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September 1999, Volume 92, Issue 6

FEATURES

Assessing True Academic Success: The Next Frontier of Reform
Dan Kennedy
Not everyone will agree with the ideas in this article, but I hope that nobody will reject them as being impossible to implement. Assessment, however we define it, is only a means to an end: the learning of mathematics by all our students. If you suspect that your assessment is getting in the way of that basic goal, then I urge you to tame whatever beast it has become. The success of your students is in your hands—for your assessment is the instrument that defines that success.

Experiencing Radians
Patrick Eggleton
As Einstein stated, most fundamental concepts in science, including mathematics, are essentially simple. Students do not have to memorize and us radian measure without understanding the concept. The simple correspondence between the radial angle and the measure of its arc to the measuring of fractional parts of a wheel in terms of the number of spokes furnishes a concrete representation of the concept of radians.

Algebra for All: Using the Elegance of Arithmetic to Enhance the Power of Algebra
Michael McConnell, Dip Bhattacharya
In this article, we produce algebraic solutions, thereby reducing the problems to equations, and arithmetic solutions, which do not use variables. We look at how the arithmetic solution helps students better understand the problem before they approach it algebraically and how logic used in solving the problem arithmetically can be directly linked to the algebraic solution.

Creative Writing in Trigonometry
Julia Barnes
These assignments bring an alternative form of assessment into my trigonometry classroom, and they combine topics from English and mathematics - two subjects that students often consider to be totally unrelated.

Ten Lessons From the Proof of Fermat's Last Theorem
Jeremy Kahan
The proof of Fermat's last theorem establishes the truth of an old mathematical conjecture in ways that are beyond the understanding of most students and their teachers. Yet the lessons from the proof process can help teachers and their students gain insight into constructing mathematics.

Discovering Optimum Networks in Triangles
Robert Iovinelli
This classroom activity is an example of how students can use the connections among different disciplines of mathematics to investigate a branch of mathematics that is not usually encountered in high school courses—graph theory.