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Mathematical Explorations: A New Twist on Collaborative Learning

classroom-ready activities

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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Improving Student Reasoning in Geometry

Bobson Wong and Larisa Bukalov

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

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Counterexamples as Starting Points for Reasoning and Sense Making

David A. Yopp

Asked to “fix” a false conjecture, students combine their reasoning and observations about absolute value inequalities, signed numbers, and distance to write true mathematical statements.

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Informing Practice: Examples as Tools for Constructing Justifications

research matters for teachers

Kristen N. Bieda and Jerilynn Lepak

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

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Proofs without Words: A Visual Application of Reasoning and Proof

Carol J. Bell

Reasoning and Proof is one of the process standards set forth in NCTM's principles and standards for school mathematics (2000).