Previous research has indicated that numerically based problem-solving can be taught to children and that it should be initiated on a continuing basis in the elementary school years, yet there is no evidence for the existence of an exact, comprehensive process through which problem-solving with numerical comparisons and addition or subtraction operations can be effectively taught to children. The ability of 6 second- and third-grade students with various learning difficulties to use problem-solving skills in making decisions about open arithmetic sentence comparisons through computer-assisted instruction was examined during a 6-week summer program. Within self-paced environments monitored by a graduate student, pairs of students made independent use of various computer softwares modified to suit individual needs across several learning modes. The results indicated that single-step problem solving can be taught in a relatively short period of time using computer assisted instructional strategies. However, complex problem solving, which involved critical thinking and multiple tasks beyond mere recognition and memorization, was not fully attainable by second- and third-grade students with learning difficulties, particularly within such a short learning period. (Appendices include 22 references, pretests, posttests, student instructional preference survey, software recommendation sheet, and student data in the form of a daily log.) (JJK)