On Similarities and Differences Between Proving and Problem Solving

Abstract

A link between proving and problem solving has been established in the literature [5,21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribe pen data from a previous study [13]. I focus on two participants' proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the mathematician and that of the graduate student. This study suggests the feasibility of an expanded framework for the proving process that can encompass both the similarities and the differences found.Keywords: undergraduate mathematics education; problem-solving; proving; proof construction Proof and proving are central to advanced undergraduate and graduate mathematics courses. Yet there is often little systematic discussion in these courses on how proofs are constructed. Since proving and problem solving overlap [5,21], one might look at the problem-solving literature in order to describe some aspects of the proof construction process. Here I use the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2], coupled with a data collection technique [13] specifically aimed at collecting the real-time actions that a prover takes, to examine the proving actions of a topologist, Dr. G, and a mathematics graduate student, L. I discuss the adequacies and limitations of this framework for describing the observed proof

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