CAS 1

COMPUTER ALGEBRA SYSTEMS (CAS)

Computer Algebra Systems have be available since the early 1990's. A CAS usually has the ability to draw graphs, produce tables of values, be programmed and run programs. All of this sounds like a graphing calculator. However, a CAS also has the ability to do algebra in symbolic form.

Some CAS are built in handheld form and look like graphing calculators; Texas Instruments, Casio and HP all make such machines. They are also available as computer software; Mathematica is probably the top of the line, but many simpler systems are available some of which are free and/or open software.

All of this make a package for DOING mathematics. Specifically, they can do all the symbol manipulation for the user. From x + x, to factoring, to finding complicated derivatives and antiderivatives, to matrix algebra and statistics computations, the CAS makes the drudgery of algebraic and arithmetical manipulation a breeze.

Nothing this wonderful is without controversy. There seems to be the opinion that the purpose of school mathematics is to teach children how to do these computations. I submit that this is not the purpose. Rather, the purpose is to know and do mathematics. It is more important that students know when they need to ___ and what the result means than to be able to ___ . (You fill in the blank with whatever you want say, factor, differentiate, antidifferentiate, solve an equation, etc.)

Computations are often the longest and most difficult part of doing a problem and the least useful and informative. You have to get past them for sure. This is where a CAS is used.

Like any tool, students need to be taught how to use a CAS. It changes the way mathematics is done. This is, to my knowledge, is not being done. Why?

For further reading see Algemetic.