(This posting was prompted in part by a brief mention of the issue inĀ squareCircleZ )

It is often claimed that Computer Algebra Systems will (or already do) eliminate the need for much of what is taught in high school and college math classes but I seriously doubt that that is the case.

In fact, despite claims of hours spent on “mindless algebra”, I believe that the amount of actual algebraic manipulation required in a typical decent high school or college math course takes less time to do by hand than would the process of learning how to use a CAS for the same purposes. And, to the extent that time is spent on algebraic manipulation, it is not wasted because it serves to reinforce the understanding of what the expressions involved actually mean.

However, even thought the CAS of tomorrow will look very different from those of today, I do not consider the learning of a CAS to be always a waste of time. Some (few) students will need to do enough complicated algebraic simplification in the course of their later careers that the time spent learning how to learn to use a CAS will actually be useful. Also some (few?) instructors will be capable of using a CAS to add so much extra richness to the learning experience as to justify the time and effort of the students, even if they will never have to do any algebra ever again.

But for those who will not ever be (aware of) doing algebra again, actually understanding the algebra will really be useful whereas learning a computer program to do it will not.