Strategies for Using a Spatial Method to Promote Active Learning of Probability Concepts

We developed and tested strategies for using spatial representations to help students understand core probability concepts, including the multiplication rule for computing a joint probability from a marginal and conditional probability, interpreting an odds value as the ratio of two probabilities, and Bayesian inference. The general goal of these strategies is to promote active learning by introducing concepts in an intuitive spatial format and then encouraging students to try to discover the explicit equations associated with the spatial representations. We assessed the viability of the proposed active-learning approach with two exercises that tested undergraduates' ability to specify mathematical equations after learning to use the spatial solution method. A majority of students succeeded in independently discovering fundamental mathematical concepts underlying probabilistic reasoning. For example, in the second exercise, 76% of students correctly multiplied marginal and conditional probabilities to find joint probabilities, 86% correctly divided joint probabilities to get an odds value, and 69% did both to achieve full Bayesian inference. Thus, we conclude that the spatial method is an effective way to promote active learning of probability equations.