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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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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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Lauren J. Rapacki and Dionne I. Cross Francis

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

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Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

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Andrew Tyminski, Corey Drake, and Tonia Land

Despite the prevalence of mathematics curriculum materials in elementary classrooms, most current mathematics methods texts provide little or no support for preservice teachers (PSTs) learning to use curriculum materials. To meet this need, we have designed and studied several modules intended to provide PSTs with opportunities to learn about and from the use of curriculum materials. This article describes our research related to 1 of these modules–Addition Starter Sentences. Our results examine the nature of PSTs' developing content knowledge and pedagogical content knowledge, evidenced through their interactions with and reflections on Standards-based curriculum materials. We conclude with implications for mathematics teacher education research and practice.