Problem solving in the mathematics curriculum: From domain‐general strategies to domain‐specific tactics

Abstract

AbstractProblem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non‐routine tasks and propose the explicit teaching of domain‐specific problem‐solving tactics that are applicable over narrow ranges of mathematical content. This is in contrast to the widespread practice of attempting to teach domain‐general strategies that are supposedly applicable across diverse content areas. The proposed approach here systematically introduces students to a well‐defined set of high‐leverage content‐specific tactics, presented in a purposeful order and taught explicitly through the use of carefully chosen problems which those tactics dramatically unlock. I argue that this sequenced approach to teaching problem‐solving addresses concerns widely reported about the apparent unteachability of domain‐general problem‐solving strategies and has the potential to enable all students to benefit from a powerful problem‐solving mathematics curriculum.