Here is a link to an interesting talk/text about how we could get people to like MATH: use computers for the tedious steps. http://news.ycombinator.com/item?id=4376306
He has a good point, but I still think children should know how to do math with only pen and paper.
Once you see what the computer can do (solve quadratic equation), then you should be able to solve it on your own too. View source, yes, but also explain source.
Come to think of it “explain source” is quite good as a name for what Minireference is meant to be. This could be the turning point in terms of naming. Come to explain source dot com and learn about anything. For any function/operation/algorithm out there, I will give you a js/py implementation and explain the source code from first principles. For example, a physics simulation engine could be used to teach you classical mechanics, wink wink.
Ok. So I hear you saying now “I am reading this blog and there is one guy saying that computers are good and another guy saying that people need to understand the details and be able to do things with pen and paper. A modernist giving a TED talk and the blogger is some sort of idealist who wants people to actually understand math.” and wondering where the story may be going.
In reality, there are not two opposing views. Both points are important. Computers need to be used to do cool math and physics stuff and demonstrations. Afterwords, the interested student can explore what is under the hood of each function/operation/algorithm whenever he wants to learn how it works. But definitely one should always start with the applications of any given concept. This is the pitch part of any lesson. Why would I want to know about that? People really don’t care about what you have to say in general, and on top of this you will be teaching them math which generally doesn’t get warm receptions as people have phobias and complexes. The pitch therefore becomes that much more important.
Ok I will end this with the summary. To teach concept c, you have to start with a really good story about c, to get people interested, then you show some cool applications of c (possibly using a computer for more wow effect) and then you explain what c is all about. Most importantly (in math) you need to discuss the connections between c and other stuff.