department of Education M in STEM project mathematics educators from Queensland universities supported teachers in clusters of schools to address their shared problem of practice in mathematics teaching. This case study employed the Most Significant Change methodology to investigate how MTEs engaged at the boundary between classroom practice and educational research. Findings indicated that MTEs, through their roles as critical friends, had opportunities to hear teachers’ stories, observe classrooms in diverse contexts, and develop new insights into teaching practices. This process also enabled the generation of new or hybrid knowledge that bridged theory and practice. Implications for initial teacher education include a strengthened capacity for MTEs to connect curriculum and pedagogy with the lived challenges of classroom practice.

The Fellowship of Practice: Facilitators’ Roles and Obligations in Mathematics Teacher Professional Development

Soobin Jeon, Patricio Herbst, Amanda Brown, Ruya Savuran — Mon, 02 Nov 2026 00:00:00 +1000

The study reported in this article explored the hypothesis that mathematics teacher educators (MTEs) have professional obligations that constitute resources and constraints for managing practice-based professional development (PD). This was done by inspecting how 12 facilitators from varied institutional positions, who led a two-year implementation of StoryCircles, reflected on their work of facilitation. Participants were interviewed using a protocol that made explicit the hypothesis proposed. Using caricature analysis inspired by The Lord of the Rings, where a fellowship of companions supports one individual in carrying the Ring, the researchers developed facilitator caricatures that capture different orientations that facilitators can take when supporting teachers’ professional development. Findings reveal that all facilitators recognised disciplinary, interpersonal, individual, and institutional obligations as relevant to their work. The distinguishing feature was the choice of obligation each treated as the anchor in moments of uncertainty, reflecting the multiple sources of legitimacy for knowledge of mathematics teaching practice that facilitators may recognise when that practice becomes the content of PD. This study contributes to theorising the professional obligations that shape facilitation of practice-based mathematics PD and how facilitator identity is jointly constituted by systemic affordances and the personal resources individual facilitators bring to their role.

Theorising Disruptive Pedagogy in Teacher Education: Mathematics Teacher Educators and Practice-theory Challenges in the Post-field Context

Annette Hessen Bjerke, Kathleen T. Nolan — Mon, 14 Sep 2026 00:00:00 +1000

An extensive body of research has examined theory-practice transitions in mathematics teacher education, where prospective teachers (PTs) move from university (theory) to field experience (practice). In contrast, the reverse transition—from practice back to theory—is underexplored. Acknowledging mathematics teacher educators' (MTEs') key role in teaching PTs to reflect critically on their field experiences and create spaces for disruption and disruptive pedagogies, this article focuses on the often-overlooked practice-theory transition. Drawing on interviews with 21 MTEs from Canada and Norway, we examine how MTEs navigate PTs' return to university following their field placement in schools. While and disruptive pedagogy literature suggests that teacher educators should challenge or shift away from certain pedagogies and practices, our findings reveal that MTEs may choose not to challenge specific beliefs/practices in the post-field context of mathematics teacher education. Reasons include PTs’ limited familiarity with theoretical discourse, MTEs' desire to reduce the pressure on PTs, and an intention to avoid reinforcing the dominant time discourse. Additionally, some MTEs are unaware that pre- and post-field practices might need to differ. We offer specific suggestions for critical reflective questions and actions that could be initiated in a post-field “third space” to promote deliberate and disruptive pedagogical actions.

Enactment of Humanising Mathematics: Mathematics Teacher Educators' Positionalities and Theoretical Stances

Nirmala Naresh, Karisma Morton, Colleen Eddy, Fardowsa Mahdi, Queshonda Kudaisi — Thu, 08 Oct 2026 00:00:00 +1000

This paper presents a self-study by five mathematics teacher educators (MTEs) at a minority-serving institution in the United States. We examined how our positionalities and theoretical stances shape the enactment of humanising mathematics for prospective teachers (PSTs). We explored how our diverse racial, cultural, and professional backgrounds influenced our teaching. Using narrative inquiry, we wrote and analysed key episodes from our pedagogical experiences, connecting them to our respective theoretical perspectives. Through this work, we present counter-narratives that empower PSTs, particularly those historically marginalised in mathematics learning spaces. Our narratives revealed how attention to identity, privilege, and experience informs not only our approach to teaching but also how we present mathematics in ways that support PSTs to foster inclusive and socially responsive classrooms. We highlight tensions that emerged in this work and describe how these have shaped our teaching, prompting us to be intentional, reflective, and transparent about our practices. These findings underscore the importance of creating spaces for collective inquiry, modelling vulnerability, and offering critical support to PSTs as they learn to enact humanising mathematics in their own classrooms contributing to the theorising of MTEs’ work.

Connecting University and Secondary Mathematics: Design Principles for Developing Prospective Teachers’ Content Knowledge and Critical Stance

Thu, 15 Oct 2026 00:00:00 +1000

In this article, we present the design of Inquiry-oriented Dynamical Systems and Modelling (IODSM), an upper-division mathematics content course that can serve as an elective for prospective secondary teachers (PSTs). The course bridges university and secondary mathematics by combining advanced content with structured opportunities to engage secondary mathematics topics, forward-looking teaching practices, and mathematical practices. Grounded in inquiry-based mathematics education and oriented toward fostering productive dispositions such as students’ embracement of a critical stance, IODSM offers a learning environment where PSTs connect mathematics with future teaching. As an Illustration of Practice article, we outline a typical session, describe the theoretical grounding, and highlight four design principles that underpin classroom activities, course materials, and instructional choices. The article concludes with evidence of PSTs’ willingness to critically reflect on their mathematical beliefs and values, resulting in PSTs embracing a critical stance.

Mapping the Landscape of Mathematics Teacher Educator Practices, Preparation, and Support

Fri, 09 Oct 2026 00:00:00 +1000

This article presents a comprehensive mapping of the field of professional practices, preparation, and support for mathematics teacher educators (MTEs). It synthesises insights from three editions of the international conference (Congress of the European Society for Research in Mathematics Education [CERME]) dedicated to this crucial yet often under-examined area of educational research and practice. The conferences, held between 2021 and 2025, have served as critical junctures for sharing cutting-edge research, innovative practices, and pressing concerns related to those who prepare and support the next generation of mathematics teachers. This conceptual contribution aims to delineate the field's historical development, identify core theoretical frameworks, analyse prevalent empirical methodologies, summarise key research findings and articulate emerging issues and future desiderata. It is grounded in the collective expertise of a team of researchers actively involved in these conferences and possessing extensive experience in mathematics teacher education. This article synthesises significant conference contributions, offering a systematic and integrated overview that reveals the field's contours, interconnections, and gaps, and draws a holistic map of the field as it has evolved over recent years.

Action Research as a Way of Working, Researching, and Reporting as a Mathematics Teacher Educator

Linda G. Opheim — Sat, 10 Oct 2026 00:00:00 +1000

This methodological article uses illustrations from my own action research projects to guide a discussion of action research as a tool for connecting research and practice as a mathematics teacher educator. I begin with a brief historical summary of the development of action research as a methodology, before presenting two of my action research projects and connecting these to the broader aims and characteristics of action research. I then discuss issues I have encountered in the process of publishing on action research, together with reflections on how the issues might be addressed. Through these discussions, I aim to encourage more mathematics teacher educators to use action research as a way of systematically examining and reporting on their practice and to contribute to the broader discussions of how mathematics teacher educators can make the processes of developing their practice visible through research.

Mathematics Teacher Educators: Theories, Methodologies and Teaching Practices

Margaret Marshman, Signe E. Kastberg, Cristina Ochoviet — Mon, 14 Sep 2026 00:00:00 +1000