The (in)effectiveness of visual representations as an aid to solving probability word problems

This article presents the findings of two experimental studies designed to investigate the use of different kinds of visual representations of mathematical relationships in helping college students solve probability word problems. Two types of multiple-event probability problems were presented: joint probability of independent events; and total probability of non-mutually exclusive events. Two treatment groups were created: the specific-representations group that was instructed in how to use tree and Venn diagrams; and the matrix group that was trained to use a matrix (a two-dimensional table). A control group was instructed only in the formulation of equations. Results from two separate experiments indicated that the control group outperformed the specific-representations group on their ability to transfer the problem-solving strategies they had learned to novel situations and that there was no difference between the matrix group and the other two groups on their ability to do this. Results further indicated higher cognitive load in the specific-representations condition, supporting the contention that a split-attention effect was responsible for the lower performance of that condition.