Something that totally drives me crazy is when I hear my colleagues complaining about the students, about how little they know, about how little they learned in school. The actual reason this upsets me is that it is sometimes given as an explanation for why one cannot teach them in the way one would have liked to be taught oneself. I find this infuriating. I mean, with the excuse of telling her that 1 = 0.9999…, I explained to the being the other day what a limit is. Evidently, I didn’t use lingo like “for all,” and I didn’t use symbols like ε or δ, but she understood that the number 0.9999… is nothing other than the limit of the sequence of finite decimal numbers, and that limit is equal to 1. I gave a few other examples, but I am sure that she has by now forgotten it all. At the end of the day, soccer is vastly more interesting. But that is not the point. I just explained it to her because it takes about five minutes, because I knew that she could understand it, and because I like explaining real things to the being. Using her language. But real. And well, if a 10-year-old who is kind of smart but neither Gauss nor particularly interested can understand what a limit is, math students can and should be challenged. Doing otherwise is doing them a disservice and a disrespect, and this is the first reason why I find it desperating when people complain about students knowing very little.

Rayfish eggs

A second reason is that I disagree. I mean, since the time of the Greeks, students have always known less than people from a prior generation. Or at least this is how things look when one listens to the older ones. Why is this? Or rather, why do people think this? Well, it might be that part of the reason is that those complaining about the level of current students were, at the time, probably among the better students—I mean, I would never complain about people nowadays dancing worse than in my day—and now they are just confronting the average. I think, however, that the real reason is that people just don’t see how much students know and how much kids learn in school. I guess that this is partly because they learned something in some way, and that way became, in their minds, the only good way to learn stuff. For example, one of my great uncles learned German at some point, and since we didn’t know all the declensions as well as he did, he was convinced that we ourselves actually didn’t learn any German. This despite us actually speaking German while he didn’t. He just knew the declensions by heart and decided in his mind that learning this was learning German. Another example with a bit of a different flavor: My mother used to tell us how much more math she learned in her pretty idealized school compared to what we learned in ours. Well, in hindsight, let me assure you that if that differential ever existed, it was completely irrelevant. Apparently, 72% of French people—among them many of my colleagues—think that public schools have gotten worse since their time there. Well, I am sure that that 72% of French people just ignore that most likely they are unable to have a conversation in any other language but French, while it is pretty easy to speak English with French people under 30. I am sure there are things that kids don’t learn now that we learned. But then, I never learned how to extract a square root, something standard not that long ago. And we all probably agree that with calculators everywhere, there is not much point in learning an algorithm to calculate the first five decimal digits of √37.

I guess that part of my confidence in the education that kids get is that I see how much the being learns and how much she already knows. Evidently, my daughter is privileged because her parents have the time and the inclination to tell her things—limits, anybody?—but she learns an enormous number of things at the totally random public school a few hundred meters from the not-well-off neighborhood we live in. Why am I so sure? Well, at home there is a mix of English, Spanish, Russian, and French, with conversations often in three languages at the same time. The only one who actually speaks French is the being. She learned it at school, has a pretty decent vocabulary, and knows useless things like the passé simple and where to put accents. Besides, the fact that the things she learns at school are in French also makes it easy to spot them. For what it’s worth, I never told her anything that could lead to the sentence, “Voltaire, Rousseau, Montesquieu, c’est grâce à eux que nous sommes libres.” She knows French geography, and since nobody drives, this is not because we made long car travels through France but rather because she learned it at school. She knows things about animals whose French names I had never heard. She learns poems. Three verses at a time, but she learns them. She learns Chinese. Although at home she hears a lot of English, we never taught her how to spell “daughter,” but that she learns at school. She knows much more than me about Africa. She learns about slavery. She learns that if you leave an egg in vinegar for a day, the shell dissolves, and if you light it with a lamp, you can see the egg yolk. She learns how to deal with kids. And with people in general. She learns how to use a computer. They have a “radio” at school where kids, the journalists, talk about things like the Paralympic Games, that in Mexico they eat burritos, or the Niagara Falls. They listen to the recordings in class, but one can also listen to them online. You go to the beach with her, you see the thing in the picture above, and she knows what it is. Do you? I didn’t. Rayfish eggs.