What About Computer Algebra Systems (CAS)?
Saturday 6 April 2013
I remember well the first time I saw a computer algebra system (CAS) in action. It was 1984 and I was in my first year of teaching. The head of the mathematics department at my school was excited (he was not easily excited) to show me something that he had just acquired. He had a computer (I think it was an Apple II) that was running a program called muMATH. If I remember correctly, he showed me how it could find the derivative of a function - symbolically. Not just find the numerical value of the derivative of a function at a specific point, but find the symbolic expression for the derivative.
In the nearly 30 years since then, computer algebra systems have been much more user friendly, more powerful, and far more accessible. It used to be that one who have to spend quite a chunk of money to buy a CAS software package such as Mathematica or Maple. One of the exceptions was the program Derive which was developed by the same company, Soft Warehouse, that produced muMATH. Derive was relatively inexpensive, did not take up an enormous amount of memory, and there were considerable number of mathematics educators actively writing materials and promoting its usefulness as a teaching and learning tool. The International Derive User Group (DUG) was founded in 1991 and is still active. Derive was purchased by Texas Instruments and the CAS capability on the handheld calculator models TI-89 and TI-92 (Voyage 200) was based on Derive.
During the latter half of the 1980s and the 1990s many teachers (me included) were convinced that CAS was going to have a major impact on how mathematics is taught. I have no research to back me up, but my sense is that the feeling that CAS can (and should?) change teaching practices is held by a significantly smaller portion of the mathematics education community than, say, 20 years ago. If so, why is that? I'm not sure, but there is no doubt that the accessibility of CAS - and, hence, the opportunity to use it in the classroom is so much easier nowadays. Take, for example, the computational search engine Wolfram Alpha - developed by Wolfram Research and based on its mega-powerful (and expensive) mathematics software pacakage Mathematica. What do you think of the following widget created by Andy Kemp from Wolfram Alpha showing the power of CAS as a teaching and learning tool ?