Concrete versus abstract examples and instructions in learning mathematics : a framework for enhancing performance of learners with different levels of math anxiety

Abstract

The debate on using concrete versus abstract materials in mathematics learning has been longstanding. Decades of research have focused on the dichotomy of concrete and abstract materials but the findings were inconsistent as both had its effectiveness in enhancing performance over others. This study extended the discussion by (1) comparing the effectiveness of abstractness and concreteness at the levels of object and language respectively, and (2) examining how the effectiveness of these teaching materials interacted with math anxiety. We compared math performance of 120 university students with high and low math anxiety, who had been randomly assigned to learn with concrete object and concrete language, concrete object and abstract language, abstract objectand concrete language, or abstract object and abstract language. Results showed that participants learning with abstract object and abstract language showed better overall and near-transfer performance. Interaction effects between math anxiety and object on overall performance, as well as between math anxiety and language on near-transfer and far-transfer performance were observed. These findings provide empirical support and important implications for educators to devise different materials in enhancing performance of learners with different math anxiety levels.