The Isis problem as a probe for understanding students' adaptive expertise and ideas about proof

Document Type

Presentation Abstract

Presentation Date

4-13-2009

Abstract

The Isis problem, which has a link with the Isis cult of ancient Egypt, asks: "Find which rectangles with sides of integral length (in some unit) have area and perimeter (numerically) equal, and prove the result." (You are invited to tackle this (simple) problem using as many different forms of argument as you can find). Since the solution requires minimal technical mathematics, the problem is accessible to a wide range of students. Further, it is notable for the variety of proofs (empirically grounded, algebraic, geometrical) using different forms of argument, and their associated representations, and it thus provides an instrument for probing students’ ideas about proof, and the interplay between routine and adaptive expertise. Results from small-scale studies of students in Belgium and the U.S. will be reported.

Additional Details

Monday, 13 April 2009
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

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