20 questions about mathematical reasoning

Twenty Questions about Mathematical Reasoning
Lynn Arthur Steen, St. Olaf College

A good read: The concluding chapter from NCTM's 1999 Yearbook, which is devoted to mathematical reasoning: "Developing Mathematical Reasoning in Grades K-12" by Lynn Arthur Steen, St. Olaf College. Lee Stiff, Editor. Reston, VA: National Council of Teachers of Mathematics, 1999, pp. 270-285.

We begin with two warm-up questions. First, why is mathematics an integral part of the K-12 curriculum? The answers are self-evident and commonplace: to teach basic skills; to help children learn to think logically; to prepare students for productive life and work; and to develop quantitatively literate citizens.

Second, and more problematic: How does mathematical reasoning advance these goals? This is not at all self-evident, since it depends greatly on the interpretation of "mathematical reasoning." Sometimes this phrase denotes the distinctively mathematical methodology of axiomatic reasoning, logical deduction, and formal inference. Other times it signals a much broader quantitative and geometric craft that blends analysis and intuition with reasoning and inference, both rigorous and suggestive. This ambiguity confounds any analysis and leaves room for many questions.\

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