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Rachael H. Kenney, Michael Lolkus, and Yukiko Maeda

Mathematics teacher educators play a key role in supporting secondary mathematics teachers’ development of effective, research-based formative assessment (FA) practices. We used qualitative research synthesis as a tool to identify actionable recommendations for mathematics teacher educators as they work with teachers on FA practices in secondary classrooms. These recommendations can strengthen the research-based practices of mathematics teacher educators as they support teachers’ collections and uses of FA data to move student thinking forward in secondary mathematics. We share and discuss recommendations for mathematics teacher educators to connect pedagogical content knowledge of students, teaching, and curriculum to FA practices. We also highlight the usefulness of the qualitative synthesis method, meta-aggregation, for generating research-based connections between theory and practice in mathematics education.

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Margaret Rathouz, Nesrin Cengiz-Phillips, and Angela S. Krebs

Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.

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Amber G. Candela and Melissa Boston

In this article we detail a research study using the Instructional Quality Assessment (IQA) Rubrics () as the frame for a professional development with mathematics teachers in grades 3-8. We wanted to create a professional development around a tool that was typically used in research as a way to observe teachers, as a tool to use with teachers on their reflection of instruction. In this study we share both the researchers’ and teachers’ perspectives of affordances and constraints of the professional development and observational rubrics.

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Jared Webb and P. Holt Wilson

ABSTRACT

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.

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Corey Webel and Sheunghyun Yeo

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.

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Enrique Ortiz

This article includes an original artwork using geometry. Art such as this can foster understanding and appreciation of fundamental concepts across fields.

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Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson, and Joan Case

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

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Julie M. Amador, David Glassmeyer, and Aaron Brakoniecki

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.

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Patricia F. Campbell, Masako Nishio, Toni M. Smith, Lawrence M. Clark, Darcy L. Conant, Amber H. Rust, Jill Neumayer DePiper, Toya Jones Frank, Matthew J. Griffin, and Youyoung Choi

This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for teacher preparation and professional development programs.

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Lauren J. Rapacki and Dionne I. Cross Francis

Share a teacher's ultimately empowering experience of transitioning into an ill-defined, unanticipated leadership position.