Provide Manipulatives (Processing Speed)¶

Strategy · All strategies
Evidence · 3 claims (3 for) · 6 studies (2 causal, 2 review, 2 associational), q2–q3 · 1 of 6 report an effect size · 1 claim rests on one study

Description¶

Providing manipulatives means giving learners physical objects (counters, base-ten blocks, fraction tiles, algebra tiles) or their virtual equivalents that they can handle and rearrange to represent abstract ideas. For learners with slower processing speed, manipulatives externalize intermediate states of a problem, so working memory is not consumed by holding and transforming mental representations while also executing procedures.

Design Implications¶

Manipulatives reduce the representational burden of abstract content by grounding it in perceivable structure, which is especially valuable when processing speed limits how much a learner can hold and manipulate mentally at once Chunking reduces working memory load. [+S]. Their effectiveness depends on the link between the object and the concept: manipulatives help when learners are explicitly guided to connect the concrete representation to the abstract notation, and can hinder learning when the objects become the focus rather than the concept [~S]. Concrete materials are most powerful when they are treated as models of something, not as the learning goal themselves.

Context¶

Requirements¶

• Manipulatives that map transparently onto the target concept's structure (e.g., base-ten blocks onto place value)
• Instructor guidance that explicitly connects actions on objects to symbols and language (Demonstration before independent use)
• A planned fade toward abstract representation, so learners do not remain dependent on the objects (Practice with and without materials)

Constraints¶

• Unguided "discovery" with manipulatives often produces play without learning; learners may manipulate objects correctly while missing the underlying concept [-M]
• Perceptually rich, feature-heavy manipulatives can distract from the mathematical or conceptual structure and impose extraneous load [~M]
• If learners must simultaneously learn the manipulative's conventions and the target concept, the material adds rather than reduces load — a particular problem for slow processors under time pressure [-M]
• Poor fit for content with no spatial or structural analog (e.g., much of prose comprehension or procedural fluency in language learning)

Implementation Variability¶

• Physical vs. virtual manipulatives (e.g., Brainingcamp, Didax virtual manipulatives, Polypad); virtual versions add color-coding and undo, physical versions add tactile feedback
• Duration: brief concrete anchoring followed by rapid abstraction vs. extended use across a unit
• Teacher-modeled (Demonstration) vs. student-manipulated use

Target Learners¶

• Students with slow processing speed, who benefit from offloading intermediate representations onto physical objects [+W]
• Novices encountering an abstract concept for the first time, for whom concrete grounding supports schema formation [~S]
• Young learners whose symbolic understanding is still developing; spatial construction experience supports later achievement Spatial skills improve through block building. [+M]
• Less beneficial for learners with strong prior knowledge, for whom concrete materials can be redundant and slow [~M]

Target Learning Goals¶

• Conceptual understanding of abstract structures (place value, fractions, equations)
• Bridging concrete and symbolic representations
• Early spatial and quantitative reasoning Block play predicts math achievement. [+M]

Instructions¶

1. Select a manipulative whose structure maps onto the target concept; avoid decorative features that do not carry meaning.
2. Model its use with explicit narration connecting actions on objects to symbols and vocabulary (Demonstration).
3. Have learners solve problems with the materials (Practice), verbalizing the connection between what they do and what it represents.
4. Pair concrete and abstract representations side by side, then progressively fade the concrete support (Fading).
5. Assess understanding with the manipulatives removed, to verify the concept rather than the material handling has been learned.

Related Strategies¶

• Accommodating Processing Speed Challenges — manipulatives are one offloading accommodation within this broader set
• Activating Background Knowledge — concrete materials anchor new concepts in familiar experience
• Unplugged coding with printable motion and trigger blocks as a physical introduction to online coding

Examples¶

• CGI (Cognitively Guided Instruction) — elementary math instruction in which students model word problems with counters and drawings while teachers interpret their strategies.
• Khan Academy — virtual manipulative exercises (fraction strips, place-value blocks) embedded in practice sets.
• Numicon — structured tile system for number sense used widely in UK primary classrooms, including for learners with slower processing.

Key Sources¶

• Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. doi:10.1037/a0031084
• Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18(1), 37-54. doi:10.1016/s0193-3973(97)90013-7
• McNeil, N. M., & Jarvin, L. (2007). When theories don't add up: Disentangling the manipulatives debate. Theory Into Practice, 46(4), 309–316. doi:10.1080/00405840701593899
• Clements, D. H., & McMillen, S. (1996). Rethinking "concrete" manipulatives. Teaching Children Mathematics, 2(5), 270–279.