Visualizing expert solutions in exploratory learning environments

Exploratory Learning Environments (ELE) are open-ended and flexible software, supporting interaction styles that include exogenous actions and trial-and-error. This paper shows that using AI techniques to visualize worked examples in ELEs improves students' generalization of mathematical concepts across problems, as measured by their performance. Students were exposed to a worked example of a problem solution using an ELE for statistics education. One group in the study was presented with a hierarchical plan of relevant activities that emphasized the sub-goals and the structure relating to the solution. This visualization used an AI algorithm to match a log of activities in the ELEs to ideal solutions. We measured students' performance when using the ELE to solve new problems that required generalization of concepts introduced in the example solution. The results showed that students who were shown the plan visualization significantly outperformed other students who were presented with a step-by-step list of actions in the software used to generate the same solution to the example problem. Analysis of students' explanations of the problem solution shows that the students in the former condition also demonstrated deeper understanding of the solution process. These results demonstrate the benefit to students when using AI technology to visualize worked examples in ELEs and suggests future applications of this approach to actively support students' learning and teachers' understanding of students' activities.