This article deals with the roles of variation problems ("one problem multiple solution" and "one problem multiple changes") as used in Chinese textbooks. It is argued that variation problems as an "indigenous" Chinese practice aim to discern and to compare the invariant feature of the relationship among concepts and…

In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication and division of fractions in two curricula: "Everyday Mathematics" (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks indicate that…

The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics…

Presents results of a study in Greece, Scotland, and the United States in lower secondary mathematics classes using haptic exploration, the intentional movements of one's hands about an object, as an alternative approach for teaching the geometry of two- and three-dimensional shapes. Students performed poorly with solids. (MKR)