Hello
I was one of the lab assistants Bob Cowen spoke of. I went on to complete degrees in Math and Physics and finally became a high school teacher. A couple of years later I abandonned that career. The test focused curriculum and the destructiveness of the political climate made it clear there was no future in teaching at the public school level. Now I work at Queens as a Lab tech and instructor. Part of my resposibility is to evaluate our labs and contribute to their effectiveness. This work and my training as a teacher has lead me back to basics. What are we trying to teach, and how best to teach it?
While completeing my undergraduate degrees I did some research in both Math and Physics and one of the most important things I realsized was that skill based courses don't prepare students for or enourage research were they have to learn to apply basic skills in new and ever more abstract ways. Students joining a project have no idea what their getting into and worse, most don't even consider it, for them Math has become a chore. How do we fix that? How do we get them ready for experiences like the Mathematica Summer Camp.
Introducing Mathematica as a tool to teach high school freshmen how to factor quadratics is,in my opinion, problimatic. These students are typically struggling with abstract thinking and, again in my opinion, need more tangible tools. Mathematica, unless very carefully used, could easily become a crutch, something that can do the work for them.
What is needed is a bridge, a research course with training wheels.
That's what Bob Cowens, M Ryohei, and others have done. The course I worked on with Bob had sections from local high schools, and others math majors, and even prospective math teachers. The problem focused, lab style course allows the instructor to choose problems of sufficient depth to satisfy many levels of mathematical maturity.
In Bob's example, the students were introduced to the Josephus problem on paper and then shown how to use Mathematica in a more or less brute force approach. The emphasis here is on the abstraction not on Mathematica. They go on to learn that simple models can be solved in many ways and learn that there are more elegant ways to solve this problem. Finally, after a couple of iterations, they chose their own research project and with guidence and peer review learned how to report their results. This works. I helped one class of high school students produce a magazine based on their research into two person impartial games. Some of our students not only contributed to the magazine, they went on to present papers at a local Mathematical Association. You can't argue with sucess.
Why does this work? This is a question with millions of research dollars behind it, here's my two cents. This style of teaching works because it's immersive and inquiry based. The students have to immerse themselves in the problem, looking for patterns abstracting the data. They also have to learn to use the tools by doing, working out methods as they go. And in the end, they get real results they can call their own.
The challange is to get this kind of learning into the high school curriculum. Bob trained high school math teachers and that's a good start. As is preparing well designed problems sets to be used at that level. Beyond that we have to get the word out that this is easy to impliment, gets results, and is fun.
