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Victor Mateas

Teachers can benefit from productive and manageable suggestions to align instruction to the intention of the Common Core's Standards for Mathematical Practice.

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Angela T. Barlow, Natasha E. Gerstenschlager, and Shannon E. Harmon

Three instructional situations demonstrate the value of using an “unknown” student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others.

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Stephanie A. Casey and Jonathan D. Bostic

Implementing the practice of looking for and making use of structure differs when addressing statistics content standards compared with mathematics content standards. Read about suggestions for tuning out noise in data to teach SMP 7 in statistics.

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Margaret Rathouz, Nesrin Cengiz, Angela Krebs, and Rheta N. Rubenstein

Tasks that have been developed to build a foundation for ratio meanings and language not only provide valuable information about student thinking but also support proportional reasoning.

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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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Katherine E. Lewis

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack. Detailed diagnostic analyses of the sessions revealed that the students understood mathematical representations in atypical ways and that this directly contributed to the persistent difficulties they experienced. Implications for screening and remediation approaches are discussed.

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Steve Leinwand, DeAnn Huinker, and Daniel Brahier

This article provides an introduction to the six guiding principles for school mathematics and eight core mathematics teaching practices that appear in the new NCTM document, Principles to Actions: Ensuring Mathematical Success for All.

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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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Laurie O. Cavey and Margaret T. Kinzel

An instructional sequence used in a course for prospective teachers directly relates to Common Core State Standards for grades 3–6.

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Juli K. Dixon and Jennifer M. Tobias

Anticipate and address errors that arise when fractions are placed in context and illustrated with models.