Background: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and…

This paper describes the rule-assessment approach to cognitive development. The basic question that motivated the rule-assessment approach is how people's existing knowledge influences their ability to learn. Research using the rule-assessment approach is summarized in terms of eight conclusions, each illustrated with empirical examples.…

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.…