Pragmatic and semantic problem solving are examined as processes that enhance acquisition of mathematical knowledge. It is suggested that development of mathematical cognition involves restructuring and that math teachers can help restructure children's knowledge systems by providing them with situations in which semantic and pragmatic problem…

Proposes analogy as the central mechanism of knowledge acquisition in formal domains. Discusses experimental data on preschoolers' knowledge of one-to-one correspondence and college students' understanding of force decomposition. Suggests that a knowledge base domain is a thematically organized knowledge structure and that thematic relations in a…