a different breed of math

I haven't blogged in about a month, and I just wrote a really bad essay, so I'm feeling the need to put something up here.

this quarter, I'm taking the graduate-level statistics I course taught by Hal Stern (totally awesomely geeky). now, granted, stats has never been my strong suit; I only took the very basic introductory stats course in undergrad. the professor spent most of the time saying "I don't know where this formula comes from, it's calculus or something, but just use it." most of the probability was a rehash of stuff I'd learned in discrete structures and math courses. half way through the semester, I stopped going, and my exam scores went up. the course here is a total contrast to that. Hal is a way bad ass teacher; he's great at explaining stuff at any level, so that the statistics ph.d. students understand it as well as the business students and others like myself who had barely any undergrad stats.

however, despite the phenomenal instruction, the course has been one of the most challenging I've had since I got to grad school. the next hardest thing would probably be the grad level formal languages and automata course I took while an undergrad. or at least, it was that difficult for about the first month. once I got the swing of it, it was able to keep up alright. not that I've been doing that well on the problem sets and exams, but at least I feel like I'm getting the concepts. part of this may be due to the fact that I haven't taken a non-computer science style math course since calc 3 my first semester of college. however, I think the lack of preparedness goes deeper than that.

statistics is a very different sort of math, similar to the way that discrete math is different from calculus, and geometry is different from algebra. it's a different way of thinking, a different mode of reasoning. yes, the guts of statistical theory is built on some pretty hardcore calculus, but the way most people use statistics seems to require a different mind set from other sorts of math. I learned arithmetic, algebra, and geometry from a rather young age, so i didn't really have a problem grasping calculus. also, in middle school, I was in the MEGSSS program, this wacky alternative math program for middle schoolers in FL. the first year curriculum teaches more or less set theory, functions and relations, and modal logic without calling them those things. when I got to college and took discrete math, these concepts came back up. I think I was able to pick it up because I had seen the stuff before.

but stats I never saw until I got to college, and even then the professor was less than helpful. I think, had I been exposed to a statistics course as a middle or elementary schooler, it would not be nearly so difficult for me to pick up now. I suspect a lot of people would argue that most kids wouldn't be able to understand stats at such a young age. I think kids are capable of way more than we give them credit for. since schools in general suck, kids aren't interested in learning and so don't really push themselves. there's also this cultural stigma that it's not cool to be smart (which is slowly lessening, but it's still there). however, these are subjects beyond the scope of this post.

also, I think some people would argue that most people won't need to know or use statistics. nothing could be farther from the truth. it's difficult to go a single day without reading something in the news that cites statistics or says that some result is statistically significant. what does that mean? people sort of take for granted that it means something, but what? having at least a rudimentary understanding of statistics not only helps one understand what statistics mean, but it also helps one realize that, with the proper manipulations, statistical data can often be massaged into saying whatever the researchers organizing the study want them to say. yes, this makes it more difficult, because you can't accept everything at face value, but one would hope you weren't doing that, anyway. furthermore, it gives one the ability to see where studies have been constructed with flaws or biases that affect the results. a working knowledge of statistics helps foster a healthy skepticism and critical judgment.

so, as much as I hate standards for public education, I'm calling for a new math standard that incorporate a statistics course somewhere in both the general middle school and high school mathematics curriculum. I don't really know where this would fit in or if it's practical at all, but I'd love to hear if someone else has thoughts on it.