Wednesday, January 30, 2008

Skyping About Math

edubuntu terminals, LEP High
I set my cell phone alarm for an early rising and hopped on a pre-arranged Skype call from Germany to chat with some young math students and their instructor about our futuristic math teaching experiments in Portland, Oregon, an open source capital.

Basically, we phase in object-oriented talk when introducing such concepts as vectors and polyhedra, and then we use those vectors to actually build those polyhedra on screen. I didn't go in to all the details, although I did hold up the MITE cube and dissect it (this was a video linkup).

In Germany, there's more of a top-down, "government tells us" approach, whereas the USA has this tradition of treating states as laboratories, where many competing approaches run in parallel, a kind of genetic algorithm wherein new hybrids at least have a fighting chance of finding a place in the sun.

Our computer math hybrid starts using Python pretty early, mainly to generate sequences at first, such as the Fibonacci numbers and successive rows of Pascal's triangle (e.g. see Pippy on the XO for a currently non-generator-based approach).

generator based Pascal's, Python 2.5.x
These are very short programs, with longer ones provided as scaffolding, so rather than losing lots of time to debugging, we stay with much of the traditional content (linear and polynomial functions, trigonometry (some spherical), some calculus ideas though with a more discrete flavor).

However, we also mix in more semi- and non-numeric algorithms (e.g. around XML), plus some elementary group theory with an eye towards explaining RSA in some detail by senior year high school (group theory also helps in later physics, intimately connects to those polyhedra and their rotations).