The Isis problem as a probe of flexible expertise and views of proof

Brian Greer, Dirk De Bock () and Wim Van Dooren
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Brian Greer: Portland State University
Dirk De Bock: Hogeschool-Universiteit Brussel (HUB), Belgium
Wim Van Dooren: Katholieke Universiteit Leuven, Belgium

No 2008/51, Working Papers from Hogeschool-Universiteit Brussel, Faculteit Economie en Management

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.” 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 provides an instrument for probing students’ ideas about proof, and the interplay between routine and adaptive expertise. A group of 39 Flemish pre-service mathematics teachers was confronted with the Isis problem. More specifically, we first asked them to solve the problem and to look for more than one solution. Second, we invited them to study five given contrasting proofs and to rank these proofs from best to worst. The results highlight a preference of many students for algebraic proofs as well as their rejection of experimentation. The potential of the problem as a teaching tool is outlined.

Keywords: Isis problem; Proof; Proving; Routine expertise; Adaptive expertise; Mathematical representations; Dimensionality (search for similar items in EconPapers)
Pages: 34 pages
Date: 2008-10
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