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Deanna Pecaski McLennan

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Amanda Milewski and Daniel Frohardt

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

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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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Agida G. Manizade and Marguerite M. Mason

When calculating the area of a trapezoid, students use a range of problem-solving strategies and measurement concepts.

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Amy F. Hillen and Tad Watanabe

Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.

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Lisa A. Brooks and Juli K. Dixon

A second-grade teacher challenges the raise-your-hand-to-speak tradition and enables a classroom community of student-driven conversations that share both mathematical understandings and misunderstandings.

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Wendy P. Ruchti and Cory A. Bennett

Solutions coupled with drawings can illustrate students' understandings or misunderstandings, particularly in the area of proportional reasoning.

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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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Jeffrey M. Choppin, Carolyn B. Clancy, and Scott J. Koch

Allowing students to reason and communicate about integer operations, or any idea, before these ideas are formalized can be an important tool for fostering deep understanding.

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Kristen N. Bieda and Jerilynn Lepak

Research explores how to help students build from, instead of building with, examples when justifying mathematical ideas.