Use templates to reflect on and classify learning interventions along the axes of concreteness and abstraction¶

Strategy · All strategies
Evidence · 4 claims (4 for) · 1 study (1 qualitative), q2 · 0 of 1 report an effect size · 4 claims rest on one study

Description¶

As its third contribution, the article offers templates for designing and classifying mathematics education interventions along the taxonomy's axes. The authors "complement this contribution with a blank template, in Appendix B (Fig. 24), that can be used to organize studies or interventions according to this taxonomy." Each axis is supplemented with a design question to make the taxonomy easier to use in research and practice.

Design Implications¶

Context¶

Requirements¶

• Users must know the targeted learners to classify along the subjective interaction-level axes

Constraints¶

• The template organizes interventions along the published axes; axes with only one coded end are indicated by dotted lines

Target Learners¶

• Mathematics education researchers and intervention designers

Target Learning Goals¶

• Designing and comparing mathematics learning interventions with precisely qualified uses of concreteness and abstraction

Claims¶

• Mathematics education literature uses the terms concrete and abstract with multiple distinct meanings [+W]
• The effectiveness of concrete representations may depend more on how relatable they are than on their real-world existence [+W]
• A single representation can be abstract along one dimension and concrete along another, and concrete for one learner but abstract for another [+W]
• Disagreements about concreteness and abstraction in mathematics education may be verbal disputes rooted in word meaning [+W]

Related Strategies¶

Examples¶

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Key Sources¶

• 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