Maths should be more practical and more conceptual, but less mechanical.
I couldn't tell you in any detail how my computer works. I use it with a layer of automation.
Computers do the calculating to allow people to transform the world.
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.
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.
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.
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.
Any tool can be used badly.
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