Reviews That Teach

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  • 1 Michigan State University

Some years ago, Gila Hanna offered the very insightful and useful distinction between mathematical proofs that prove and those that also explain (Hanna, 1989). Proofs that explain not only state the deductive logic that justifies their mathematical claims, they lay bare the mechanisms and structures that underlie that logic, making content and logic more properly align. In so doing, they more effectively teach mathematics than do proofs that only prove.

Contributor Notes

John P. Smith III, 513H Erickson Hall, Michigan State University, East Lansing, MI 48824;

(Corresponding author is Smith
Journal for Research in Mathematics Education


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