Reasoning, our ability to solve novel problems, has been shown to improve as a result of learning experiences. However, the underlying mechanisms of change in this high-level cognitive ability are unclear. We hypothesized that possible mechanisms include improvements in the encoding, maintenance, and/or integration of relations among mental representations -- i.e., relational thinking. Here, we developed several eye gaze metrics to pinpoint learning mechanisms that underpin improved reasoning performance. We collected behavioral and eyetracking data from young adults who participated in a Law School Admission Test preparation course involving word-based reasoning problems or reading comprehension. The Reasoning group improved more than the Comprehension group on a composite measure of four visuospatial reasoning assessments. Both groups improved similarly on an eyetracking paradigm involving transitive inference problems, exhibiting faster response times while maintaining high accuracy levels; nevertheless, the Reasoning group exhibited a larger change than the Comprehension group on an ocular metric of relational thinking. Across the full sample, individual differences in response time reductions were associated with increased efficiency of relational thinking. Accounting for changes in visual search and a more specific measure of relational integration improved the prediction accuracy of the model, but changes in these two processes alone did not adequately explain behavioral improvements. These findings provide evidence of transfer of learning across different kinds of reasoning problems after completing a brief but intensive course. More broadly, the high temporal precision and rich derivable parameters of eyetracking make it a powerful approach for probing learning mechanisms.