Mathematical Analysis and Its Discontents, or: WTFCYDWT?!?
It is impossible to escape the impression that people commonly use false standards of measurement — that they seek power, success and wealth for themselves and admire them in others, and that they underestimate what is of true value in life.
-Sigmund Freud, Civilization and Its Discontents
I have opinions, and an internet connection!
Disclaimer: You don’t have to listen to what I say. In fact, I’m actually weirded out about how little push back there is on these blogs. Especially mine, since I spend more time floundering and being a shitty teacher than most. So, maybe not so much backslapping or grabassing or whatever.
Second disclaimer: I AM NOT DISCOURAGING THE USE OF WCYDWT.
Third disclaimer: I am sure that those cited in this post would totally agree with me, and have probably actually said the same thing at some point in the past.
Here are some fun facts:
- 50% of all people looking for roommates on Craigslist will be heroin junkies.
- 100% of all girls you date that you met at Daniel Johnston concerts will recently have been convicted of a crime.
- 50% of visits to Columbus, OH will result in being punched in the face by a stranger (and for no reason!).
- 33.3% of all visits to Six Flags will result in being taped as part of a Candid Camera show.
Of course, these are ridiculous. But true (!), if I limit the data to only my life experiences.
I have a real worry about unbridled WCYDWT (or #anyqs). I mean, I guess I have a real worry about bastardized math. Not just because it can be wrong, but dangerous. Look at the shit that Harold Camping just did: pulled together a bunch of random ass numbers with arbitrary significance and convinced a decent number that the rapture would occur.
I’m not saying that any of you guys are Harold Camping, or that using this stuff in your class makes for bad math. Just the opposite is true. But we have students who are going to experience bad journalism, or politicians invoking some think tank that is politically backed and uses biased data to say whatever they want. And so when people make these lessons that come out all neatly tied up with a ribbon around it and everything works out perfectly, kids begin to make bad assumptions about the way the world works, and the way math works. Like, that it ALWAYS WORKS.
We’ve all seen the magic that Dan Meyer pulls. We’ve also got the heir apparent, Dan Anderson, who keeps finding some really great ideas and is running full speed ahead with the “3 Act” stuff. I love how you are immediately drawn in. I love the story aspect. I love the engagement aspect. I love how well everything is done.
I’m not sure I always love the conclusions that are drawn.
THE SONG OF ROBERT WADLOW
I totally goofed by not framing this lesson in the 3 Act form, but you totes could. Start with the picture of Wadlow. They will freak out and be totally into it.
I was doing a unit on regressions, and so I had everyone collect data. They had to get the shoe size and height of 10 other people in the classroom. They plotted the points and found the line of best fit for height vs shoe size. Because everyone took different data, everyone had different resulting equations. I had them figure out how tall I should be given my shoe size of 12 (which, FUN FACT: is the same size I wore in 7th grade). I seem to have slightly bigger feet than I should, because most people went over my height by a couple inches. But everyone was pretty close, and thank god no one had me at a gangly height of like 6’6″.
Anyways, then I put up this picture. I hadn’t had this great of a reaction in a while. Of course, the first question they all asked was, HOLY SHIT, HOW TALL IS THAT GUY?
I mean, HOLY SHIT. So, I put up this picture too.
They had answers all over the place. 7′ to 12′ was the range, if I remember right. They were really confused. Wait, what did we do wrong?
How can we all be this far off?
How can we make our answers better?
Uh.. is it because we all started with different data points? What if we combined all of our data? What if we took more data? I just kept shrugging my shoulders.
What followed was a really good discussion on the dangers of extrapolation, really led by them. They talked about predictions that they had heard about fossil fuels or the price of milk or world population and how it would be really hard to predict what these things would be like way down the road, like when they were 60 years old.
I followed the next day with some canned data (sorry, everybody) that modeled growth rates of sharks over time (I wanted something that they had a little less knowledge of). Plugged it all in, they did a linear regression, and BAM! We could predict the length of a shark given how old it was! The problem was, when we looked at old sharks, they should be something like 70 feet long. And the data just never really seemed to fit right anywhere. So we had to add another tool. Logarithmic regressions to the rescue!
I kept giving them data and kept just letting them assume stuff. We ended up with coffee that cooled to absolute zero, or the population of Brooklyn being that of India in the future. We kept having to refine our tools and refine our methods. (Editor’s note: You know, like logarithmic or exponential regressions. Because not everything is a line, dammit).
We are all afraid of being messy or things not working out, but those are the most valuable lessons. I’ve said before that people who observe my class loved how my classes didn’t get mad when we chased things that were totally wrong. We would just try a new approach when we saw that our answer was incorrect or unreasonable. I think that that is a much more important skill.
Editor’s note: Oh yeah, maybe I should emphasize that I did use the regression to make a prediction that was pretty close, when they found my height. Then, whenever we used a new tool, like a logarithmic regression, we would see the validity of our work. I’m not saying throw the baby out with the bathwater. Just, I guess, throw out a lot of bathwater.