Wolfram suggests that the way to teach ´understanding´ of maths is not by insisting that the maths be done by hand, but by insisting that the maths be demonstrated by ´COMPUTER PROGRAMMING´. whoohoo!
Hmmm...can you give an example of this?
Yes, I have uploaded two examples of this in the past week (compute.rex) and (pdeclib.py pilib.py) ! Neither of those scripts can be written without a thorough knowledge of integral and differential calculus; end of story.
Its one thing to be able to write out (on paper) what you think you understand about mathematical relationships. It is a horse of another color (however) to place that understanding into a computer program and run it! If it runs, you pass... if it doesn´t run, well you may get partial credit for trying but its not an A.
For example how can computer programming help teach those magical first steps in differential calculus. That moment when 0/0 suddenly disappears and you get a useful result. That moment when the students mind reels, whoa you can't do that!, oh but yes you can.
I remember that day well (1973) when I ´finally´ got the idea that a first derivative of a function was the slope of the line (function) tangent at that point on the curve... but, if I had had the Wolfram modeling in front of me demonstrating the limit (and showing me the tangent line, so that I could ´feel´ it) I would have picked it up much quicker. I did manage to learn differential and integral calculus (but Wolfram would have made things a lot more fun!)
Granted you can replace the medium of pencil and paper with the medium of mouse and screen. Does that really help? Doesn't it just make the whole process more expensive?
Maybe. The RPi sure helps with that... I mean, yeah, its taken a long long long time to get affordable ´free´ (as in Libre) computers into the hands of kids... and its about time... and I´m all for the revolution in maths education that I think is about to happen; whoohoo