Studying worked examples improves novices' algebra performance on problems with the same structure as the examples¶

Claim · All claims
Evidence · 2 studies · 2 causal r? · q2–q3
Currency · newest study 2016 · 1 of 2 entries checked against their sources (automated) · not reviewed by a person

In mathematics learning, worked examples can improve performance by making solution structure visible before learners attempt similar problems on their own.

Subclaims¶

q3 i? For novices, studying worked examples instead of solving conventional algebra problems led to faster, more accurate solutions on later problems of the same structure, though not on problems of a different structure. → Sweller & Cooper 1985

q2 i? Variants of worked examples can improve mathematics understanding when they direct attention to structure and error. → Barbieri & Booth 2016

Evidence¶

Primary evidence link: https://doi.org/10.1037/0022-0663.77.1.59

Sweller & Cooper 1985¶

Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59-89. https://doi.org/10.1207/s1532690xci0201_3

q3 · peer-reviewed experiments (five) · i? · the abstract prints no effect size; the full text may · n=five experiments with Year 9, Year 11 and university students · causal · r?

In five experiments on algebra manipulation problems, worked examples took considerably less time to process than conventional problems, and students who studied them then solved similar problems faster and with fewer errors. The authors stress that both gains were specific to problems identical in structure to the examples: novices had not yet abstracted general algebra rules, which the authors argue takes considerable practice across a wider range of problems.

Barbieri & Booth 2016¶

Barbieri, C., & Booth, J. L. (2016). Support for struggling students in algebra: Contributions of incorrect worked examples. Learning and Individual Differences, 48, 36-44. https://doi.org/10.1016/j.lindif.2016.04.001

q2 · peer-reviewed experiment · i? · no source text available to check; the entry prints no effect size · n=classroom sample · causal · r?

This algebra study found that worked-example variants, including incorrect worked examples, supported struggling students by making mathematical structure and common errors more visible.

Discussion¶

The current page supports a moderate claim about mathematics performance, not a definitive universal estimate across all grade bands and formats. Stronger confidence would require a dedicated meta-analysis page or broader synthesis.

Related Claims¶

• In one experiment with 256 undergraduates, computer-based lesson versions that included practice produced significantly higher posttest scores than versions without practice — the general claim this finding bears on, with the studies behind it
• Worked examples reduce unnecessary search for novices.
• Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer
• Erroneous examples improve conceptual understanding by forcing comparison with correct models.
• Lower-prior-knowledge learners scored higher on an algebra posttest after full-worked than completion-worked examples, while higher-prior-knowledge learners' non-significant advantage ran the other way — related
• No significant interaction between prior knowledge and task difficulty was observed in a worked-example algebra study — related
• Studying solved problems improves algebra achievement compared to solving practice problems alone, though the evidence base is rated minimal and one study found negative effects — a narrower finding that bears on this claim
• Variability of practice interacts with problem format: high variability aids learning from worked examples but harms learning from conventional problems — related
• Use of worked examples in the Cognitive Tutor Algebra course was discouraged by collaborating instructors — related
• Adaptive fading of worked examples based on current skill level produced better learning outcomes than fixed fading or tutored problem solving — related
• Split-attention worked examples lose their advantage over conventional practice, while integrated formats restore it — related
• Example-first conditions outperformed problem-first conditions on an immediate circuit test — related
• Example–problem pairs and examples-only are more effective than problem–example pairs for novices, with no significant difference between the first two — a narrower finding that bears on this claim
• Worked examples result in better performance than conventional problem solving with no guidance, per prior work cited in the thesis — a broader claim this one bears on