By using high-leverage models to connect student learning experiences to overarching concepts in mathematics, teachers can anchor learning in ways that allow students to make sense of content on the basis of their own prior experiences. A rectangular area model can be used as a tool for understanding problems that involve multiplicative reasoning.…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children's ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional…

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…

At the heart of the recent focus on mathematics has been an increased emphasis on developing students' "number sense." Ironically, although growing as a force in the education literature, number sense has not been clearly defined for teachers. Teachers need specific support in understanding how to develop number sense in students, to…

This article "opens up" the study of the relationship between quadrilaterals and circles to two sets of quadrilaterals--those that can be drawn either inside (cyclic) or outside (tangential) a circle (or both). Of course, "all" triangles are both cyclic and tangential. Or, to use the traditional Euclidean language for triangles, a unique…

The objectives and the scope and sequence for the elementary school mathematics program of the Denver Public Schools (Colorado) are presented. The guide begins with a statement of the philosophy and general objectives of the K-12 mathematics program and a discussion of the methods of achieving those objectives. Several important ideas and concepts…