Research in this project studied cognitive processes involved in understanding and solving problems used in instruction in the domain of mathematics, and explored implications of these cognitive analyses for the design of instruction. Three general issues were addressed: knowledge required for understanding problems, knowledge of the conditions for applying problem-solving operators, and strategic knowledge for problem solving. Computational systems were developed in which graphical displays present explicit information to students that allows them to reflect on processes that are usually implicit, construct representations of problem information, specify assignments of variables, and learn from strategic errors. Research is described that provided analyses of cognitive processes on which instructional designs were based, and preliminary empirical results from use of the systems are presented. (Author/JM)