So, it is spring break of my first year of teaching, and from conversations with my first year teacher friends it seems that I am not alone in feeling like most days (and nights) swing wildly between “too many thoughts and not enough” about what to do in the classroom and how to get drier behind the ears ASAP.
Instead of trying to barf all of that up at once, some thoughts on this post and lesson: Life Expectancy, and a lesson that didn’t work.
Rational Expressions is definitely one of the blogs which I read completely and occasionally with notebook in hand. (I’m currently drafting a post re: the mathtwitterblogosphere and how Michael Pershan is basically the Dangermouse of the MTB. He’s big on mistakes and how to learn from them, and as a frequent mistake-maker myself, I appreciate that.)
This instantly brought that post to mind:
Gross?
I tweeted it over to Michael and he was kind enough to reply, but I fell back into first-year teaching constant behind-ness and never followed up (sorry).
Now, I’m against “edutainment” as such, but if my lesson openers grabbed my students half as quickly as that billboard stopped me (at 7 pm, after a 11 hour day, in January) then I would consider it most of the way to a lesson well done.
HOW did they get that number?
WHO will that person be?
WHEN will the first 200-year old be born?
HOW gross is that, perhaps?
Some of these questions are not particularly well-formed, but more and more, I think that is fine. As a math teacher, I want more of my job to be helping students figure out what is within reach of mathematization. One of the reasons this post is so delayed is that this stuff goes over my head pretty quickly. Even more tenuous than life expectancy predictions are maximum life span predictions. For example, the oldest verified human life span is 122 years. Unraveling these and some related actuarial definitions can get confusing and life expectancy itself is a great Bayes’ Theorem lesson waiting to happen.
The more I dug into this, the more it seemed that this might be a case of “bad stats,” at least as presented to the public. I’m sure Prudential and other insurance companies know what they are doing (see this article on “longevity risk transfers”), but there seems to be a conflation of expected value (life expectancy) and some sort of outlier (maximum life span).
For example, here’s Prudential’s Superbowl ad:
At the beginning of the ad, Daniel Gilbert mentions that the life expectancy in the US was only 61 when the official retirement age was established at 65. But then the question asked is “How old is the oldest person you’ve know,” essentially asking for some sort of local maximum estimation rather than a mean. The music swells as everyone builds a dotplot centered somewhere in the low 90s, the glistening recent skyline of my hometown in the background meant to evoke a sense of progress (and elderly joggers).
How many of my Stat students would notice the implicit faulty comparison?
How many of them could hypothesize why I saw this billboard over the Midtown Tunnel and not in the Bronx? (I saw a second in Tribeca and a Twitter search suggests they are also in SF and Boston.)
How many of them could watch that ad and break it down into a question that we could tackle statistically?
(Some of) my students “know” that outliers and linear regression do not play well together as a general rule, but how many of them would see the connection?
As someone who is (1) teaching Statistics as half of his course load and (2) has never taken a Stat class ever, I’m often looking for examples in context of good stats or bad stats, and life expectancy quickly gets messy in a good way. The first time around, I was too nervous to drop something this messy and ill-defined on my kids, but I’m (slowly) realizing that changes I make in how I run my classes should be with the goal in mind of being able to play with messier ideas like this.
Compact Spaces 