Category Archives: Mathematics and its discontents

Why Are Children Forced To Study Mathematics At Gunpoint?

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In the United States children are required to study mathematics for most of the time they’re required to attend school and yet essentially everyone hates it. Not just students, but parents and teachers as well. Very few remember any of it once they’re done with school, which strongly suggests that all those years of mandatory mathematics education aren’t serving the students themselves. If they were it wouldn’t be necessary to criminalize nonattendance, to force children into schools to learn mathematics at the point of a policeman’s gun.
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Leonhard Euler, Denis Diderot, Augustus De Morgan, William Gillis, and the Weaponization of Scientific Knowledge Authority

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There is a story, universally known to mathematicians, about Leonhard Euler, Denis Diderot, Catherine the Great, and the epistemological authority of mathematics. It apparently first appeared in English in Augustus De Morgan‘s book A Budget of Paradoxes:

Diderot paid a visit to the Russian Court at the invitation of [Catherine the Great]. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her councillors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced towards Diderot, and said gravely, and in a tone of perfect conviction: Monsieur, $\frac{(a + b^n)}{n} = x$, donc Dieu existe; repondez!1 Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.2

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If it’s actually true that building more homes makes the rent go down then it’s also true that intentionally keeping units vacant will increase profits

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If you pay any attention to online housing discourse you’ve heard repeatedly that we can eliminate homelessness by just building more houses. The most idiotic versions of this theory rely on the (putatively obvious) idea that if the demand for a good is fixed then the price is roughly inversely proportional to the supply. My personal feeling about all theories like this is that they are framing phenomena created by state violence as if they were the result of universal natural laws, but that doesn’t mean we can’t learn something from them.

In particular we can learn that this supply/price assumption implies that under apparently normal market conditions landlords with more than a few units can maximize their profit by intentionally keeping apartments vacant to artificially restrict supply. If it’s actually true that increasing housing supply functionally decreases housing costs then all else being equal it will lead to house-hoarding. This appears to be a contradiction in the theory.
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How I’m Grading Now and Why

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Introduction

There is a great deal of pedagogical literature concerning the harm done to students by the practice of ranking them with letter grades.1 The authors of these papers, self-styled ungraders, focus on the effects of letter grading on students’ mindsets. Ungraders generally agree that letter grades distract students away from true understanding because, as widely cited ungrader Alfie Kohn puts it, “too many [of them] have been led to believe the primary purpose of schooling is to get As.”2.

That students believe this is universally acknowledged, at least by teachers. But why they believe it, in particular why they believe it so tenaciously even though their teachers have been telling them the opposite since forever, is not so clear. Also, I’m not sure that students “have been led to believe” this by anything other than their own accurate observations, or even that the students are wrong about “the primary purpose of schooling.”

The ungrading community believes that, as Susan Blum puts it, “when we grade, we really convey very little information about what is being assessed”3 and their arguments are convincing. Just for instance, there are too few letter grade options to differentiate between the wide variety of student achievements, even in a single class. My institution only offers ten choices, which isn’t granular enough even to draw a conclusion from the bare fact that two students received the same grade in a given class.4

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