Using a balance-beam task, studied 48 preschoolers to elucidate the process of knowledge construction from the emergence of new representation to transformed problem solving. Analyses revealed a multifaceted development from the first signs of weight representation to fully elaborated weight-based problem solving. Case studies of five children…

Tested three models of children's mathematics word-problem solving based on developmental differences in quantitative conceptual structures: (1) quantitative relations represented as ordered array of mental objects; (2) numbers represented on two tentatively coordinated mental number lines; and (3) numerical operations represented as objects on…

Devised a model that hypothesized that students, in discriminating relevant information in mathematical story problems, search for values of semantic categories that match those in the problem. Two experiments assessed the validity of the model. Results indicated that the model was an accurate predictor of discrimination performance for successful…

Analyzed a corpus of videotapes in which university students solved physics problems to determine how students learn to understand a physics equation. Found that students learn to understand physics equations in terms of a vocabulary of elements called symbolic forms, each associating a simple conceptual schema with a pattern of symbols. Findings…

Investigated the cognitive gains of interacting pairs of Grade 10 students who show low levels of competence and fail to solve a task individually but who improve when working in peer interaction. Found that this phenomenon may occur when the two students disagree, have different strategies, and active hypothesis testing is made possible. (JPB)