The path taken and the turns made as a turtle traces a polygon are examined to discover an important theorem in geometry. A unique tool, the Angle Adder, is implemented in the investigation. (Contains 9 figures.)

Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

The first introduction to molecular geometry should be through the simple and easily understood VSEPR model, as the Valence Bond Theory and MO Theory suffer from limitations as far as understanding molecular geometry is concerned. The VSEPR model gives a perfectly satisfactory description of the bonding that follows directly from the Lewis model…

This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…

In texts on vector analysis one finds many different methods of proving the vector triple product identity. Most of these rely on complicated geometrical constructions or theorems drawn from vector space theory. The component method is generally regarded as being merely long and tedious. Yet, viewed in the correct way, the component method is…

This article employs the Archimedean method of estimating the value of pi within an inscribed pentagon. We show how to write these approximations in terms of the golden ration.

Many science topics can naturally be integrated with a variety of mathematical concepts, including the study of light and optics. In the hands-on activities described here, students explore the properties of light energy while building their understanding of geometric concepts. (Contains 2 figures.)

Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, "Mathematics and Computer Education," 39(3), 198-205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry,…

This study examined the improvement of students' comprehension of geometric concepts through analytical writing about their own misconceptions using a reflective tool called an ERNIe (acronym for ERror aNalyIsis). The purpose of this study was to determine whether the ERNIe process could be used to correct geometric misconceptions, as well as how…

This paper was developed with the goal of enhancing the mathematical preparation of secondary school teachers in the technological paradigm. It shows how two-variable inequalities can be utilized as models for the construction of geometric objects using the software Graphing Calculator 3.5 (produced by Pacific Tech) as a relation grapher. An…

There are diverse ways to construct instructional activities that teachers can use to foster their students' development of mathematical thinking. It is argued that the use of computational tools offers teachers the possibility of designing and exploring mathematical tasks from distinct perspectives that might lead their students to the…

According to the National Council of Teachers of Mathematics (NCTM) (1989, 2000), students at all levels should be exposed to geometry and measurement topics. Standards documents have identified the importance of primary school students selecting appropriate units for measurements in one- and two-dimensional space (NCTM 1989, 2000). This paper…

This article examines three important facets of the incorporation of new technologies into educational practice, focusing on emergent usages of the mathematical tools of computer algebra and dynamic geometry. First, it illustrates the interpretative flexibility of these tools, highlighting important differences in ways of conceptualizing and…

This paper examines some of the complexities involved in the actual work of classroom instruction by examining interactions among the goals of teaching. The research is part of a case study of teaching a Year 7 Singapore class comprising students of average mathematical ability. Among the complexities of teaching analysed here are the problems…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…