This was a week of few mathematically-themed comic strips. I don’t mind. If there was a recurring motif, it was about parents not doing mathematics well, or maybe at all. That’s not a very deep observation, though. Let’s look at what is here.
Liniers’s Macanudo for the 18th puts forth 2020 as “the year most kids realized their parents can’t do math”. Which may be so; if you haven’t had cause to do (say) long division in a while then remembering just how to do it is a chore. This trouble is not unique to mathematics, though. Several decades out of regular practice they likely also have trouble remembering what the 11th Amendment to the US Constitution is for, or what the rule is about using “lie” versus “lay”. Some regular practice would correct that, though. In most cases anyway; my experience suggests I cannot possibly learn the rule about “lie” versus “lay”. I’m also shaky on “set” as a verb.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th shows a mathematician talking, in the jargon of first and second derivatives, to support the claim there’ll never be a mathematician president. Yes, Weinersmith is aware that James Garfield, 20th President of the United States, is famous in trivia circles for having an original proof of the Pythagorean theorem. It would be a stretch to declare Garfield a mathematician, though, except in the way that anyone capable of reason can be a mathematician. Raymond Poincaré, President of France for most of the 1910s and prime minister before and after that, was not a mathematician. He was cousin to Henri Poincaré, who founded so much of our understanding of dynamical systems and of modern geometry. I do not offhand know what presidents (or prime ministers) of other countries have been like.
Weinersmith’s mathematician uses the jargon of the profession. Specifically that of calculus. It’s unlikely to communicate well with the population. The message is an ordinary one, though. The first derivative of something with respect to time means the rate at which things are changing. The first derivative of a thing, with respect to time being positive means that the quantity of the thing is growing. So, that first half means “things are getting more bad”.
The second derivative of a thing with respect to time, though … this is interesting. The second derivative is the same thing as the first derivative with respect to time of “the first derivative with respect to time”. It’s what the change is in the rate-of-change. If that second derivative is negative, then the first derivative will, in time, change from being positive to being negative. So the rate of increase of the original thing will, in time, go from a positive to a negative number. And so the quantity will eventually decline.
So the mathematician is making a this-is-the-end-of-the-beginning speech. The point at which the the second derivative of a quantity changes sign is known as the “inflection point”. Reaching that is often seen as the first important step in, for example, disease epidemics. It is usually the first good news, the promise that there will be a limit to the badness. It’s also sometimes mentioned in economic crises or sometimes demographic trends. “Inflection point” is likely as technical a term as one can expect the general public to tolerate, though. Even that may be pushing things.
Gary Wise and Lance Aldrich’s Real Life Adventures for the 19th has a father who can’t help his son do mathematics. In this case, finding square roots. There are many ways to find square roots by hand. Some are iterative, in which you start with an estimate and do a calculation that (typically) gets you a better estimate of the square root you want. And then repeat the calculation, starting from that improved estimate. Some use tables of things one can expect to have calculated, such as exponentials and logarithms. Or trigonometric tables, if you know someone who’s worked out lots of cosines and sines already.
Henry Scarpelli and Craig Boldman’s Archie rerun for the 20th mentions romantic triangles. And Moose’s relief that there’s only two people in his love triangle. So that’s our geometry wordplay for the week.
Bill Watterson’s Calvin and Hobbes repeat for the 20th has Calvin escaping mathematics class.
Julie Larson’s The Dinette Set rerun for the 21st fusses around words. Along the way Burl mentions his having learned that two negatives can make a positive, in mathematics. Here it’s (most likely) the way that multiplying or dividing two negative numbers will produce a positive number.
This covers the week. My next Reading the Comics post should appear at this tag, when it’s written. Thanks for reading.
nebusresearch 
Some jokes I’m seeing elsewhere about parents not being able to help with math homework have to do with Common Core and new processes the parents weren’t taught.
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That’s certainly one thing that fuels jokes about parents not being able to help with homework. And, certainly, it’s a fair complaint of parents. If they don’t know how a technique is supposed to work, or what the point of a technique is, then they are going to be unable to help, and rightly annoyed at being unable to help. (I’m thinking particularly of parents who complain that it’s a waste of time to “estimate”, say, 112 minus 46 when you could just do an exact subtraction. That estimation is a valuable skill also needing practice can escape attention. But I understand the parent who doesn’t see why 60 or 70 would be a better answer than 66 here.)
But the motif of the parent who can’t do grade school mathematics anymore goes back a long way. The comic value of the helpless authority figure is too good to not be used. And, of course, any person stays proficient only in the things they practice regularly. If they haven’t had to think about how to divide 96 by 7 in years, why would they suddenly be good at it? And that’s so however division gets taught.
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All good points. I myself use estimation in daily life. It’s good for quick risk benefit analysis, on the fly budgeting, etc.
As far as losing skills, I had an odd experience with revisiting a math concept the other day. When I was a kid I never mastered canceling when multiplying fractions, but I recently had to help my son with that and related concepts. As soon as I sat down with the book, I found I actually understood things I had always thought I was incapable of. The curriculum was certainly better (Life of Fred). But it seemed as if the years had pared away the contradictory thoughts and left the simple apprehension of reality. Had my frustration with myself from 25 years ago been churning away in the background all this time?
Anyhow, my son was frustrated like I had been, so I told him to take a break. A couple of hours later we were taking a walk and suddenly he began explaining fractions to me in a way completely different from the textbook and the way I had been explaining it. Yet it was accurate. It was like he had to find his own way to understand it.
Both of these leaps to understanding happened behind the scenes while not working, which is what I find really curious. Then again, being a full time homeschooling mom (not just for coronavirus) maybe I’ve kept the gears oiled a bit more than others have to. As for my son, I’ve tried to keep compulsion out of math learning. I actually let him take two years off. He loved numbers as a little boy, and we used to have whole conversations that just consisted of numbers and their relationships. Sometimes he would say things I couldn’t even understand. Somehow that was all dying… I couldn’t bear it.
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Learning is a strange thing, and it’s not something we fully understand yet, even now. Mindful practice is something important to it, sure. But somehow breaks are also important. It’s true not just in learning but in developing new mathematics too. Everyone has stories of how they focused hard on a problem for a great while, and got nowhere, and then after giving up and going off to do something relaxing instead, inspiration strikes and everything fits into place in a new way.
Teaching, or at least explaining, is also somehow a way that we learn. Part of what delights me in doing the A-to-Z sequences, as I’m hoping to start soon, is that I get to stare at topics I thought I knew, and try to think of something new to say about them.
So at least part of learning is the pause, and the disruption in thinking, and the attempt to think in different ways. I don’t know that anyone has good hypotheses about why that works, but it does seem like a lot of learning happens while we don’t think we’re doing it.
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