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2 references
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- Vol 4 RE: Chapters 7, 14
- Vol 7 PE: App D
worked examplescognitive loadfading guidanceproblem solvingschema constructionbackward fadingself-explanationprior knowledgeJournal article Evidence summaryAt a glance
Renkl and Atkinson address how instruction should move from studying worked examples to independent problem solving. Early in skill acquisition, conventional problem solving can overload working memory because novices must search for solution steps while also trying to learn underlying principles.
Key ideas
Complete worked examples reduce unproductive search and support schema construction. As knowledge develops, however, repeatedly studying complete solutions becomes redundant and may impede active learning; learners need increasing responsibility for producing steps. The authors propose fading: begin with fully worked solutions, then successively omit steps that students must complete until they solve entire problems. Backward fading can align with the natural subgoal structure of some domains, while prompts for self-explanation help learners process principles rather than imitate procedures.
Why it matters
The transition should be adapted to prior knowledge because support that helps novices can become extraneous for more advanced learners. For educators, the implication is a planned continuum, not an abrupt switch between explanation and practice: model the process, remove support gradually, require explanation, monitor success and mental effort, and adjust the pace of fading.
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- Vol 1 RE: Chapters 8, 12, App B
- Vol 1 TE: App A
- Vol 2 RE: Chapter 8, App D
- Vol 5 RE: Chapter 7
spaced practiceinterleaved practicemathematics problem solvingstrategy selectionproblem discriminationdelayed performancepractice schedulingJournal article Evidence summaryAt a glance
Rohrer and Taylor separate two features of the “shuffled” mathematics practice found in some textbooks: spacing practice across sessions and interleaving different problem types. In the first experiment, college students learned one problem type and practised either in a single massed session or across multiple sessions.
Key ideas
A week later, spaced practice produced much better performance. In the second, students learned several types and practised problems either blocked by type or randomly mixed. On a delayed test, mixed practice produced a large advantage. Blocking can look effective during practice because the preceding examples reveal which procedure to use; interleaving makes practice harder but requires learners to discriminate among problem structures and choose an appropriate strategy. The studies used limited mathematical tasks and student populations, so effect sizes should not be assumed for every curriculum.
Why it matters
For educators, practice sets should revisit earlier material and mix confusable problem types after initial instruction, while preserving enough support for success. Immediate practice fluency should not be mistaken for long-term retention or independent method selection.
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Edition abbreviations
- TE
- Teacher Edition
- PE
- Practice Edition
- RE
- Research Edition
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