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- Vol 4 RE: Chapter 10
mathematical problem solvingproblem-solving heuristicsmetacognitive controlstrategic flexibilitymathematical beliefssolution monitoringmathematical reasoningsense-makingBook Evidence summaryAt a glance
Schoenfeld investigates why knowing mathematical facts and procedures does not guarantee success on unfamiliar problems. Detailed analyses of learners’ work show that performance depends on four interacting components: resources such as concepts and procedures; heuristics for exploring, representing, and transforming problems; control or metacognitive decisions about planning, monitoring, and allocating effort; and beliefs about mathematics and oneself.
Key ideas
Students may possess relevant knowledge yet pursue an unproductive path because they fail to assess progress or abandon it. The book combines empirical problem-solving sessions with instruction designed to make strategic decisions visible. Teachers model questions, compare solution paths, discuss errors, and help students justify why an approach is promising rather than simply name a heuristic. Schoenfeld treats mathematical competence as sense-making within a community, not the memorization of tricks.
Why it matters
Productive instruction therefore develops knowledge, strategic flexibility, monitoring, and beliefs that mathematics is intelligible and that solutions should be explained and checked.
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Edition abbreviations
- TE
- Teacher Edition
- PE
- Practice Edition
- RE
- Research Edition
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