The lesson was vaguely three-acty.
How long does the calculator say that a person born in the 90s will live? The 80s? The 1890s? Why the difference?
I asked one class: "When will you have to be born to expect to live to 100?" The other class got "How long can you expect to live if you're born in 2010? 2050?"
What do you notice about the table? Take a guess for 1980. My guess is 60 years. You guys like that? Why not?
How good is the following rule: "life expectancy = years * 10"? Is the rule "life expectancy = years * 9" better or worse? How can you find a rule that's better than either of them? What are you changing in the equation?
Can you find an equation that fits it pretty well? How far off would the predictions be?
Here's our most recent data. What do your equations predict?
What went wrong?
- Kids didn't seem into it.
- Kids didn't know where to jump in.
- Kids were confused by the idea that it has to be a rule that gives a line.
- Kids thought it unnatural to make a prediction based only on a few prior data points.
- It wasn't clear to me or them what they were trying to predict. Since we can't check their actual predictions (cuz they're in the future) we have to just limit the data that we make available to them. This seems to be a limitation of the "data analysis of social stuff" type of problem, and an argument for doing regression problems with stuff that we can actually test in the classroom.
- We'd done a similar, and superior, problem last week with data from 100m dash times. I wanted kids to end up with actual equations as models, and I don't think this was different enough to necessitate equations. A lot of kids repeated their tricks from last time: averaging the rate of change, coming up with recursive rules instead of closed-form rules. I didn't feel as if anything, other than my insistence, was pushing them towards closed-form equations.
- Post it as a historical puzzle. Let's say you were in 1960: how far off would your best prediction be for life expectancy in 2010?
- Find a better hook. I needed something like that life expectancy calculator just to make sure kids knew what "life expectancy" means.