In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

Differentiation and integration played large roles within classic developmental theories but have been relegated to obscurity within contemporary theories. However, they may have a useful role to play in modern theories as well, if conceptualized as guiding principles for analyzing change rather than as real-time mechanisms. In the present study,…

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.…

Two experiments examined development of economic understanding among 5-, 7- and 9-year-olds. Found that most 5-year-olds understood the goal of acquiring desired goods, and most 7- and 9-year-olds also understood the goals of seeking profits, acquiring goods inexpensively, and competing successfully with other sellers. Results suggest that older…

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.…