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April 2004, Volume 97, Issue 4

FEATURES

The Triangles of Aristarchus
Alan Hirshfeld
The ancient Greek mathematician Aristarchus demonstrated for the first time how it was possible, using simple observations and elementary geometry, to measure distances to bodies in the solar system. Aristarchus' methods used a lunar elcipse to approximate the diameter of the Earth, and used the shadow cone of a lunar eclipse to form similar triangles and proportional measurements. The mathmatics can be easily understood by a high school geometry student.

Fostering Mathematical Inquiry with Explorations of Facial Symmetry
Michael Edwards
Ways in which teachers and students can use image-processing software and dynamic geometry tools to explore symmetry from algebraic and geometric perspectives. Students use technology to construct their own symmetry algorithms and examine their own photos to determine facial symmetry.

Focusing on Students' Mathematical Thinking
M. Breyfogle, Beth Herbel-Eisenmann
The importance of focusing on student mathematical thinking during classroom discussions, and practical suggestions to classroom teachers to help keep the focus on student thinking. Probing students to share thinking processes leads to better understanding of mathematics for all students.

Discover Mathematical Knowledge through Recreational Mathematics Problems
Amar Sodhi
How a student approached the task of solving a historically challenging mathematical problem. The author uses recreational mathematics problems in a summer program for Women in Science and Engineering. A student partners with a mathematician to explore mathematics from a researchers point of view.

Building Your Own Regression Model
Robert Horton, Vicki Phillips, John Kenelly
A method used in Algebra II class to explore regression with a spreadsheet. Several advantages helped the students learn at deep levels: they were not restricted to predetermined models available on their graphing calculators, they were forced to think about and estimate the parameters, and they could define the error in the model and then minimize it.