Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

This study explores, from both constructivist and cognitive perspectives, teacher guidance in student-centered classrooms when addressing a common learning difficulty with equivalent fractions--lines or pieces--based on number line models. Findings from three contrasting cases reveal differences in teachers' facilitating and direct guidance…

Describes how 2 10-year olds developed drawings and numeral systems to symbolize their mental operations while dividing unit bars into thirds and fourths using TIMA: Bars, a computer microworld, as a medium for enacting mathematical actions. The symbolic nature of their partitioning operations was crucial in establishing more conventional…

Describes the development, refinement, and validation of a framework for nurturing and assessing multidigit number sense in young children. Major constructs incorporated were counting, partitioning, grouping, and number relationships. The framework was validated through case studies of six first-grade children. (30 references) (MKR)

The Proceedings of PME-XI has been published in three separate volumes because of the large total of 161 individual conference papers reported. Volume I contains four plenary papers, all on the subject of "constructivism," and 44 commented papers arranged under 4 themes. Volume II contains 56 papers (39 commented; 17 uncommented)…

The Proceedings of PME-XVI has been published in three volumes because of the large number of papers presented at the conference. Volume 1 contains: (1) brief reports from each of the 11 standing Working Groups on their respective roles in organizing PME-XVI; (2) brief reports from 6 Discussion Groups; and (3) 35 research reports covering authors…