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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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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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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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Barbara Zorin, Patricia D. Hunsader and Denisse R. Thompson

Learn how to modify classroom evaluation items to avoid potential difficulties that limit a teacher's insight into students' mathematical understanding.

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John K. Lannin and Kathryn B. Chval

Use these specific strategies to confront assumptions about teaching and learning mathematics.

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Rochelle Goldberg Kaplan and Sandra Alon

Professional development equips practitioners with skills to enhance student learning.

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Jennifer Noll and J. Michael Shaughnessy

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.

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Jenni K. McCool and Carol Holland

Collaborating with a researcher, this teacher uses two fifth graders' assessment results to inform her whole-class instruction and gain insight into all her students' conceptual knowledge.

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Aimee J. Ellington and Joy W. Whitenack

A mathematics specialist has great success using a pattern-block configuration to help a small group of fifth graders understand that fractional parts of a whole unit must be equal in size. That's just the way the funky cookie crumbles.