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Carolyn James, Ana Casas, and Douglas Grant

Encouraging students to justify earlier as they attempt to solve an open-ended task can lead to greater understanding and engagement.

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Stephanie M. Butman

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

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Ryota Matsuura and Yu Yan Xu

This activity involves finding the distance between two points in a coordinate plane and emphasizes reasoning from repeated calculations, which is one of the mathematical practices specified by the Common Core State Standards for Mathematics.

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Hyewon Chang and Barbara J. Reys

Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.

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Anne Roche and Doug M. Clarke

Students display a wide variety of creative mathematical thinking and misconceptions when they complete a classroom task that focuses on proportional reasoning.

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Quick Reads: Sure, We Can Make Smaller Pieces

a good idea in a small package

Michael J. Gilbert

The topic of limit is explored by examining a circle's successively smaller sectors.

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Sherri Ann Cianca

Communicating reasoning and constructing models fold nicely into a geometry activity involving the building of nesting boxes.

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Tutita M. Casa

This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.

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Cory A. Bennett

Address the needs of diverse learners with a class structure that is designed around a crime scene theme and based on student choice and perceptions of the math being studied.

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Katie L. Anderson

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.