On Thursday, August 30, 2012 2:09:19 AM UTC-6, Alexei Boulbitch wrote:
> Let me just point out that the origin of this interesting and passionate discussion was the > question of what should be the content and tools of the mathematical education for students in > non-mathematical specialities at present, observing that since long computers have become the > reality of our world.
The nature of mathematics is very relevant here. If mathematics is the product of a magical sense that detects objects in a supernatural world, then it is impossible to scientifically approach the problem of teaching mathematics. But if mathematics is a product of the natural processes of cognition that humans use to find their way in the world, teaching mathematics is similar to other kinds of teaching. Then, the methods and insights of cognitive science are likely to be of use in answering your question.