How To Teach Maths?

A recurring question which keeps coming up in discussions is how mathematics should be taught. There is a strong view that given the computing power which is available to us, we should relook the basic maths curriculum. So i went looking, and found this video which i feel looks at the problem in a logical way.

Conrad Wolfram is giving some compelling reasoning for why maths education should change, and gives a description of how it should change, too.

Hand-culcating the mundane way should not be the focus on the curriculum. Rather, the focus should be on building and enforcing the concepts, and leave the calculating to computers. In other words, as he says, students should be taught the procedures which define fundamental concepts, but the implementation of those should be left to computer programs. For example, students should know what a square root it, how it is calculated, but they shouldnt have to calculate, beyond illustrations. And here is the cool part he says … focus on teaching students how to write programs to calculate square roots, rather than having them mechanically execute the procedure for calculating. This will immensely help students clarify their concepts (how can one write a program without understanding the underlying principles to a very large extent?), while at the same time help them become more comfortable with the concept of application of these concepts. In other words, our mathematics curriculum should stress understanding and application (application to real world problems is a very good way of teaching these concepts) rather than stress on the mundane calculations which stress out students as well as parents alike. After all, why should a child lose marks in an exam (thats what happens) if he or she takes the square of 5 to be 10 when all the conceptual aspects of the solution are correct, and the only mistake is a calculation mistake?

Connect this with the post i had written earlier, and a rather innovative picture of mathematics teaching emerges.