This study investigated several aspects of a teaching experiment which focused on five seventh grade students' performance on nonroutine number theory problem-solving with a close look at the role of heuristics, concrete models, and the relationships between these variables. In the experiment, students were given a series of lessons on number theory, heuristics, concrete models, and the microcomputer. The microcomputer was used to present the problem, facilitate hint selection through the use of a menu, and to record student work. Interest was in identifying student behaviors after the experiment, not on identifying cause-effect relationships or predicting future behaviors. Three questions were addressed: (1) Is there an observable pattern of self-directed use of concrete models? (2) Will students who choose to use the provided concrete models improve as problem solvers? and (3) What motivates these students either to use or not to use the provided concrete models? Results indicate that all students showed improvement in problem-solving ability and increased use of concrete models. Compared to above-average and below-average students, the average ability students showed the greatest gain in demonstrated problem-solving ability and the greatest use of concrete models. (Author/JN)