ABSTRACT
This chapter provides a perspective for understanding and interpreting the existing cognitive research concerning algebra problem solving and learning. It presents a model of the related processes of algebra problem solving and understanding and utilizes this model to discuss the cognitive research on algebra learning. The chapter suggests that some points where mathematics educators may have to take up interpretive work to translate the cognitive research on algebra into their practice of designing instructional activities. In practice, educators may want to include other considerations in their designs, such as student interests and capabilities, as well as classroom constraints. The goal of problem-solving research reflects the goal of cognitive psychology in general: to understand the sequence of mental operations and their products in performing a cognitive task. Cognitive studies of algebra learning tend to examine issues from the point of view of cognitive performance models.
