This is a multi-part series about my visit to second grade and our exploration of fair sharing.

This Friday (March 3rd), I went to Mrs. Valentine’s second grade class. I go once a year and this was my third total trip. We tie in topics that they have had experience with, but are outside of the curriculum, yet still within the standards; in second grade it is primarily arithmetic, measurement, and geometry.

Here is a write-up of my first visit. You may be wondering where the write-up of my second visit is … It’s in a very long draft mode, but it was a lesson about secrets. So it’s fitting that that visit should remain shrouded in mystery.

Anyway … this third visit was all about sharing. Here’s how it went.

Mrs. Valentine and I got to her classroom around 8:30am. She went to make some photocopies and I spent the time learning the kids’ names and where they were seated. I like to connect with them by showing that I do know their names. After all, they already know my name. So it’s only fair.

By the time the kids trickled in around 8:45am, I had committed their names to memory and knew where they were sitting. Now it was a matter of associating faces to those names. As an aside, when I know I’m going to be interacting with an adult and I’ve been told their name, I have some mental image of what they would like. That image is always wrong. With kids, believe it or not, I have no mental image. If anything, I think I have a generic kid face in my mind. So as they came in, I started matching their faces to their names. This was easy because I knew where they were sitting.

The first half hour was mostly the kids getting settled in. We stood for the Pledge of Allegiance, the morning announcements, they turned in some work, they did a morning activity, and their morning greeting. The morning greeting is a cute ritual they do in Mrs. Valentine’s class. The kids sit in a circle and with a funny voice, imitating a robot, or a lion, or a witch, or some character, and one kid starts with saying good morning to the person to their right and the person to their left. Then, the person to the left repeats this until it comes full circle. I think it’s a nice way to build a bond and camaraderie.

In all this, and for the first time in my visits, the kids generally didn’t notice I was in the room. Or if they did notice, they didn’t say anything. In the past visits, they speculated that I was someone’s dad, or that I was a lawyer observing, or a different school’s principal. I was in business, mostly-formal, attire. Not a suit, but dress pants, button down, tie, and a blazer. So, I’ve always looked “official” to the kids. I wore the same get-up this time. I did overhear one student say “Is that Manan”? This class had actually seen a picture of me and I’m not sure if that, ironically, corrupted their mental image of what I looked like. The other classes never had.

In any case, for me, the important thing was that I had memorized their names. At around 9:15 when all the usual morning routines had come to an end, Mrs. Valentine introduced me. She had been talking about my visit for a few months and she had told her students what I do for a living — I work as a mathematician. But we also saw that we all draw, we all play a musical instrument, and we all like to sing!

I asked the students what they thought mathematics was. Their responses were what you would expect. Mathematics is adding numbers! Multiplying! And the obligatory non-sequiturs of so-and-so is really good at math and those eventually led to more non-sequiturs about what their interests were. One girl wants to be a programmer. One girl wants to go into drama. One boy wants to make games — that’s what he’s been researching in his genius hour.

Now that we had built a rapport we introduced our first activity. It was an arithmetic race. The class versus me with a few twists. The notion of a race against me had some kids really excited and some kids already capitulating. But then we spelled out the twists. The first twist was they would get together into pairs. One person would do an addition worksheet, the other person would do a subtraction worksheet. But they had to decide who was going to do which. The next twist was that I had to do both worksheets. That got them really excited. The next twist was that each group had two and a half minutes to finish their worksheet [50 problems each, single digit addition] *and* that I had to do *both* worksheets in the same time. Now, they were really excited.

Today’s lesson was a lesson about fairness. So, given their excitement, I asked if this set up was now fair. Most of them eagerly agreed. They reasoned that since I’m a mathematician and that they’re second graders, it’s fair that I have to do more because I am, presumably better. Two students disagreed. They said that the setup wasn’t fair because everyone wasn’t being treated equally. That in fact, I had a harder task. They argued that I should get a partner or that I should only have to do 50 problems or that I should get twice as much time. Interesting! Don’t you think?

After a little bit more of that discussion we handed out the worksheets, the students got to see the problems for probably a full two minutes as they were deciding who would do addition and who would do subtraction. Once they got settled in, we started the timer.

I finished in one minute. But that wasn’t the point. The point was about fairness. After two and a half minutes, all pencils went down and Mrs. Valentine revealed my time and score. While the students were baffled at the speed, we now pivoted the conversation to fairness. [We addressed the matter of speed by explaining that this was the result of a lot of practice. Some students attributed my speed because I’m a mathematician, which is an understandable, but circular argument.]

We asked that if we had to do this type of race again, what would be a fair amount of time for me to get for 100 problems, if they got two and a half minutes each as a team? Now, the answers were of the type, “Well, he shouldn’t get two and a half minutes. He should get one second.” Some said, zero seconds! Others took an empirical approach and suggested that one minute would be fair. Others extrapolated from the data point and suggested that I should have to do 200 problems in two and a half minutes while they have to do 100 as a team in the same time. And still others remained adamant that I should get the same amount of time that they get for the same number of problems.

What we have here are three understandings of fairness. One understanding is clearly biased in their favor [zero seconds!]. Another understanding is an intuitive sense of a handicap as seen in sports like bowling or golf. And still another understanding of fairness was based on equal footing for everyone.

We addressed each suggestion. Why is it fair if I have zero seconds? There were no responses other than silly laughter and other students jumping in saying that it was unfair.

Why is it fair that I get less time (or more problems)? One student said that it was fair because then “it would be 50/50 who would finish first”. A budding understanding of martingales! How exciting!

Why is it fair that everyone gets the same set up? One student appealed to the idea that if there were six cookies, then it would be fair for one person to get three cookies and the other person to get three cookies. And by extension, if one person has to do 50 problems in two and a half minutes then so should everyone else. It didn’t matter to some students that I would win every time. For them, it just meant that I was better and that’s that. Everyone got the same set up and someone won (or will win every time). They also alluded to what they know to be experientially “true” — some students are smarter than others, but no one is getting special treatment. The special treatment was the unfairness. Or in my case, the harder constraint was the unfairness to me.

This is, of course, a much larger conversation about resource equity, access to opportunity, etc. We see this type of debate rage on in the political space when discussing fairness and equity for people of different races, religions, sexual orientation, etc. One side argues for competitive fairness (adjusting the situation so that, head-to-head each side is equally matched) while another side argues that the situation is fair, we just have to do what we can (the old chestnut: “pick yourself up by your bootstraps and make something of yourself” kind of thing) and still another side argues for maintenance (or creation) of *unfairness* — you get zero seconds!

We left the debate unresolved about how much time I should get and segued into the main topic of fair sharing. Continue on to part 2 for what second graders did with two shapes below. Incidentally, several students said that the second shape [the one on the right] wasn’t a shape — an interesting conflation of “shape” and “regular polygon”!

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