Thursday, March 08, 2007

Time Wasting with Probability

OK, I'll be the first to admit that I have been known to stoop to the level of pandering to the masses. The topic for class tomorrow is dimensions and the fourth dimension, and I am planning on showing a seven-minute clip from The Simpsons where Homer visits the third dimension. However, I must point out that tomorrow is the Friday before spring break, and I'm anticipating massive absenteeism, so the 50-minute lecture on essential material didn't seem to be the best pedagogical choice. Plus, it's not like I'm claiming that this is a good idea that you should all go out and do -- unless you also want to pander to the masses, of course.

While proctoring the calculus exam this morning (more on that later -- haven't started grading yet, as I'm waiting for the viral particles to degrade), I read the latest issue of Mathematics Teaching in the Middle School. This article about probability games presents ideas that put my time-wasting activities to shame. This must have taken way more than seven minutes of class time.

I can sort of see the point of playing games of chances, like the dreidel game, if the point of the lesson is clear, the students keep careful records, and the data analysis is thoughtful and well-summarized.

However, one of the activities suggests having the middle schoolers play mancala and keep track of whether the first player wins or the second player wins and to calculate the probability that the first player wins. This is primarily a game of strategy, not of chance. I can think of no reason why middle schoolers should be playing this game during a probability lesson.* The article claims that this is an example of experimental probability and that by seeing that different groups get widely varying results that this can be used to show that there isn't an underlying probabilistic mechanism. To me this seems more likely to foster the simplistic view that any so-called study that collects data shows what you want it to show -- even if the methodology is crappy.

When about half of the fantastic students in my wonderful calculus class can't work with rules of exponents, my gen-ed students can't do simple problems with the Pythagorean Theorem, and thousands of entering freshmen are so lacking in algebra skills that they struggle to pass an algebra course, I bristle at the idea of suggesting such serious time-wasting in middle school math.

*unless you want to use the game board as a model for Markov Chains.