Reassessing Pólya’s Problem-Solving Model in Contemporary Mathematics Education: A Critical Synthesis and a Proposed Recursive Framework

Abstract

George Pólya’s four-phase model of problem solving, which comprises understanding the problem, devising a plan, carrying out the plan, and looking back, remains one of the most widely cited heuristics in mathematics education. This conceptual paper examines the extent to which the model, as it is commonly enacted in secondary school curricula and classrooms, accounts for problem solving as contemporary research describes it. The paper distinguishes Pólya’s original heuristic programme from the reductive checklist into which it has frequently been transformed, and it directs its critique principally at the latter. Adopting a theory synthesis design, the paper examines six dimensions: the recursive rather than linear character of problem solving, the continuous role of metacognitive regulation, the diversity of learners’ conceptual, linguistic, and affective resources, the mediating influence of digital technology, the socially mediated nature of classroom problem solving, and the place of creativity and insight. The paper also engages counterarguments from cognitive load theory, which support explicit and structured guidance for novices. The synthesis concludes that Pólya’s model is not a historical artefact; rather, it offers a sound foundation that requires reconceptualisation. The paper therefore proposes a recursive, regulated, and mediated framework in which Pólya’s phases form an iterative core, metacognitive regulation operates across all phases, and social, digital, linguistic, and affective conditions shape the process. The paper closes with implications for classroom practice, teacher education, curriculum and assessment design, and future empirical research.