Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

When the author first started teaching twenty years ago, he thought that as long as he was using dynamic geometry software (DGS) for students to "discover" conjectures instead of them learning the conjectures from a lecture or the textbook, he was maximizing their learning potential because they were using technology. Over the years, he…

In this article, the author presents one instructional strategy--scribing--tailored to the Tablet PC. He illustrates the role of the scribe during discussion through two classroom examples: (1) generalizing the polygon sum theorem; and (2) proving the third angle theorem. Then he analyzes scribing as an instructional strategy as well as students'…

This book's 28 chapters are adapted and updated from articles published in NCTM's "Journal for Research in Mathematics Education" between 2000 and 2010. The authors have rewritten and revised their work to make it clear, understandable, and--most of all--useful for mathematics teachers today. To help teachers even more, these articles…

The number [pie] [approximately] 3.14159 is defined to be the ratio C/d of the circumference C to the diameter d of any given circle. In this article, the author looks at some surprising and unexpected places where [pie] occurs, and then thinks about some ways of remembering all those digits in the expansion of [pie].

This book introduces concepts of geometry that students use throughout middle-grade and higher-level mathematics courses. These concepts, presented through the study of transformations, provide a framework for other important topics such as number, measurement, proportional reasoning, and graphing on the coordinate plane. The book is designed for…

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

The experiences of elementary teachers who invited their students to verify geometric theorems prior to the introduction of protractors form the basis of a pedagogical strategy for a sequence of learning activities offered here. Discussion focuses on the students learning strategies about angle concepts utilizing the dynamic interpretation of a…

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

This guidebook is designed to assist teachers and other local school district personnel in the planning and the teaching of the high school geometry course, with essential elements as mandated by the Texas State Board of Education in 1989. Research on student learning in geometry provides the logical rationale for the instructional sequencing and…

Described is a two-week summer residential program designed for students who have been identified through one of several middle school talent searches. Discussed are the assumptions and goals, course content and pedagogy, evaluation, and materials of the program. (CW)

Properties of information most likely to attract student attention and how students use information they generate are clarified. Students' expectations of empirical information in geometry and the design of a new version of the Geometric Supposer are discussed. (CW)

A method for helping students to find formulas involving symmetry under various conditions is explained. Necklace symmetries, orbit counting, tetrahedra and cubes, relationship patterns, and finding patterns are discussed. (CW)

Identified are three obstacles which students must overcome when examining and interpreting diagrams. The resources of the Geometric Supposer, a set of microcomputer tools designed to aid students, are outlined. The advantages of the use of this software are emphasized. (CW)

Described is a short program for teaching and learning about geometric transformations. The integration of geometry problem solving and BASIC programing is discussed. Applications of computer graphics are illustrated. (CW)