Towards a taxonomy of concreteness and abstraction in mathematics education


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Date

2025-08-25

Publication Type

Conference Paper

ETH Bibliography

yes

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Abstract

The words concrete and abstract are extensively used in mathematics education as re searchers aim to better understand how concrete examples support or hinder learning of mathematics. However, it is often unclear what is meant by concrete or abstract, and researchers have called for a finer-grained semantic framework. Indeed, concrete could mean familiar, tangible, or specific, while abstract could mean meaningless, ideal, or universal. This is important as different aspects of concreteness and abstraction may support different learning mechanisms. In this work, we follow a data-driven qualitative approach over 318 articles and a total of 3717 paragraphs including morphologically related words of abstract and concrete. Through this process, we (1) highlight the existence of a verbal dispute, that is a semantic disagreement within the field, and (2) start resolving this dispute by offering a multi-dimensional taxonomy accounting for the various meanings of concrete and abstract in mathematics education. We believe this work contributes to theory, to better situate research on the role of concreteness in mathematics education, and to practice, by supporting actionable design guidelines.

Publication status

published

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Journal / series

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Pages / Article No.

Publisher

ETH Zurich

Event

EARLI 2025

Edition / version

Methods

Software

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Date created

Subject

Mathematics education; Concreteness; Abstraction; Taxonomy; Verbal dispute; Virtual reality

Organisational unit

09590 - Kapur, Manu / Kapur, Manu check_circle
09812 - Rau, Martina / Rau, Martina check_circle

Notes

Conference lecture held on August 25, 2025.

Funding

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