At Weston High School we’re considering the use of mathematical symbol-manipulation software such as Mathematica or Maple. Our theory is to pick one of these for a trial run for a year — just one copy per teacher, for use in planning lessons and in class demos. Then we will reconsider whether they would be appropriate for college use. The arguments on each side are pretty clear: this kind of software brings extra power to students and lets them accomplish things that they couldn’t do without it, but it also risks erosion of techniques that many people consider to be basic skills. For example, why learn to factor if the computer will do it for you?
One possible response is to acknowledge that maybe the computer should do it for you. After all, we no longer teach the pencil-and-paper square root algorithm, and its loss doesn’t seem to have damaged anyone.
This isn’t just an argument about math teaching. The whole notion of what skills are basic changes from generation to generation. We can no longer do a lot of things that our great-grandparents could do, but there are a lot more things that we can do. Isn’t it more important in this day and age for me to be able to fix my computer when it stops working than to make candles or construct wagon wheels? Who knows what basic skills are anyway? I have an intuition about them in math, but my intuition is based at least as much on my own training as it is on a reasoned consideration of what’s basic in this decade and the next. A local tutor objects to our inclusion of cryptography in our high-school math curriculum, thinking that it’s a frill that replaces important things like the measure of an angle inscribed in a circle. Her argument? The SAT includes a question on the latter but nothing on the former. But surely there are more authentic ways of determing what’s important than the College Board’s outdated ideas of what ought to be on the SAT. Cryptography may well be the single most important application of mathematics today, regardless of what the College Board says.