A K-12 Mathematics Curriculum with CAS: What Is It and What Would It Take To Have It In Schools?

Abstract

Hand-held four-function arithmetic calculators first appeared in the early 1970s. A few years later, I gave a talk entitled "What Happens to Arithmetic Now That There are Calculators?" The essence of my remarks was that most of arithmetic instruction at that time dealt with achieving student competence on paper-and-pencil computational algorithms, and that the availability of technology that could do these computations faster and more accurately obligated us to rethink the entire arithmetic curriculum. In 1983, I had the opportunity to give a major address on the subject of a new curriculum for secondary schools in the United States. The title I chose was "We Need Another Revolution in School Mathematics", and in the talk I exhibited the wonders of muMath, the mother of the computer algebra system (CAS) called Derive that is available today on some calculators. At both these times, 20 years and 30 years ago, I thought that a revolution would occur reasonably quickly as people realized the power of these new technologies. I was wrong. In most countries of the world, arithmetic instruction in grades K-6 is about the same as it was 35 years ago. Early algebra instruction remains the same despite the existence of computer algebra systems. The big change has come from a third type of technology ?the graphing calculator. In the United States, well over 80% of all 11th and 12th grade classes use graphing calculator technology, and students are expected to have these calculators for college entrance tests. Similar situations exist in many other places of the world. So we have to ask why one technology has been successful and two others have not. In this presentation, I focus on the technology of computer algebra systems because so much has been said about calculators. Today most teaching that involves CAS is at the tertiary level. But my remarks are aimed at the primary and secondary levels, and in particular on the teaching and learning of algebra at these levels. I will describe what it means for a curriculum to use CAS and the obstacles that have kept CAS from most classrooms and that need to be surmounted before such a curriculum could be implemented on a wide scale. Although it is necessary for me to speak from the perspective of the USA, because my work has been done there, I hope that my remarks will also be felt to apply to other countries and that some of what I say will be applicable to mathematics other than algebra.