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…

Discusses metacognitive and associative models of children's strategy discovery and use. Contends that models based on only one type of mechanism cannot entirely account for observed variability and constraint revealed by microgenetic studies of children's strategy change. Proposes a new model of children's strategy development in which…

Two experiments demonstrate that 10- and 13-year-olds can learn to detect interactive patterns in data. Results also indicate the advantages of creating formal models of solution strategies and using them as a basis for instructional procedures. (Author/DEP)

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…

Analyzed 1.5- and 2.5-year-olds' problem solving and learning. Found that changes in toddlers' strategies could be assessed reliably on a trial-by-trial basis, that changes followed the basic form predicted by the overlapping waves model, and that analyses could reveal information about the qualitative and quantitative aspects of their learning.…