Mathematics education literature uses the terms concrete and abstract with multiple distinct meanings¶

Claim · All claims
Evidence · 1 study · qualitative r3 · q2
Currency · newest study 2025 · checked against its sources 2026-10-20 (automated, 1 of 1 entry) · not reviewed by a person

Subclaims¶

q2 i? Systematic coding of a corpus of mathematics education papers identified multiple distinct meanings of concrete and abstract, organized into eleven axes. → Julia Chatain 2025

Evidence¶

Julia Chatain 2025¶

Julia Chatain, Charlotte Müller, Keny Chatain, Leon Calabrese, Manu Kapur. (2025). Concreteness and Abstraction in Mathematics Education: A Taxonomy of the Semantic Landscape. Educational Psychology Review. https://doi.org/10.1007/s10648-025-10073-9

q2 · i? · qualitative · r3

Qualitative corpus study: the authors searched the ERIC database for peer-reviewed journal articles on concreteness and abstraction in mathematics education and retrieved "the content of 368 papers" as their final sample. The authors collected 4309 contexts from that sample, which four researchers double-coded; a corpus added after the first revision round gave a further 592 contexts per reviewer, coded after the taxonomy was built.

"From this sample, we could retrieve the content of 368 papers through open or institutional access, which constitutes our final sample"

Discussion¶

Related Claims¶

• A single representation can be abstract along one dimension and concrete along another, and concrete for one learner but abstract for another — a narrower finding that bears on this claim
• A systematic review argues that concrete materials aid mathematics and science learning when they are explicitly and gradually connected to the abstract symbols they represent — related
• Concreteness fading helps learners interpret ambiguous or opaque abstract symbols in terms of well-understood concrete objects — related
• The review's coding framework showed very good inter-coder agreement (κ = 0.89, p < 0.001) on a random sample of six papers — a narrower finding that bears on this claim
• Concreteness fading guides learners to strip away extraneous concrete properties and distill generic, generalizable properties — related
• Concreteness, imagery, and verbal associative processes play major roles across multiple educational domains — related
• Concreteness fading enables learners to build a store of memorable images usable when abstract symbols lose meaning — related
• Disagreements about concreteness and abstraction in mathematics education may be verbal disputes rooted in word meaning — a broader claim this one bears on
• Concreteness fading may not be as broadly generalizable across mathematics and natural science domains as has been suggested — related