I present a novel way to introduce the lunar orbital eccentricity in introductory astronomy courses. The Moon is perhaps the clearest illustration of the general orbital elements such as inclination, ascending node, eccentricity, perigee, and so on. Furthermore, I like the students to discover astronomical phenomena for themselves, by means of a…

Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…

In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the derivative of the exponential functions and the derivative of their inverses, the logarithmic functions. I extend this approach to generate formulae for the…

Because of the extensiveness of the course outline for Math 301 (Manitoba Department of Education), schools would have had to purchase several different textbooks to cover the material adequately. Therefore, a set of materials to supplement the guide was developed. The exercises, projects, and reviews contained in this package are keyed to the 301…

The authors hypothesize that a means-end strategy places a load on cognitive processing capacity which retards knowledge acquisition. Three experiments using trigonometry problems with high school students were conducted in which the problem goal was modified to disrupt strategy used by novices. Results supported the authors' hypothesis.…

Utilizes vector mathematics to explain the reflective properties of a corner cube retroreflector, consisting of three plane mirrors assembled at right angles with a common vertex. Analyzes the useful property that an incident beam of light at any point in this reflector will return on a parallel path. (MDH)

Discusses solutions to the problem of maximizing the range of a projectile. Presents three references that solve the problem with and without the use of calculus. Offers a fourth solution suitable for introductory physics courses that relies more on trigonometry and the geometry of the problem. (MDH)

Utilizes a computer-generated graph to solve an equation for methods using trigonometric tables or less sophisticated calculators would likely fail because of round-off errors and limitations of the instruments. Discusses how this new technology can be utilized in mathematics instruction. (MDH)

Described is a solution to the problem and a discussion of a computer estimation of the probability. A computer program written in Turbo Pascal and two sample runs are provided. Computations for a more general problem of this nature and changes in the program necessary for use with Apple Pascal are appended. (CW)

The concept of waves is fundamental due to its occurrence throughout the natural world. Because the concept occurs in so many places, students come to the classroom with prior knowledge, as well as misconceptions, about waves. Students have misconceptions about what is waving in a wave, what properties of the medium determine wave speed, and how…

"Lesson plan study" (LPS), adapted from the Japanese Lesson Study method of professional development, is a sequence of activities designed to engage prospective teachers in broadening and deepening their understanding of school mathematics and teaching strategies. LPS occurs over 5 weeks on the same lesson topic and includes four opportunities to…

The purpose of high-school education has generally been twofold--not only to furnish preparation for college, but also to provide some of the elements of a liberal education for those whose formal and directed study is to go no further. In not a few communities high schools were established in which the former purpose was expressly waived; but…