TED talks: Teaching kids real math with computers

http://www.ted.com/talks/lang/eng/conrad_wolfram_teaching_kids_real_math_with_computers.html

I came across this very interesting TED talk by Conrad Wolfram, the brother of Stephen Wolfram. Surprisingly, his ego is a punctured balloon next to his brother's zeppelin; but I digress.

He outlines a novel way of teaching mathematics: using computers to perform calculations in the classroom. While the former is a commendable idea, I don't see this working, at least not in such a way. Note that I certainly don't object for this idea to be implemented in universities and advanced high school classes, but I think it is not realistic for elementary school and early of high school.

Don't get me wrong, I am a huge fan of Computer Algebra Systems (CAS). There is, however, an inherent problem in adding a layer of abstraction on top of mathematics. I'm not convinced that being taught to solve linear systems by typing LinearSolve, or expand binomials by using Expand, teaches anything about the fundamental process of mathematics. Doing it by hand reveals the process - solving for variables, FOIL, substitution, etc. Sure, the process could be taught in addition to the shortcut, but if we are to believe Conrad, only a very minimal treatment is necessary. It's analogous to teaching assembly language with BASIC: yes, you can do many (actually all, it's Turing complete!) of the same functions easier, but are you learning anything about assembly language?

Mathematics is an incremental process; new knowledge must be based on old. Can someone who doesn't understand binomial expansion understand factoring quadratics? Not likely. Without understanding of the process, more complex topics cannot be understood, and eventually we'll get schoolhouses full of children mindlessly copy-pasting arbitrary commands from their work e-books to their CAS and back. Not that this is very different from school mathematics today, but the value in following a logical order of calculations instead of receiving instant output cannot be ignored.

In terms of interactivity and learning to solve real-world problems, I wholeheartedly agree. I often hear complaints and questions as to the real-life applicability of high school math, and it is often true. More work must be done in developing problem solving and pragmatically-oriented math classes.

Please post your opinions on the subject, I'd love to hear them!