Date of Graduation


Document Type


Degree Type



Eberly College of Arts and Sciences



Committee Chair

Philip N. Chase.


Mathematics education has long been in need of improved methods of instruction, particularly in the area of problem-solving skills. This study compared three methods of training rules about laws of exponents and order of operations. All three training methods used the same mastery criterion for training each rule and included the same number of practice trials during review sessions that preceded each test. The difference between conditions involved what types of problems were presented during the reviews. For each review session, the cumulative group (n = 11) practiced 50 problems covering all rules learned up to that review. The simple review group (n = 11) practiced 50 problems on one previous rule, and the extra practice group (n = 11) practiced 50 more problems of the same rule they had just mastered. Tests were administered after each review.;Though no initial differences existed between groups on any measure, the last test revealed that the cumulative group scored significantly higher than the other groups on items that involved novel applications of the individual rules. Moreover, the cumulative group outperformed the other two groups on untrained, complex problem-solving tasks that required novel combinations of the individual rules. In addition, the cumulative group performed the problem-solving tasks at a significantly faster rate than the other groups. There were no statistical differences among groups on a retention test, however, which was partially due to a reduction in sample size, as well as increases in variability of performance within groups.;Overall, the findings support the viewpoints of behavioral educators that mastery of component skills facilitates performance on higher-level skills and that novel behavior is fundamentally related to its component parts. The results also extend the research of behavioral educators by removing the confounded variables of simple review and extra practice found in previous studies and by showing the effects of cumulative practice on problem-solving behavior. Finally, the results suggest that an approach to training problem solving similar to the one presented in this study may yield higher levels of success than methods used by traditional mathematics educators.;This research was partially funded by dissertation grants from the Office of Academic Affairs and the Psychology Alumni Fund at West Virginia University.