Multiple symbolic representations: The combination of formula and text supports problem solving in the mathematical field of propositional logic

Abstract

As multiple representations are common in math education, we examined different combinations of representations (text, formula, graphic) in the field of propositional logic. In two experiments, we investigated whether participants benefit from multiple representations, and whether the kind of representational combination affects performance. For the first experiment, 146 university students were divided into six groups: two single-representation groups (text or formula), three dual-representation groups (all possible pairs), and one triple-representation group. Results indicate that the combination of multiple symbolic representations (text + formula) was as helpful as combining analog and symbolic representations (text + graphic and text + formula + graphic): the participants provided with all such types of multiple representations outperformed all single representation groups. In a second experiment (N = 19, within-subjects) we compared the gaze behavior when working with multiple symbolic representations (text + formula) or combined symbolic and analog representations (text + graphic). The results demonstrate that text was the one representation that was attended most and can therefore be regarded as the reference representation in all useful combinations. Even though fewer gaze switches were observed between text and formulas than between text and graphics, performance (time on task and accuracy) did not differ. This research emphasizes the importance of various forms of multiple representations in mathematics learning and assessment, and sheds light on how different kinds of representations and their combinations are processed.