Category theory concept of a commutative diagram was used to construct a model of the way in which symbolic processes are applied to problem solving. It was shown that several different levels of thought can be distinguished within the basic model. Two experiments testing the theory are reported. (Author/RD)

A psychometric model called Saltus, which represents the qualitative aspects of hierarchical development in a form applicable to additive measurement, was applied. Both Piaget's theory of cognitive development and Gagne's theory of learning hierarchies were used to establish the common features of hierarchical development: (1) gappiness--the…

The focus of this report is children's construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in their strategies for dealing with isomorphic combinatorial problems presented in "hands-on" and written form. Case studies of 9-year-olds, one low and one high achieving in school…