Concrete Taxonomy

The role of concreteness in grasping abstract mathematical concepts has been widely explored in the Learning Sciences. However, empirical results send a conflicting message: while some concreteness can help students reach abstract levels of representation, starting with concrete examples may also prevent students from transferring to abstract symbolisms. We argue that such discrepancies might result from a verbal dispute in our field. Indeed, while the words concrete and abstract are often used in the field of mathematics education, they are not always used with the same meaning. For example, the word "concrete" can be used as specific, relatable, visual, tangible, while the word abstract can be used as general, reusable, vague, symbolic. With this project, we offer three contributions: First, we empirically identify the verbal dispute, second, we resolve the verbal dispute by offering a taxonomy of concretenesses and abstractions in mathematics education, third, we offer a template for the design of future mathematics education interventions and studies.

Ongoing project... More information coming soon.

Team

• Julia Chatain - Concept, research, tool implementation, data annotation, analysis, paper writing
• Charlotte H. Müller - Concept, research, data annotation, analysis, paper writing
• Keny Chatain - Concept, research, data annotation, analysis, paper writing
• Leon Calabrese - Data collection, data annotation
• Manu Kapur - Supervision

Publications

Under review