Fifteen years ago desk top computers and calculators
were viewed as quite different. Computers were powerful, expensive,
and ran sophisticated software. Calculators were inexpensive
and did only elementary numerical computations. Scientific calculators
are now very inexpensive ($10 to 20 US) and have significantly
changed some of the mathematics curriculum taught in most countries.
For many years desktop computers have remained expensive and thus
still are not used nearly as widely as they should be in the teaching
and learning of mathematics in colleges and universities. Ten
years ago calculators took a giant evolutionary step and added
new software functionality in ROM found only desktop PC computers.
These were the so-called graphing calculators, first invented
by Casio in 1985. Graphing calculators started a revolution in
the teaching and learning of mathematics in the United States
and in many other countries as well. Before graphing calculators,
professors had to rely exclusively on expensive computers (usually
housed in a separate computer laboratory) to deliver computer
enhanced visualization in mathematics teaching and learning.
Only a few elite colleges and universities could provide such
an experience to all mathematics students on a regular basis.
A CAS (computer algebra system), available usually only on expensive
PC's, generally consists of three main software packages - symbol
manipulating software, numerical solvers, and computer graphers.
1995.
In late 1995 Texas Instruments introduced the
TI-92, a relatively inexpensive hand-held computer with
built-in computer symbolic algebra system (using powerful DeriveTM
algorithms) and computer interactive geometry (an almost
complete version of Cabri IITM). It was about 2 times
the cost of a graphing calculator but probably 25 times more powerful!
It was the first of a no doubt new generation of powerful hand-held
computers for mathematics education representing the merging
of calculators and computers. It is clear to us that inexpensive
CAS technology will change the nature of the current style of
"computing" in the teaching and learning of mathematics
from an almost exclusive paper and pencil symbol manipulation
approach to a more balanced approach.
CAS allows new pedagogical methods. For example,
calculus procedure are presented as "white box" procedures
where we allow student use of some algebraic, non-calculus, "black
box" procedures. The white-box/black box principal was
first introduced by Professor Bruno Buchberger from the Research
Institute for Symbolic Computation in Linz, Austria. We now
need to be more specific and explicit about a controversial issue.
We can no longer spend out time in the mathematics classroom
doing everything we did in the past paper and pencil era and
adding on the many topics and methods our students need for the
technological intensive future they face. We have much to learn
about our future mathematics curriculum and the details of how
we will get there.
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Plenary Sessions |
© Asian Technology Conference in Mathematics, 1997.