This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making "vertical articulation" a cooperative and tangible part of the…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Provides several problems and their solutions for a descriptive statistics course. Included are problems related to measurement, data collection, sample construction, applications, and computation. Discusses the misleading nature of statistics. (YP)

Argues that there is a sense of surprise and wonder that can result from looking back at problem solutions and there is a potential for then creating unexpected, even memorable, alternative solutions. Example problems with routine solutions and alternative approaches uncovered while "looking back" at the solution are given. (PK)

This project was based on recent interview research which suggested that in choosing operations for story problems in mathematics many students are guided by computational considerations rather than meanings for the operations. This project aimed to refine the catalogue of strategies used by students and to design and test instructional materials…

Introduces the constructivist theory of mathematical learning, and illustrates its application in a curriculum focusing on fundamental concepts. How knowledge is constructed, how concepts mature, and what it means to learn and to know mathematics are presented. Pedagogical implications of adopting a constructivist perspective on knowledge and…