A Meta-Analysis of the Worked Examples Effect on Mathematics Performance
Barbieri, C. A., Miller-Cotto, D., Clerjuste, S. N., & Chawla, K. · 2023
grade Cmeta-analysisindependentunreplicatednumbers spot-checked
Sample
55 studies / 181 effect sizes (53/55 randomized)
Population
Elementary to postsecondary math (algebra/geometry heavy); ~22 teacher-run studies in real classrooms.
Design
Best current worked-example meta. More classroom-embedded than retrieval/spacing lit, but outcomes are researcher-designed aligned accuracy, mostly immediate. Severe heterogeneity (I2=94%).
Key findings
Best estimate of the math worked-example effect: g~0.48 (0.44 bias-adjusted), more classroom-embedded than retrieval/spacing. Outcomes are researcher-designed aligned accuracy (standardized equivalent likely ~half), I2=94%. Correct > incorrect examples; strikingly, self-explanation prompts NEGATIVELY moderated in aggregate (opposite to lab optimism).
Genetic confound
Domain problem-solving; no g. Prior-knowledge ATI real but direction inconsistent across studies.
Replication notes
g=0.48 and negative self-explanation direction verified; standardized/delayed equivalent likely ~half.
DOI / URL
10.1007/s10648-023-09745-1
Effects
| Outcome | Metric | Value | Measure | Timing | Vs | Horizon | Class |
|---|---|---|---|---|---|---|---|
| Overall worked examples vs problem solving (math) | g | 0.48 [0.36,0.60] | researcher-designed | mostly immediate; classroom+lab+tutor | active-alternative | end-of-treatment | domain-skill |
| Publication-bias adjusted | g | 0.44 [0.32,0.56] (effect survives) | researcher-designed | immediate | active-alternative | end-of-treatment | domain-skill |
| Correct vs incorrect examples | beta | +0.26 (correct examples more effective) | researcher-designed | immediate | active-alternative | end-of-treatment | domain-skill |
| Adding self-explanation prompts | beta | -0.24 (prompts REDUCED benefit — opposite to lab) | researcher-designed | immediate | active-alternative | end-of-treatment | domain-skill |
Cited by
- Worked examples (studying solutions vs solving problems)moderate supportconf: mediumgc: low