Describes an attempt to encourage fifth- and sixth-graders to invent their own ways of solving problems involving division with fractions. Emphasizes the importance of social interaction in Piaget's constructivism and explains why debate and verification are important for children's construction of logico-mathematical knowledge. (22 references)…

Presents a computational framework for modeling cognitive development that provides a language paradigm with which to compare and contrast different facets of children's knowledge. Describes the generative connectionist algorithm "cascade-correlation," the successful use of the algorithm to model cognitive development in various…

A 14-year-old Brazilian boy in the fourth grade was given 170 problems orally, each asking for the sum of 2 2-digit numbers. Responses indicated he had invented his own algorithm for addition, similar to the school one, based largely on his experiences with money. (Contains 13 references.) (JAF)