ABSTRACT
Exploration can be an effective learning experience, if suitably constrained and guided. Moreover, it can provide this benefit for specifically targeted formal skills in the arithmetic curriculum. This paper presents two complementary techniques for promoting success in computer-based exploration environments. Semantic constraints on eploration cut out meaningless options, and heuristic guidance facilitates search on the basis of a heuristic function with both cognitive and problem-solving components. We have implemented an environment that permits semantically constrained exploration for subtraction, as well as a related environment that facilitates the transition to paper-and-pencil subtraction. The authors tested the system in individual hour-long sessions with more than twenty children in grades 1-3.
