Research in goal theory has often relied on the general linear model, ignoring some central assumptions of the theoretical framework under investigation. The purpose of the two studies reported here was to illustrate how the Rasch model can supplement traditional statistical analyses when evaluating the effects of goal orientations on persistence. In Study 1, 41 adolescents participated in a series of insolvable puzzles. Means analyses failed to reveal differences between mastery-approach and performance-approach students. Application of the Rasch model, and in particular the differential item functioning procedure, indicated that mastery students were more severely challenged by the last puzzle, compared to performance approach students, with their probability of persisting being significantly lower. The findings of Study 1 were replicated in Study 2 with a sample of 37 college students who were also given a series of insolvable puzzles. The findings suggest that use of the Rasch model can be particularly fruitful for our understanding of the complex achievement-goal relationship. (Contains 4 figures and 6 endnotes.)