math gets all over your face

Math is a problem.  In fact, math is several problems, or many problems, or a multitude of problems, depending on who you ask.  Having survived first year math at UVic, my problem with Math is in the teaching.

The issue here is simple:  hidden under all the rote learning and memorizatiom, math is actually a *creative* subject.

Let me be more explicit:  The most important skill in math is to be able to solve a problem using the tools and information that you have at hand.  This gets harder when you have to transform the given information to get what you need – and it gets harder still when you have to transform the tools you have to get the correct result.  These require increasing degrees of creative thought, or imaginative thought, or abstract thought, or whatever you want to call it.  Newton and Leibniz had it in spades, to dream up calculus.  So did Euler, to conjure up i out of nothing.  Likewise whoever thought up the concept of zero in the 7th century or so.

Is there a way to teach this sort of skill?  In a perfect world, we’d have one math teacher per child, and everyone would learn algebra in grade 4.  But we live in a brutally imperfect world.  Is there, then, a way to make a game along the lines of Brain Age that could teach synthesis of concepts like this?  And could it be made fun?

On the face of it, that doesn’t seem like a very tough thing to do.  Line up a series of questions & problems, sort them into sections, allow for a varying number of valid solutions…and we’ve just described a typical math textbook.  Oops.

What we need is a game that is more than a game:  a system that allows for answers that may come from outside the system.  And that’s where things get difficult, because it then becomes impossible to have a concrete set of answers, or even a concrete set of methods and hints.  The way I solve a problem about area may not be the way you solve a problem about area, and neither of them may be the ‘traditional’ way of finding the answer.  I’ll point you to the diabolical Ovuerture Facile as a kind of inverse reference:  OF forces you to do something odd and non-linear to find the ‘answer’.  Our hypothetical math-game would have to support any odd and non-linear way possible to find the answer.