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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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Deann Huinker, Steven Leinwand and Daniel Brahier

The knowledge of fractions and decimals that children develop in the elementary grades provides an essential foundation for the study of algebra and more advanced mathematics, but most teachers and students consider the topic challenging. Share your approaches to facilitating children's understanding of fractions and decimals. What classroom activities and ideas do you use to help children make sense of fractions and decimals as numbers, benchmarks, measures, quotients, or as operators? The TCM Editorial Panel invites you to share your ideas on developing K–grade 6 students' number sense for fractions and decimals. We are especially interested in manuscripts that describe ideas that have been informed by research and implementation in classrooms.

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Jo Boaler

This department publishes brief news articles, announcements and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

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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.

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Penny Cataldo

In addition to differentiating and developing curriculum, this teacher's transition to coaching in an early childhood setting involves a complex blend of mentoring teachers, teaching students, and discovering resources.

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Kimberly M. Lilienthal

Collections of short activities, Math by the Month articles aim for an inquiry or problem-solving orientation focused on a unifying theme and include four activities each for grade levels K–2, 3–4, and 5–6. In anticipation of October's Fire Prevention Week, September's problems involve firefighters and real-life math applications.

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Renee Parker and M. Lynn Breyfogle

This student-friendly rubric helped improve third graders' competencies when explaining solution strategies in writing.