Customer Reviews

The Thirteenth Yearbook: The Nature of Proof (NCTM Yearbooks)

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This short book discusses the purposes of proof in high school geometry, and concludes that one of the major roles is not being fulfilled: students do not learn how to apply logical reasoning skills in life outside the geometry classroom.

The author then presents a curriculum designed to emphasize the transfer of logical reasoning skills to everyday real-world problems. In addition to having *students* write definitions of terms like "triangle", and recognize the need for undefined terms like "point" and "line", he asks them to define terms like "restaurant" for the purpose of analyzing a state law on sales taxes to be collected.

While the amount of geometry covered in such a curriculum is undeniably less than what you'd see in a standard text, it is abundantly clear from the discussion that students will remember what they've learned for far longer than they would in a typical geometry class.

Left unanswered are questions about what expertise would be required of a teacher who tries to manage this type of curriculum.

It's also interesting to compare this curriculum reform with modern trends; this book, which reads quite a bit like it comes from the recent constructivist movement, was first published in 1938!