The efficiency of the butterfly catastrophe model for describing and predicting performance changes in an educational setting was studied. Subjects were 455 introductory psychology students. Changes in performance on the first exam and three subsequent exams were examined, plus extra credit for participation in psychology experiments. The butterfly difference equation was tested using hierarchical stepwise regression. The model, which assumes nonlinear change, predicted performance more accurately than two linear alternatives. Where the goal was to predict performance at the end of the program, the butterfly model offered a 37.7 increase in utility. Larger positive changes in performance were observed for successive administrations of the course, indicating that the course was steadily improving. The degree to which the course was perceived as important for career goals (extrinsic instrumentality), was found to be a significant bifurcation variable. Women showed more favorable performance changes compared to men. The butterfly model described the motivational dynamics taking place in the classroom. The collective learning curves varied along four parameters: extrinsic motivation, intrinsic motivation, programmatic differences, and ability. Equations and explanations of the model, including applications for training evaluation, are included. (SW)