When we last left our hero, he was wringing his hands about teaching stats and being behind; we saw a combination of atavistic coverage-worship and stick-it-to-the-man, can-do support for authenticity in math education. The gaping hole in the story was what was actually happening in the classroom. The plan in this post is to describe an arc of lessons we’ve been doing, tell what I like about it, and tell what I’m still worried about. Along the way we’ll talk about trusting the data. Ready? Good.
You know how students are exposed to proportional reasoning in Grade 5 or earlier, and they spend most of their middle-school years cementing their this essential understanding? And how, despite all this, a lot of high-school students—and college students, and adults—seem not to have exactly mastered proportional reasoning?
I figured this was likely to be the case in my class, so when someone showed me the Kaiser State Health Facts site, I jumped right in, and pulled the class in with me. In it, you find all kinds of stats, for example, this snip from a page about New Mexico:
When you see something like this, you can’t make sense out of it until you know more, for example, what does the 96 mean? You have to look more carefully at the page to discover that it’s “per 100,000 population.” And nowhere do you see that it’s also “per year.”
But once you decode it, you can answer some questions. An obvious one is, “how many teenagers died in New Mexico that year?” Before we jump into proportions, though, let’s point out that this is probably not a very interesting question unless you live in New Mexico, and maybe not even then.
So I just did one quick example in front of the kids, and then the assignment was to spend at least 15 minutes on the site, finding some rate of any interest at all, decode it, and report one calculation you can make. We started in class. Kids found things that interested or horrified them. Abortion, pregnancy, and STD rates figured prominently.
For example:
“Mr. Erickson, look at this: the chlamydia rate in California (where we live) is 407!”
I ask, “is that big?”
“Yes!” she says.
“What’s that per?”
“100,000”
“So we have about 800,000 people here in San Francisco. How many cases does that make?”
Pause. Wait time wait time wait time. “About, um, like 3200? Wow.”
There is a lot to like about that. I’m pleased: the student did a proportion without making a big symbolic deal; the use-of-math feels very real-world to me—it’s the way we would do it as adults; the context came from the student’s interest and discovery; and the student was impressed and suitably horrified. I love the way the abstract rate became 3200 real people with an STD.
Students had varied data and varied math techniques; some did these proto-Fermi problems in their heads; some set up proportions on paper. I prompted some to apply rates to our school population (440 students), which gave a truly alarming number when we used the California teen birth rate: 8 students giving birth this year. We could then ask, does that make any sense at all?—and begin what will be a year-long discussion about representativeness of the population. (In this case, I focused for now on the idea that a lot of the teen moms are probably 18 or 19.)
They were to finish the assignment—make one calculation and write it up—for homework. (Not everybody actually did the assignment; that’s another problem.) The next assignment was to construct several rate questions in different forms; I will choose from these to make the quiz on a “rates” learning goal (a.k.a. Standard). We’ll see how that goes on Tuesday.
This general idea—letting students loose to find what they’re interested in—looks like a success for finding meaningful contexts. The jury is still out whether the anecdotal success I felt in class is truly representative. But it did dispel one important fear: that “go find what you’re interested in” would result in a total evaporation of effort into (a) flakiness in the face of a vague assignment or (b) something interesting but not pertinent. I think the key here was the restriction to the Kaiser site and the specific type of problem. Giving them a limited palette of data to choose from helped them focus, and kept them in the proportion/rates zone. Of course, that the Kaiser site had data about sex, drugs, and death really helps.
I realized in retrospect that I had trusted the data to do a good job. That’s based on my own personal experience, and I didn’t really know if it would transfer. For me, I know that I can stand up in front of a group of 100 math teachers, start up Fathom, download Census data, and with some suggestions from the participants, find an interesting conjecture I have never found before. The data and tools always come through. But I’m a data geek: most things are interesting to me, and I can make them at least briefly interesting to a captive audience. Would students find something interesting on their own? Yes, it turns out.
The trick will be to keep this up as things get deeper. I know that not every problem will be student-generated, but the idea of data environments that promote your own problem-posing is really intriguing. The next best thing—as with the assignment reading the New York pedestrian safety study, or a directed Census data investigation—is real, live, current, non-manufactured data where I go ahead and pose the question. I hope I can stay away from those typists (see previous post) learning the new computer system.
A Best-Case Scenario 
Very cool. It might also be pretty interesting to use the Census data to compare mean & median income levels in the U.S. and other countries, and income distributions in general. The open-ended question might be something like, “Where would you rather live?”, and you could bring something like the Veil of Ignorance into it. Just an idea.