I saw something on twitter a couple of days ago, and I promised to write this blog post about it. As usual, I'm behind on all the stuff I want…
Stupid Grading Tricks
A bunch of people have been mailing me links to an article from USA today
about schools and grading systems. I think that most of the people who’ve
been sending it to me want me to flame it as a silly idea; but I’m not going to do that. Instead, I’m going to focus on an issue of presentation. What they’re talking about could be a good idea, or it could be a bad idea – but because the
way that they present it leaves out crucial information, it’s not possible to meaningfully judge the soundness of the concept.
Idiot Math Professors, Fractions, and the Fun of Math
A bunch of people have been sending me links to a USA Today article about a math professor who wants to change math education. Specifically, he wants to stop teaching fractions, and de-emphasize manual computation like multiplication and long division.
Frankly, reading about it, I’m pissed off by both sides of the argument.
Dirty Rotten Infinite Sets and the Foundations of Math
Today we’ve got a bit of a treat. I’ve been holding off on this for a while, because I wanted to do it justice. This isn’t the typical wankish crackpottery, but rather a deep and interesting bit of crackpottery. A reader sent me a link to a website of a mathematics professor, N. J. Wildberger, at the University of New South Wales, which contains a long, elegant screed against the evils of set theory, titled “Set Theory: Should You Believe?”
It’s an interesting article – and I don’t mean that sarcastically. It’s over the top, to the point of extreme silliness in places, but the basic idea of it is not entirely unreasonable. Back at the beginnings of set theory, when Cantor was first establishing his ideas, there was a lot of opposition to it. In
my opinion, the most interesting and credible critics of set theory were the constructivists. Put briefly, constructivists believe that all valid math is based on constructing things. If something exists, you
can show a concrete instance of it. If you can describe it, but you can’t build it, then
it’s just an artifact of logic.
Some of that opposition continues to this day, and it’s not just the domain of nuts. There are
serious mathematicians who’ve questioned the meaningfulness of some of the artifacts of modern
set-theory based mathematics. Just to give one prominent example, Greg Chaitin has given lectures in which he discusses the idea that the real numbers aren’t real: they’re just logical artifacts which can never actually occur in the real world, and rationals are the only real real numbers. (I don’t think that Greg really believes that – just that he thinks it’s an interesting idea to consider. He’s far
too entranced with set theory. But he clearly considers it valid enough to be worth thinking about
and talking about.)
Innumerate School Administrators
Have you ever wondered about the real reason why math education in our schools is so awful? Why despite the best efforts of large numbers of parents, the schools seem to be incapable of figuring out why they’re so dreadfully bad at recognizing the difference between a halfway decent math curriculum and a trendy piece of garbage?
Read below the fold for a perfect example of why. The short version: the people who are involved in running education in America consider it perfectly acceptable to be idiots when it comes to math.