The Disappearing "Advantage of Abstract Examples in Learning Math"

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.

Detailed bugs or bugging details? The influence of perceptual richness across elementary school years

Visualizations are commonly used in educational materials; however, not all visualizations are equally effective at promoting learning. Prior research has supported the idea that both perceptually rich and bland visualizations are beneficial for learning and generalization. We investigated whether the perceptual richness of a life cycle diagram influenced children's learning of metamorphosis, a concept that prior work suggests is difficult for people to generalize. Using identical materials, Study 1 (N = 76) examined learning and generalization of metamorphosis in first- and second-grade students, and Study 2 (N = 53) did so in fourth- and fifth-grade students. Bayesian regression analyses revealed that first and second graders learned more from the lesson with the perceptually rich diagram. In addition, fourth and fifth graders generalized more with the bland diagram, but these generalizations tended to be incorrect (i.e., generalizing metamorphosis to animals that do not undergo this type of change). These findings differ from prior research with adults, in which bland diagrams led to more correct generalizations, suggesting that the effect of perceptual richness on learning and generalization might change over development.