Mathematics teacher educators play a critical role in translating research findings into frameworks that are useful for mathematics teachers in their daily practice. In this article, we describe the development of a representation that brings together four research-based learning trajectories on number and operations. We detail our design process, present the ways in which we shared this representation with teachers during a professional development project, and provide evidence of the ways teachers used this translation of research into a pedagogical tool to make sense of students' mathematics. We conclude with revisions to the representation based on our analysis and discuss the role of mathematics teacher educators in translating research findings into useful tools for teachers.

This study examines teachers' discussions in a professional development setting to understand the ways in which learning a mathematics learning trajectory may change aspects of their discourse about students as learners. Using mixed methods, we bring together two theoretical frames that use a Vygotskian perspective on learning to analyze professional discussions among 22 elementary-grade teachers participating in a yearlong, 60-hour mathematics professional development program. Results indicate that over time, some discursive patterns for explaining students' academic performance P. HOLT WILSON is an associate professor of mathematics education at

This chapter provides a set of recommendations for teacher educators interested in using simulated teaching experiences to support teacher learning of pedagogical practice in the post-COVID era. Built from existing research, the recommendations from the study come from lessons learned as five elementary mathematics and science teacher educators used a simulated teaching experience to support preservice teacher learning during the COVID-19 pandemic. The authors begin by situating this work in the larger context of practice-based teacher education and then provide an in-depth description of how five teacher educators at different universities integrated a simulated teaching experience into their elementary mathematics or science methods course. The chapter ends with a discussion of lessons learned and how educator preparation programs and teacher educators can leverage the opportunities created by using simulated teaching experiences in the post-COVID era.

In this article, we describe rehearsals designed for use in professional development (PD) with secondary mathematics teachers to support them in reimagining and refining their practice. We detail a theoretical framework for learning in PD that informs our rehearsal design. We then share evidence of secondary mathematics teachers’ improvements in classroom practice from a broader study examining their participation in a PD that featured the use of rehearsals and provide examples of the ways two teachers’ rehearsals of the practice of monitoring students’ engagement with mathematics corresponded to changes in their practice. We conclude with a set of considerations and revisions to our design and a discussion of the role of mathematics teacher educators in supporting teachers in expanding their practice toward more ambitious purposes for students’ mathematical learning.