In order to provide teachers with support for the improvement of computer-based problem solving, this paper considers the following research questions--and provides answers--about how to teach students problem solving and how to design training courses for teachers: (1) What are the teachers' and researchers' assumptions about the relation between teaching and learning?; (2) What constitutes "good teaching" in technology-based classrooms where problem solving is a goal and what do "good" teachers do that their colleagues don't do?; (3) What is the relation, if any, between "good teaching" and students' ability to problem solve successfully?; (4) Have schools or school systems successfully overcome teachers' resistance to using technology and how successfully have those teachers been trained?; (5) What results, in terms of student learning, have accrued from change strategies directed at increasing or improving the teaching of problem solving?; (6) What types of training for what duration and with what frequency with what types of teachers--veteran teachers, new teachers, teachers who believe in "hands-on" and teachers who "go by the book"--produce "good teaching?"; (7) How do different training strategies produce positive changes in students' problem-solving behavior?; (8) What different types of training strategies need to be employed to deal with differences in teachers' beliefs about what should be taught and how it should be taught?; (9) What types of training are needed to provide teachers with both the mathematical knowledge necessary to conduct problem- solving lessons and the pedagogical skill to use technology for those lessons?; (10) What differences, if any, are there in the outcomes in students' learning to be problem solvers when computation is the sole or major focus of computer use versus experience with problem solving software, and does ILS use contribute to or detract from problem-solving expertise?; and (11) What role does the choice of measures play in efforts to learn about the impact of technology on students' performance? (Contains 16 references.) (Author/AEF)