This paper explores one student's attempt to apprehend an abstract mathematical structure (similar to Z[99]). We discuss Karmiloff-Smith's theory of representational redescription as a model for the development of structural understanding and contrast this with existing process-object theories. We use two cycles in Molly's movement from an action…

This paper uses data from two mathematics lessons to explore the nature of progressive discourse and examine critical features of teacher actions that contribute to mathematics classrooms functioning as communities of inquiry. Features found to promote progressive discourse include a focus on the conceptual elements of the curriculum and the use…

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. "Reducing abstraction" is a theoretical framework that examines learners' behavior in terms of coping with abstraction level. This article extends the scope of applicability of this…

This paper examines the cognitive process of concept development in preschool children, based on recent psychological research. Rather than attempting an exhaustive review of the more than 7000 articles written on children's concepts of categories, the paper highlights and illustrates four key themes that emerge from recent research: first,…

"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…

This paper poses and answers 20 questions about mathematical reasoning. Questions include: (1) Is mathematical reasoning mathematical? (2) Is mathematical reasoning useful? (3) Is mathematical reasoning an appropriate goal of school mathematics? (4) Can teachers teach mathematical reasoning? (5) Can mathematical reasoning be taught? (6) Do skills…

This study investigated the moral reasoning of 17 Finnish adolescents (ages 14,15) gifted in science. Students completed tests of their scientific and moral reasoning and wrote essays on moral dilemmas in science and everyday life. On the test of moral reasoning, the students' average score was that of the average 18-year-old. On the test of…

The development of concepts of equivalence was studied in a group of 256 children, ages 4-8. The relative difficulty of these concepts is interpreted in terms of the young child's difficulty in understanding spatial arrangement and heterogeneity as irrelevant to numerical size. (Author/KM)

This experiment investigated performance on a reasoning task in which the subjects had to say which of four half-hidden cards they needed to see fully in order to determine the truth or falsity of a conditional sentence. (Authors)

Two experiments are reported on the effect of negation on reasoning with conditional rules. (Author)

Aimed at teaching kids how to recognize metaphors. (Author)