Examining the Learning Effects of Concrete and Abstract Materials among University Students Using a Two-Dimensional Approach

Background: The debate on using concrete versus abstract materials in learning mathematics has been longstanding. For decades, research has focused on the physical characteristics of materials when defining them as concrete or abstract. Aims: This study extends the field by proposing a two-dimensional classification, which defines materials as concrete or abstract based on the two dimensions of representation, namely object (i.e., appearance) and language (i.e., label). Sample: A total of 120 university students participated in the study. Methods: Participants were randomly assigned to learn the concept of modular arithmetic with one of four types of learning materials: concrete object labelled with concrete language, concrete object labelled with abstract language, abstract object labelled with concrete language and abstract object labelled with abstract language. They were also divided into high and low maths anxiety groups. Results: Results showed that the students who learnt with abstract objects, regardless of the level of maths anxiety, outperformed their peers who learnt with concrete objects. However, for students with low maths anxiety only, those who learnt with materials labelled with abstract language showed better far-transfer performance compared with those who learnt with materials labelled with concrete language. Conclusions: The findings offer a new direction in the conceptualization of concrete and abstract learning materials by specifying the dimensions of representation.