I couldn't tell you in any detail how my computer works. I use it with a layer of automation.
Conrad Wolfram
Maths should be more practical and more conceptual, but less mechanical.
Computers do the calculating to allow people to transform the world.
Any tool can be used badly.
Answers are what we are trying to get at; search is a process by which you may be able to get answers, but it's not the end goal. It's a mechanism.
Maths is fundamentally a different process in education than it is in the real world. There is an insistence that we do maths by hand when most of it is done by computers. The idea that you have to do everything by hand before you can operate a computer is nonsense.
Calculating does not equal mathematics. It's a subsection of it. In years gone by it was the limiting factor, but computers now allow you to make the whole of mathematics more intellectual.
Every math curriculum in the world is based on the idea of hand-calculating, and most of what you're teaching is how to calculate. And I think the resistance to this is very variable.
One thing is for sure: most of the people admitting candidates to universities for technical subjects are pretty dissatisfied with the level of math education.
