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

Abstract

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.

Junior High School Mathematics Teachers’ Perceived Knowledge of Problem-Solving and Practices of Teaching Mathematics Through Problem-Solving in the Tamale Metropolis

“…According to Foster (2023), teaching through problem-solving will allow students to construct their mathematical concepts and take responsibility for their own learning.…”

Challenges in applying principles from cognitive science to the design of a school mathematics curriculum

“…For worked examples, where possible, we employ the signalling, spatial contiguity and multimedia principles to ensure that steps are appropriately supported with diagrams and colour. To address the expertise-reversal effect, we reduce the number of worked examples as a unit progresses and expertise increases, and, correspondingly, we increase the prevalence of more open, exploratory and problem-solving tasks to foster deeper thinking (Foster, 2023a). We also aim to present worked examples so that they generate questions for discussion that probe and develop students' understanding, rather than serving merely as a template.…”

“…Two of us are academics with previous experience as school teachers (Foster, Francome); one currently teaches both in university and school (Shore); one is a postdoctoral researcher whose recent PhD studentship involved collaboration with a global educational publishing company (Woollacott); and two are mathematics education doctoral students (Morley, Peters). In this paper, we document our attempts to navigate challenges that emerged in seeking to apply cognitive science principles to the design of a free, fully‐resourced, coherent and research‐informed school mathematics curriculum (Foster, 2023a; Foster et al., 2021). We recognise the importance of curriculum development sites (Priestley & Philippou, 2018) and have partnered with schools and teachers to ensure the practical relevance of the eventual result.…”