A single representation can be abstract along one dimension and concrete along another, and concrete for one learner but abstract for another¶
Claim · All claims
Evidence · 1 study · qualitativer3·q2
Currency · newest study 2025 · not yet checked against its sources · not reviewed by a person
Subclaims¶
Reading the evidence codes
q is the design tier, i the impact, n the sample, and the kind with its r
the rigour judged within that kind: what each code means.
This claim: no standardized effect is recorded in observations/ for it yet, so no benchmark reading is possible.
q2 i? The multidimensional taxonomy entails that representations can be simultaneously abstract on one axis and concrete on another, and that concreteness is relative to the learner. → 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
Analytical result of the taxonomy: the article illustrates with "a simulation of an excavator" that is virtual yet situated in real life, and notes a mathematician finds equations familiar while a high school student may find them unfamiliar. This follows from organizing meanings along multiple axes rather than a dichotomy.
"Crucially, one representation may now be abstract along one dimension and concrete along another. For example, a simulation of an excavator is virtual ( physicality → abstract) and situated in real life ( situatedness → concrete)."
Discussion¶
Related Claims¶
- Mathematics education literature uses the terms concrete and abstract with multiple distinct meanings — a broader claim this one bears on
- The effectiveness of concrete representations may depend more on how relatable they are than on their real-world existence — 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
- Identical representational designs produced wide individual variation in what felt helpful versus overwhelming (representational fit) — related
- Disagreements about concreteness and abstraction in mathematics education may be verbal disputes rooted in word meaning — related
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
representation-abstract-one-dimension-concrete-another |
title |
A single representation can be abstract along one dimension and concrete along another, and concrete for one learner but abstract for another |
description |
A single representation can be abstract along one dimension and concrete along another, and concrete for one learner but abstract for another |
status |
review |
evidence_strength |
moderate |
newest_evidence |
2025 |
generated |
by process:wiki-ingest on 2026-10-20 |
trust |
unverified — no one has confirmed this page's content |
sources |
1 — julia-chatain-2025 |
Frontmatter is the page's machine-readable record — see the Schema & Guide.