TED: Teaching math
A little while ago, I voiced my desperation about teaching stats to computer scientists. Or rather the problems of framing this so they would find it interesting.
I went with some problem descriptions and trying to reduce stats to "figuring out what is going on" rather than arithmetics. I don't think I nailed it that well, but at least I tried.
This TED talk is quite relevant to this:
Math is not arithmetic, but ways of reasoning about the world in a quantitative way.
The introduction to Modern Heuristics, that describes that without a context getting you thinking about the right models, most people cannot solve rather elementary math problems. Not even math professors. Math is about formulating the models, identifying the problems, it is not about doing equations.
I wish I was better at teaching this.
The arithmetic (or in general most of the equation manipulation) is something computers do better. Let's focus on modeling the world.
February 3rd, 2011 at 7:33 pm
But "reasoning about the world in a quantitative way" sounds more like physics, or science in general rather than math, doesn't it? Math doesn't have anything to do with the world in general, although a subset of it can be used as a scientific tool for understanding the world, much as a subset of biology can be used as a medical tool.
That being said, not being a mathematician (rather farther from being one than you are, in fact), I do agree that motivating the problem makes it more interesting for students who want to use the math to solve actual problems. I remember the couple of stats courses I took to be rather dry and theoretical and it was hard to see how what I learned could be used to analyze actual data.
February 3rd, 2011 at 7:39 pm
Actually, I agree that math is not science. Nor, I think, is computer science. Both are tools we use, nothing more. If the math or cs doesn't fit with reality, it isn't really a problem.
My point, though, was that both are tools we can use to reason about the world, and -- I guess this is my point -- nothing more.
It is not about the math you do, but about the reasoning about the world that makes it useful for science.
Without math, we end up with "just so" stories. With it, we have something to quantify the world and our theories with.
Too often, I fear -- and in my own studies that was definitely the case -- it is about being right or wrong. Applied math is not about being right or wrong, but about making useful predictions about the world.
I think we actually agree on this, from how I understand your comment. I didn't mean to say that math was about understanding the world. What I meant to say was it was a language to discuss the world in, and we shouldn't be bogged down in the arithmetic.