In this article, I examine changes in the field of cognitive development and in my own thinking over the past 40 years. The review focuses on three periods. In the first, Piaget's theory was dominant, and my research and that of many others was aimed at understanding the many fascinating changes in children's thinking that Piaget documented, and…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Reviews evidence that children use diverse cognitive strategies; discusses the adaptive value of using diverse strategies; describes models of strategy choice based on rational calculations; and presents an overview of the distributions of associations model of children's strategy choice. (RH)

Preschoolers 4 and 5 years of age were found to use four strategies differing in temporal characteristics as they solved simple addition problems with sums of 10 or less. Three strategies had visible and/or audible aspects, and one was covert, involving retrieval from memory. The harder the problem, the more often the children used an overt…

This paper describes and discusses three studies concerned with the representation of children's knowledge as revealed in the ways that children, ages 5 to 17, perform a scientific induction task. A variant of Piaget's balance scale prediction problem was chosen as the experimental task; a formal model for different levels of children's knowledge…