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2 references
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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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- Vol 4 RE: Chapter 10
disciplinary literacycontent-area literacysourcing and corroborationscientific evidencemathematical reasoningtext structuresapprenticeship modelsJournal article Evidence summaryAt a glance
Shanahan and Shanahan argue that adolescent literacy instruction should move beyond generic comprehension strategies toward the specialized ways disciplines create and evaluate knowledge. Their research teams paired literacy specialists with experts and teachers in chemistry, history, and mathematics.
Key ideas
Observations and think-aloud work showed meaningful differences: historians attended to authorship, sourcing, context, and corroboration; chemists moved among prose, equations, diagrams, and experimental evidence; mathematicians read compressed symbolic text recursively and tested definitions and proofs. These practices reflect each field’s purposes, standards of evidence, language, and text structures. The authors propose a developmental pyramid: basic literacy supports broad intermediate strategies, which in turn support increasingly discipline-specific practices. Content teachers therefore should not simply become generic reading teachers.
Why it matters
They can apprentice students into how experts in their field interrogate texts, represent claims, resolve ambiguity, and justify conclusions, while literacy educators help make those normally tacit processes teachable.
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Edition abbreviations
- TE
- Teacher Edition
- PE
- Practice Edition
- RE
- Research Edition
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