ABSTRACT
Research on mathematical problem solving has been influenced by both mathematical content and instructional methods on the one hand and by research methods extraneous to the subject field on the other. Many examples come instantly to mind: group theory, attempts to describe mental operations in group-theoretical terms, and subsequent efforts to validate these structures psychologically (Gay & Cole, 1967; Piaget, 1970); the structure of the disciplines movement and attempts to find correlations between structural presentations and achievement (Rudnitsky, 1977; Shavelson, 1972, 1973); increasing interest in graph theory and attempts to describe cognitive structure by way of trees (Shavelson, 1974a, 1974b; Stanton, 1980); growth in computer science and a proliferation of attempts to describe mathematical behavior in terms of information processing (Greeno, 1978; Paige & Simon, 1966). Clearly, we could extend the list and supply pages of references in each category.
