This research is aimed at diagnosing the problem-solving skill of elementary school children and subsequently improving their competence in early mathematics. To reach this goal, a computer assisted instruction (CAI) program on open sentences, incorporating knowledge about students' problem solving strategies and misconceptions, was constructed. Two studies are reported, the first to gain more insight into the process of problem solving and the second to evaluate the functioning of the CAI program in the classroom. In the first study, 339 pupils in grades 2 and 3 were given a test, followed by interviews with 16 high performers and 16 low performers. Their answer patterns are discussed, and models of knowledge, the diagnostic program, and the remedial program are described. In the second study, the CAI program was evaluated with second-grade pupils in five schools. It was concluded that children can learn fundamental concepts relatively quickly with a computer program; one-third profited significantly. (MNS)