Mathematics Teacher Education and Development

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

Verónica Molfino — 2026-09-14

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 — 2026-09-14

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 — 2026-09-14

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.

Mathematics Teacher Educators: Theories, Methodologies and Teaching Practices

Margaret Marshman — 2026-09-14

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

Annette Hessen Bjerke — 2026-09-14

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.

Mathematics Teacher Educators’ Orientations Towards Academic and School Mathematics

Jonei Cerqueira Barbosa — 2026-09-14

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 — 2026-09-14

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.