Hi Mike,
I have been using Mathematica since Version 2, a bit over twenty years, and I am a real proponent of math education. I am not an educator, but I think Mathematica would be a great tool for helping students develop intuition in math. A good example is looking at the solution to a 2nd order differetial equation as the initial conditions, resonant frequency, and damping factor are adjusted. However, my first real exposure to that demonstration was in TV programs aired by the Open University, in the UK, before Mathematica became availabe.
Having said that, I think there are risks to computer-based math education. It could lead to the attitude that it's just the results that count. If I know how to put the problem into a computer and get the answer, that's all I need. Learning math is a lot more than that. It's about how to find the path between facts and their implications. How to formulate a question that can be asked of the knowns, and a process for getting to the unknowns. And even the ability to know when the knowns aren't enough to provide an answer. Maybe you can determine the loan payment for that car on your computer, and also balance your checkbook (does anybody still do that?) and decide if you have enough for a downpayment, but can the computer tell you if you can afford it? Even for people who will never work in a field employing math, math is important. (Especially the dreaded story problems.)
For those who will work in mathematics, doing it yourself is a critical part of understanding. Mathematica can solve that high order differential equation for you, but the process of learning to reduce that equation to a set of coupled first order equations, diagonalize the coupling, and transform the basis to a linearly independent set, provides an insight that will transfer to many other mathematically similar situations.
In short, I think computer-based instruction can be very useful. But mathematics is not a spectator sport.
Kind regards,
David
