How I Teach Calculus: A Comedy (The Papoose is Imminent)
What situation comedies have gained the modern married couple is a vocabulary of sarcasm, the rhetoric of man-children, and tacit approval of snide dispositions. While this infantile image of marriage is quite funny to those who are unmarried, it’s a pale, sad homunculus compared to the work and triumph that is a real marriage.
That said, I put my foot in my mouth down to the ankle the other day. Let’s watch!
Enter Shawn, holding the baby, fitfully bobbing up and down and left and right. Baby is emitting sounds that evoke some strange amalgam of rhinoceros and a whoopee cushion. Wife is sitting, conversing intently with the mother-in-law.
Shawn: Phew! My arms are tired, this baby is heavy!
Wife: without turning head, in a perfect dead pan. She sure is.
Shawn: I mean, it’s like carrying a football that wants to be fumbled!
Wife: That’s nice; trying carrying her for nine months!
Shawn: a pensive moment passes where the incorrect neuron fires in shawn’s don’t-be-stupid filter. Well, it’s not like the baby was this big the whole time. I mean, it’s a question of time and weight, isn’t it?
Mother-in-law and Wife: death glare.
So, I did what any reasonable husband-cum-father would do, I brought the story up with my calculus class, and they totally bit. They came up with the following question:
How long will it take for Mr. Cornally to have done the same baby carrying as his wife, if he holds the baby nonstop after she is born?
This question took a lot of arguing to develop. Some students claimed that my wife and I would probably split time holding the baby. Some argued that we’d need to include all of the extra weight that women have to gain during pregnancy (uterus, placenta, extra blood, reserves, etc…)
This is exactly the kind of conversation I want to be having with my students. It shows me they are thinking quantitatively about a situation with a buhjillion different variables. This is especially difficult when the situation involves real curvy things, because then it requires calculus.
The Quest for baby(t)
So, we set off. The students knew that they had to find the weight of the baby over time. The first thing they did was ask me for this data (surprise!). I didn’t have it. However we did know one thing: at 9 months 3 days, my baby weighed 9 pounds.
So, the students looked up data (they used babycenter.com) and then adjusted it to match my baby. This was awesome, because it turns out my baby was a tank. They had to make all sorts of assumptions about when my baby would have diverged from the average baby. This forced us to talk about the science of fetal development and many other rich things that aren’t math but are still classified as learning.
The students then went about fitting functions to their data. This was a crapshoot. Some wanted to use regression methods, others were happy letting Excel fit a random trendline, others even used OSX Grapher to fit a line, which was nice because it actually does the Chi-Squared testing somewhat transparently. I really didn’t care what method they used, just that they knew they had to use some method for fitting a curve other than the extended-thumb-and-shut-one-eye method.
Here’s what we came up with:
My wife’s component is then the integral from 0 to 37 weeks. My ouptut is another graph, which starts after this one ends.
The next graph was slightly more difficult to come by. We don’t really know what my baby’s weight will be in the future, what we do know is that the my baby was gaining about an ounce per day, they ran with this simple model:
Where t is in weeks.
The students then set the two integrals equal to each other in order to find the time when I’ve done the same amount of carrying as my wife:
This integral was super awesome for them to work out, because we’ve never had a situation in class where the limits of integration represented an answer to our question. They came up with the idea of solving it from the fundamental theorem, and I was proud.
About 2 months. This of course is silly, as I can’t get enough of holding my cooing little swaddle monster, but hey, at least the argument was settled: I’m an idiot.