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Designing for Sensemaking of Research: The Mathematics District Leader Research Group

F. Paul Wonsavage

In this article, I share a design-based research intervention meant to help mathematics district leaders build their capacity to engage with research quality. I present my design (i.e., principles, key features, and intervention structure) and elaborate on how the features of the design allowed for mathematics district leaders’ sensemaking of educational research quality, especially regarding the process for collecting data and research implications. I conclude with recommendations for mathematics teacher educators on how they might adapt my design to their contexts.

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Using a Practical Measure to Support Inquiry Into Professional Development Facilitation

Hannah Nieman, Kara Jackson, Michael Jarry-Shore, Hilda Borko, Elham Kazemi, Starlie Chinen, Anita Lenges, Zuhal Yilmaz, and Cara Haines

Despite the complexity of facilitating professional development (PD) and growing attention to supporting facilitators, few tools exist for facilitators to engage in ongoing inquiry into their practice. In this article, we offer a practical measure, the Collaborative Professional Development Survey (CPDS), designed to provide facilitators with information about teachers’ perceptions of aspects of the PD learning environment that research indicates matter for teachers’ opportunities to learn. We illustrate how facilitators used the CPDS to support their collective inquiry into facilitation. We also illustrate the social processes that appeared to enable facilitators’ productive use of the CPDS, including a routine to analyze the resulting data, and the orientations that underpinned their analysis. We discuss implications for facilitators’ use of the CPDS.

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Dilemmas and Design Principles in Planning for Justice-Oriented Community-Based Mathematical Modeling Lessons

Jennifer M. Suh, Holly Tate, Maryanne Rossbach, Samara Green, Kathy Matson, Julia Aguirre, Padhu Seshaiyer, and Sam Steen

This article details the development of design principles to support teachers in planning for a Community-Based Mathematical Modeling task with a focus on social justice in the elementary grades. By reflecting on the dilemmas we encountered in the design and enactment of the tasks, we developed five design principles that allowed us to address issues of social justice as well as attend to powerful mathematical ideas to bring awareness and take action around a local problem. Through our article, we hope to share with mathematics teacher educators design principles to help plan for tasks with pre- and in-service teachers that prioritize connecting mathematics to social issues and empower both teachers and students to take action to make a positive impact in the community.

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When Only White Students Talk: EQUIP-ing Prospective Teachers to Notice Inequitable Participation

Sunghwan Byun, Niral Shah, and Daniel Reinholz

We introduce a teacher learning practice called EQUIP-ing, which aims to foster sociopolitical noticing by leveraging EQUIP, an equity-oriented classroom observation tool. We detail our iterations of EQUIP-ing to a field-based Number Talk experience in a secondary mathematics methods course with 25 White prospective teachers (PTs). We offer empirical accounts of how EQUIP-ing empowered PTs to connect their teaching practices with racialized and gendered patterns of student participation; as a result, PTs began to reconsider taken-for-granted practices. However, we also found that PTs demonstrated potentially detrimental ways of attributing marginalizing patterns to minoritized students without actionable plans to redress the inequity. We conclude by inviting mathematics teacher educators to apply EQUIP-ing while emphasizing purposeful support for asset-based noticing.

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Formative Assessment in Secondary Mathematics: Moving Theory to Recommendations for Evidence-Based Practice

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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Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board

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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Centering Professional Development Around the Instructional Quality Assessment Rubrics

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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Designing Rehearsals for Secondary Mathematics Teachers to Refine Practice

Jared Webb and P. Holt Wilson


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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Developing Preservice Teachers’ Understanding of Area Through a Units Intervention

Megan H. Wickstrom

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

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Developing Skills for Exploring Children’s Thinking From Extensive One-on-One Work With Students

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.