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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.\

Read More:
http://www.stolaf.edu/people/steen/Papers/99reason.html