With respect to the innovative roles of technology within the educational realm, an important task of educational research is the investigation of how school children accommodate themselves to innovative computer-based learning environments. This paper describes the strategies and techniques employed and extended by above-average second- through fourth-grade students in a suburban Tel Aviv school within a self-paced learning environment of new arithmetic concepts and algorithms under the guidance of a widely used computer-managed learning system, the Computer-Based Practice in Arithmetic. These high-achieving students managed to provide correct responses to exercises that they did not fully understand, nor to which they had previously been exposed, by the application of resourceful problem-solving methods. Descriptions and examples are provided for the following observed student strategies: (1) analogy by recognition of a pattern within structure or notation; (2) analogy by generalization of notation, operation, or rule to novel situations; (3) synthesis of previously relevant knowledge or rules; (4) reduction of the observed difference between problem statement and problem goal through the use of means-ends analysis; (5) examination, and subsequent utilization, of special cases or examples; (6) use of heuristics to eliminate computational procedures deemed inappropriate in attempting to shorten the search for correct solutions; (7) use of probabilistic considerations when faced with a reduced list of options; (8) induction from trial-and-error procedures; and (9) acquisition of assistance outside of the computer-based learning environment. The fact that students actively learn and attain satisfactory conceptual knowledge within this system is noteworthy because the system is primarily designed to provide drill and practice as a complement to class instruction rather than being the supplement of innovative and substantive educational materials. (JJK)