A Meta-Analysis of the Efficacy of Teaching Mathematics with Concrete Manipulatives
Carbonneau, K. J., Marley, S. C., & Selig, J. P. · 2013
grade Cmeta-analysisindependentreplicated
Sample
55 studies / N=7,237, K-college
Population
Typically developing students, K through college.
Design
Manipulatives vs abstract-symbols-only. Outcome classes coded separately; moderators: guidance, perceptual richness, age, topic. Exact pooled d paywalled (~0.37 commonly cited, unverified).
Key findings
Manipulatives help — conditionally: with high instructional guidance, perceptually bland objects, ages ~7-11, and especially fractions. The effect is a guided-representation effect, not a 'hands-on learning' effect; rich/toy-like objects hurt transfer.
Genetic confound
Mostly experimental comparisons.
Replication notes
Categorical pattern (guidance matters; bland > rich distally) consistent with Kaminski/Sloutsky and Peltier 2020.
DOI / URL
10.1037/a0031084
Effects
| Outcome | Metric | Value | Measure | Timing | Vs | Horizon | Class |
|---|---|---|---|---|---|---|---|
| Retention of taught content | d | small-to-moderate overall (exact value unverified) | mixed | mostly immediate | business-as-usual | end-of-treatment | domain-skill |
| Problem solving / transfer | d | small | mixed | end of treatment | business-as-usual | end-of-treatment | near-transfer |
| Moderator: instructional guidance | contrast | HIGH guidance > low for retention/problem-solving (transfer direction unresolved — one summary reports a low-guidance transfer advantage) | mixed | end of treatment | active-alternative | end-of-treatment | domain-skill |
| Moderator: perceptual richness | contrast | BLAND objects beat rich ones on distal outcomes (rich manipulatives distract) | mixed | end of treatment | active-alternative | end-of-treatment | near-transfer |
| Moderator: age/topic | contrast | ages 7-11 > 12+; fractions strongest topic | mixed | end of treatment | business-as-usual | end-of-treatment | domain-skill |
Cited by
- Manipulatives and concrete-representational-abstract (CRA) sequencesmoderate supportconf: mediumgc: low