Calculators Do More Than Compute

Summary

This paper describes changes in the approach to algebra and geometry that have resulted from using handheld calculators with remedial students at Ohio State and with twelth grade students who have no skills in elementary algebra.

The approach described is highly numerical and depends on concrete problem situations to suggest key concepts of algebra. Calculators are used to give students greater confidence, to get them past arithmetic difficulties and into significant mathematics more quickly, and to enable the investigation of realistic problems. More importantly, calculators provide an entrance to mathematics quite different from traditional approaches. Several features of this numerical approach are discussed:

• using numerical methods to solve problems that students are not ready to solve algebraically or that are more appropriately solved numerically.

• encountering basic concepts and relationships in problem settings before the concepts are formalized.

• investigating problems in many special cases so that variables can be introduced in a natural way to describe the general case.

• using calculators to draw students’ attention to arithmetic ideas that otherwise would be of little interest to them.

• using calculators to permit the early introduction of graphing so that graphing can provide a bridge between numerical work and the formalism of algebra.