Computers in mathematics teaching = more math thinking

There is a very good TED talk (17min) below by Conrad Wolfram who makes a very powerful argument about how Maths teaching can be enhanced with the aid of computers. But it is very sad to read the initial comments on the TED site from the quite smart people who use TED. Most of didn't hear much of what he said. If you view the video you find that

Wolfram was at pains to say that Maths is about thinking mathematically, and its declining status in schools and broad aversion by many people is because the calculating (computation) part of Maths dominates what happens in schools and the other aspects are neglected. He says more attention should be spent engaging students with the three other aspects listed here. But the critics of changing the way things are done in the classroom often do not value the end point of learning. They think it is important for students to put in the hard work of learning how to calculate, remember, perform base level skills in the expectation that one day they will get a chance to apply these skills on real world problems.

For those interested in just one example of how this can work in practice, the Alice programming language is a wonderful tool to use from mid primary to advanced programming levels.