This paper discusses an investigative approach to problems concerned with approximations. Two problems are analysed in detail and both are inspired by their historical origins. The first examines an ancient Chinese formula for calculating the area of a segment. The second looks at Durer's construction for the trisection of an angle. It is argued…

By stretching the area under the curve x[superscript [alpha]] it is shown to be of the form x[superscript [alpha] + 1] p([alpha]). Geometry is then used to prove p([alpha]) = 1/([alpha] + 1).

Hexaflexagons (or flexagons) have a magic that has enthralled some of the greatest minds for over half a century. Their name comes from "flexible hexagon", which is the form in which they were first discovered by their inventor, Arthur Stone, an English graduate student at Princeton in 1939. In this article, the author talks about using flexagons…

In this note, we recall the convex (or barycentric) coordinates of the points of a closed triangular region. We relate the convex and trilinear coordinates of the interior points of the triangular region. We use the relationship between convex and trilinear coordinates to calculate the convex coordinates of the symmedian point of the triangular…

The aim of this study was to compare motivation of sixth-grade students engaged in instruction using reform-based curriculum with sixth-grade students engaged in instruction using a traditional curriculum. There were 273 sixth-grade mathematics students, 123 in the control group and 150 in the treatment group, involved in the study. This study…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

The purpose of this study was to examine the effects of the use of technology on students' mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of…

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the second term of a one-year course, or for the second year of a two-year…

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. The thrust of this module is to introduce the student to transformations by having the student physically transform sets of points. Heavy use of manipulatives is made to aid the student in the transforming activity. Individual sections…

Presents a geometry exercise which is designed to help students create three-dimensional clay figures, think in three dimensions, and develop vocabulary. Reproducible worksheets are included. (PK)

Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)

A mult tile is a set of polygons each of which can be dissected into smaller polygons similar to the original set of polygons. Using a recursive LOGO method that requires solutions to various geometry and trigonometry problems, dissections of mult tiles are carried out repeatedly to produce tile patterns. (MDH)

Described is a theorem which is generally not present in most high school geometry textbooks. Presented are two proofs and two cases which illustrate the use of the SSA theorem. (CW)

Presents a lesson in which students communicate verbally and in writing to create and describe geometric transformations, develop vocabulary, demonstrate ability to give unambiguous instructions to translate a triangle, form and test conjectures, and create extensions of problems. Includes reproducible student worksheets and questions for…

Geometry is the study of shape and space. Without spatial ability, students cannot fully appreciate the natural world. Spatial ability is also very important for work in various fields such as computer graphics, engineering, architecture, and cartography. A number of studies have demonstrated that technology has an important potential to develop…