Problem solving in the mathematics curriculum: from domain-general strategies to domain-specific tactics

Problem 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.