A
K12 Mathematics Curriculum with CAS: What Is It and What Would
It Take To Have It In Schools?
Zalman Usiskin
zusiskin@uchicago.edu
The University of Chicago
U.S.A.
Abstract
Handheld fourfunction 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 paperandpencil 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
K6 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.
