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We explore how different elements of student persistence on computer programming problems may be related to learning outcomes and inform us about which elements may distinguish between productive and unproductive persistence. We collected data from an introductory computer science course at a large midwestern university in the U.S. hosted on an open-source, problem-driven learning system. We defined a set of features quantifying various aspect of persistence during problem solving and used a predictive modeling approach to predict student scores on subsequent and related quiz questions. We focused on careful feature engineering and model interpretation to shed light on the intricacies of both productive and unproductive persistence. Feature importance was analyzed using SHapley Additive exPlanations (SHAP) values. We found that the most impactful features were persisting until solving the problem, rapid guessing, and taking a break, while those with the strongest correlation between their values and their impact on prediction were the number of submissions, total time, and (again) taking a break. This suggests that the former are important features for accurate prediction, while the latter are indicative of the differences between productive persistence and wheel spinning in a computer science context.