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Merav Weingarden and Einat Heyd-Metzuyanim

One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion, depicting the realizations of the mathematical object manifested during the discussion and the narratives that articulate the links between these realizations. We applied the tool to 34 classroom discussions about a growing-pattern algebraic task and, through cluster analysis, found three types of whole-class discussion. Associations with classroom-level variables (track, but not grade level or teacher seniority) were also found. Implications with respect to applications and usefulness of the tool are discussed.

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Gwyneth Hughes, Michele B. Carney, Joe Champion, and Lindsey Yundt

Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students’ opportunities to struggle, have been consistently linked to improving students’ mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of professional development (PD) offerings. We describe three examples of how the framework is used to support teacher learning and classroom instructional practice: a state-mandated course, lesson studies, and a large-scale teacher–researcher alliance. Initial findings suggest that consistently emphasizing this framework provides both content and structural guidance during PD development and gives coherence and focus to teachers’ PD experiences.

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David B. Custer and Ksenija Simic-Muller

We reflect on recent presentations at the NCTM annual conference and articles in MTLT that address statistics, data modeling, and data science. We observe that such presentations and articles are increasingly common, and encourage readers to use them in their teaching and write about their own adventures with data.

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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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Kym Fry and Lyn D. English

Grade 4 students engage in problem solving through inquiry in an agricultural science context.

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Ricardo Martinez and Ji Yeong I

Ear to the Ground features voices from serveral corners of the mathematics education world.

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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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Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, Jared Bukarau, and Introduction by: Wendy Cleaves

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.

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Kathryn Early, K. Elizabeth Hammonds, Brea Ratliff, Mariya Rosenhammer, and W. Gary Martin

A high-leverage strategy first discussed more than 50 years ago, wait time has many benefits for both teachers and students yet is not used to its full potential. See how it can enhance your students’ mathematical discourse.

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Alessandra King

This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.