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.
Americans are not necessarily docile in the face of government-imposed educational requirements1 and yet they are docile with respect to mandatory mathematics. Intense government propaganda on the goodness of STEM education surely encourages this. Such propaganda rarely consists of more than unsupported claims that STEM training prepares future generations to be happy in their work, which, translated, means that it prepares children to enter or to remain in the middle or upper class.2
Even the acronym STEM, which stands for Science, Technology, Engineering, and Mathematics, is part of the propaganda. In actual practice these fields have little in common other than that capitalism requires a lot of people trained in them and even more people with the deeply felt and formative experiences of shame and failure associated with their study.3 There’s no reason other than the needs of capital to group these subjects together.4
The expenditure of significant resources is required to maintain the math education social system and yet, not only do most kids not know any math when they graduate, but there’s really no reliable body of knowledge one can assume they have on graduation beyond knowing how to read.5 So the people who have the power to create and maintain this social system aren’t expending all the necessary resources solely to create a bunch of mathematicians, scientists, and technologists.6 Why are they spending it?
Whatever they’re after it must be valuable given the value of the resources committed to the project. These don’t just include money for staff, supplies, and real property, but also a range of other complex and expensive institutions, roles, and physical plants. Universities are necessary to train teachers, school administrators, and the professors who train these people. Laws, cops, courts, and jails are required to mete out the violence necessary to get kids into the system and keep them there.7 Universities also train the people who staff these institutions. The entire work of all these systems isn’t dedicated solely to mathematics education but some valuable fraction of it is. This incomplete list of the costs willingly paid by capital to support mandatory mathematics education shows its high value.
Resistance is one of capitalism’s perennial problems, to which one of its perennial solutions is camouflage. When judging potential profits capital must take potential resistance into account and weigh the potential gains against the increased risk of exposure and its subsequent threats to stability. The process of creating and maintaining mandatory schooling has been no exception to this process. Instituting such a complex and comprehensive social system over the last 150 years has required many risks to capital, taken to maintain and extend its ability to extract value from people.
Which is why even now capital has to sell us on the benefits of violently enforced mandatory schooling by touting the benefits of forcing other people’s children rather than our own. No one wants guns pointed at their own kids but at least some are willing to point them at other people’s kids if it suits their needs. There was, is, and will be popular resistance to capital’s daring, risky, and ongoing project. Mandatory schooling is a site where the contradictions of capital are close to the surface, increasing the risk of ongoing and recurrent resistance.
Such risks measure capital’s valuation of the system.8 When mandatory schooling was first proposed there was a great deal of resistance, and why wouldn’t there be? Capital uses the system in part to reproduce a self-replicating working class whose members will send their kids to be transformed into workers without being directly forced to do so. Before this was normalized it didn’t look attractive to the people it acted on, and it still doesn’t if considered too closely.
This answer, that capital requires its victims to undergo twelve years of mandatory math education to maintain its self-reproducing working class, is correct, but it’s not at all clear how this process got started and how works. Also it’s easy and tempting to reframe as a conspiracy theory, making it easily dismissable by people who haven’t spent time sitting with the facts. Zillionaires didn’t get together at Davos and plan it all out step by step like an algorithm. It’s the unplanned but very carefully managed result of centuries of selection and equilibration.9
How this process got started and why conspiracy theories aren’t required to explain its continued existence are topics beyond the scope of this post, which is only about how mathematics education serves capital.10 That is, about what capital gets in exchange for the valuable resources it commits to the project from the twelve years of mathematics education which it requires of our kids. Some kids do learn mathematics and the intrinsic value of such kids to capital is clear in that capital needs technocrats and the kids who do learn some math are good fits for that role. But mathematics is far from all of what gets learned in math class.
Kids don’t all learn math but they all learn something. The grading system, the teacher’s mood, the rewards, the praise, the errors, the humiliation, the corrections, the blurring of the lines between authoritative knowledge and coercive authority, all teach their lessons, some but by no means all of them directly about mathematics. The cultural context of mathematics teaches them other things. They learn that mathematical knowledge grants social power. It allows those who do learn it to talk to teachers, representatives of power, in their own language, a language that the non-math-learners come to realize is the only way particular kinds of truth can effectively be expressed.
Often they learn that their parents aren’t able to help them even with elementary school math homework, which teaches a powerful lesson about their families’ place in the social hierarchy.11 Another important lesson to be learned is that there’s one right answer to every question. No matter what anyone remembers from their math classes, they remember this lie. It helps people to believe that not only are there right answers to find, but that scientists know how to find them, which covers up the role of violence in determining what counts as truth. Mathematics creates a facade of objectivity behind which capital’s violence hides. When violence is the authority behind truth obscuring that fact stabilizes capitalism.
Also mathematical knowledge, although it is not propositional knowledge, can very easily be made to appear to be.12 Algebra is especially vulnerable to this kind of sleight.13 One of the lessons children learn in algebra class is that all important knowledge is propositional knowledge and that it all builds sequentially on prerequisites. That it can and must be learned in even measured steps and that each step represents a uniform quantum of knowledge. If this is true then we must trust the experts because they’ve taken more steps towards the truth than we have. Since there is one right answer there’s one objective truth, and the more steps one has taken towards it the closer to the truth one’s ideas must be.
Mathematics education diverts and repurposes the instinctual human respect for authoritative knowledge by subbing coercive authority into its place.14 The idea that mathematics is the language of science and science the language of truth reinforces the cultural narrative that all truth consists of bloodless propositions, that truth is necessarily detached from human considerations. This in turn acclimates kids to the idea that their own experiences are irrelevant to every possible discussion unless they can be expressed in a reasoned and detached style, effectively silencing a great deal of dissent.
The formal reasoning style associated with mathematics teaches its own lessons. For instance that decontextualization and abstraction are the only valid routes to truth, that the only correct way to understand anything is by analyzing relationships between abstract concepts, because this is how mathematics is taught to kids. This is true throughout K12 mathematics, but it’s very clear in relation to word problems, where students must often suppress their own concrete and specific knowledge in order to get what passes for the right answer.15
For instance, the meaning of the slogan “Black lives matter” relies on its place in a deep and broad historical context involving chattel slavery, police violence, capitalism, racism, prisons, and on and on and on. Part of the context is the understanding that society already acts as if white lives matter without anyone having to say it out loud. Lacking that context, or mapped to a different context, the phrase means something very different. And once decontextualized it becomes conceptually equivalent rather than intentionally and implicitly contrasted to statements like “all lives matter” or “white lives matter.” Even wildly skewed transformations like “blue lives matter” move from absurdity to debatability, which is a win for capital’s stability.
Victims of American mathematics education may be powerfully tempted to refute such nonsense on its own terms, i.e. abstractly rather than by screaming out the concrete truth that’s obvious to anyone who shares the context. We’re tempted to clarify the definitions and explain the distinctions abstractly, which of course is a trap that transforms meaningless claims into debatable claims. We instinctually feel the socially created weakness of arguments that rely on context, on personal, concrete, experiential, spatially localized knowledge. That such arguments are, contrary to this position, not only valid but are arguably the only valid arguments is sufficient explanation for the value of this mathematics-mediated mental trap to capital.
Math teachers can project enthusiasm for extremely esoteric subjects, e.g. into how many distinguishable orders can the letters of the word “MISSISSIPPI” be arranged? Students may take this as affirmation of their own esoteric interests, which marks them as potential techhnocrats.16 Others learn different lessons, e.g. that mathematicians along with the world-rulers they advise aren’t entirely human given their apparent passion for inhuman subjects. Since they’re not entirely human, humans can’t expect to understand their reasoning, let alone the value of their conclusions. It’s better to follow their orders, then, even if it fucks us up personally, and we’ll never be one of them because we’ll never care as much about such things.17
It’s not that such questions aren’t to be enthused over. They are interesting, but no more interesting than any numbeer of other subjects, none of which children are forced at gunpoint to study. The question isn’t whether the topics really are worthy of enthusiasm. The question is why it’s valuable to capital to expend resources pushing this kind of enthusiasm on kids who not only don’t share it but who often have the seeds of their own genuine intrinsic enthusiasms crushed rather than nourished by the system.
I could add plenty of examples but if the point can be made I’ve made it, leaving only my confessions to close this essay. I didn’t create and I don’t control the system I’m describing here, but I do actively work in it, maintain it, benefit from it, so am complicit in its operation. One major benefit I take from the system is that it makes my job possible. Part of that process is that the system creates a market for the skills I teach and violently forces people into that market, all of which contributes to the existence of paid work for me to do. I doubt that without coercion there’d be enough demand for advanced mathematics education to support me personally working at it full time. Without the system providing a steady supply of students for me to teach I wouldn’t have a job.
The system also ensures the feasibility of my job by producing a reliable supply of students prepared to take my classes. The preparation includes the requisite mathematical background, but also the rigorous behavioral training necessary to create students who will sit quietly in class and unquestioningly obey my often-arbitrary commands without the need for overt threats. This is no small accomplishment. It takes years and many, many wasted lives to produce properly trained students.18 That is, capital in general and the mathematics education system in particular benefit me by violently creating conditions which enable me to support my family and myself.
That I benefit from capital’s violence in these particular ways is a form of complicity, but I’m able to see it passive and unavoidable. I have to have a job because capital forces me to work to support my family and myself and most jobs involve this kind of complicity. If I could choose freely I’d choose something very different, which absolves me as much as it absolves everyone who has to work for a living. I’m not sure how much absolution that is, but it’s what’s available.19
I’m also complicit in capital’s violence in ways that I didn’t understand as complicity when I enmeshed myself in them. Many of these relate to my confusion about my purposes for my job and some of them are within my power to change. For instance, during most of my career I assigned letter grades to students based on very normal, very familiar kinds of criteria, with assigned cut-off scores for As, Bs, and so on. As I came to understand capital’s role in creating and shaping the world I began to see that such letter grades didn’t help students to learn mathematics and in many ways hindered learning. I saw that letter grades aren’t designed to help students in any way and in many ways they’re harmful.
They don’t do anything to help students learn mathematics, although they do a lot to shape and rank students according to capital’s needs. If I understand the purpose of my effort to be teaching mathematics to willing students in a human social context rather than furthering capital’s goals there’s no reason at all for me to participate in the system this way. Thus I’ve changed my grading system to implement as much as possible incentives which are good for my students in that they further the intrinsic value of learning mathematics as a social good between me and my students. In that context letter grades are easily seen to be without value, and in fact, as something students need to be protected from if possible.20 There are other ways I’m complicit that are similar to this.
The worst ways in which I’m complicit are those where I knew and know better abstractly than to use my power like that but in order to protect my ego used this knowledge to avoid seeing the concrete badness of my behavior. Briefly, I’m talking about the fact that exercising arbitrary personal power over people can be immediately satisfying and therefore a temptation. Forcing people to comply with arbitrary rules can sooth egos hurt by years of having to obey arbitrary rules, even more so from behind a shield of numeric and, therefore from the point of view of properly trained students, objective and so indisputable grading standards. Peer-validated and therefore righteous anger about plagiarism or other turpitudes can build professional community. All of this is done at the expense of students’ well-being because the punishments are grade-based.
A few failing grades can lead to suspension or expulsion from school or from dorms. This can lead to low pay and lingering student loans without sufficient income to service them, which can mean a whole lifetime of working for other people’s benefit. But a single failing grade doesn’t have much effect by itself. This fact allowed me to avoid facing the implications of grades as a tool of social control. Giving an F grade is like a single firing squad bullet being a blank. Both moves allow killers, both direct and indirect, to imagine that they aren’t guilty, even though all of us are.
Power famously corrupts, which is a pleasantly entertaining aphorism to apply to Henry Kissinger and his ilk but not so much to oneself. Police are the ultimate source of violent power in our society, so expressing personal power in cop-like ways can be an easy and therefore attractive default. I don’t like facing the fact that I’ve acted this way throughout my career and might still be doing it in ways I haven’t come to understand yet. Also I don’t feel like I understand the situation well enough yet to give an complete honest account of my actions.21
And ultimately there’s nothing very special about mathematics in relation to capitalism and compulsory education. The ways in which capital exploits the intersection of mathematics and coercion are specific to mathematics, some of which I’ve described here, but the general system is not. It must in fact be the case that every subject taught in compulsory schools stabilizes capitalism in whatever ways can be used to do so. Certainly capital won’t fund activities that undermine its stability, and activities neutral to capital’s stability don’t exist.22 Making mathematics an elective, therefore, won’t solve the problem, which is due to coercion rather than any inherent qualities of mathematics or other subjects taught in K-12 schools.
I believe the only solution is to abolish compulsory schooling.23 This argument is too much for a brief summary, but it’s based on the simple fact that I can’t see any possible moral justification for compulsory schooling enforced by police at gunpoint, not if my kids are being forced and therefore not if other people’s kids are being forced. I don’t mean we should abolish free public schools, just that attendance should be voluntary. If you disagree is there an argument in favor of forcing children at gunpoint, under threat of violence, to engage in activities that putatively benefit them?
- If the recent and ongoing fuss over critical race theory teaches us anything it’s this.
- There are surely many, many reasons why people don’t rebel over mandatory mathematics education or, for that matter, over mandatory education in general. In addition to the propaganda I’d guess that parents wanting their children to be upper or middle class is the most important. Very few people are willing to put ideals before their children’s economic well-being, nor should anyone judge them for this. And of course it’s not just economic well-being that’s at stake. Money protects people from infinitely many dangers, so it’s very, very natural to want this for one’s kids even at the expense of other people’s kids It’s a reliable instinct so capital can rely on it. Any intrinsic goodness associated with STEM stuff is absolutely not a factor, or only a factor for people who already have money.
- Here’s how I use some words in this essay. “Capitalism” is an economic system that relies on violently excluding people from the means of production in order to force them to submit to exploitation. “Capital” referring to a group of people means the same thing as “the ruling class.” It’s a collective noun for the class of people who are able to control some of the coercive tools of the state, to use them to effect their purposes.
- If there were it wouldn’t have been necessary to coin the word “STEM,” there would already have been a word, just as there’s already a word, “science,” to describe the commonalities of such disparate fields as physics and sociology.
- The system does effectively teach them how to read in certain specific ways, which is an important fact. From it one can draw the conclusion that capital actually requires most people to know how to read in these ways, but with respect to mathematics only requires that everyone be put through the system. In order to determine what the system-wielders want out of the systems they wield it’s necessary to look at what comes out rather than what they say is supposed to come out. It’s similar to how the public care systems are very good with respect to fires, moderately with respect to building codes, and very, very bad with respect to health care. This ranking reflects capital’s priorities. The system produces what it’s meant to produce without correlation with what it’s said to be meant to produce, so that the best explanation for a given component of a social system is that someone with the power to modify the rules had a need for the component. Other wielders may well later repurpose the capabilities toward other goals, which doesn’t mean that the tool had to have been created to effect those particular ends. Useful tools are useful in many contexts.
- There’s a tempting counterargument to this position consisting of a claim that the entire STEM education system functions to create as many mathematicians etc. as can be produced from a given population and that it’s only wasteful because talent in those areas is rare. Thus the math education system, with its massive wastage of human blood and treasure, is like the baseball farm system, which requires a vast apparatus to seek out, sign, and train baseball players who will never make it to the big leagues, but the ones who will also need people to play the game with. Perhaps all the wasted years trying to teach the quadratic formula are the only way to find the next Einstein. This argument is wrong, though, as tempting as it is. One counterargument is capitalism’s famed efficiency. They wouldn’t waste all those kids who don’t learn math as long as money can be made from them, and boy can it ever! Another counterargument is that even if the principle is correct, that mathematical talent is rare and the only way to develop it is with a massive farm system where most students’ roles are limited to providing bodies to keep the system running, even then, whose benefit is this for? To whom is the waste of time, life, resources, labor, and humanity worth it to make sure there are enough scientists for capital to keep moving?
- There must be violence because violent enforcement is the only distinction between rules and laws.
- Mandatory schooling is also an effective part of the camouflage system and so tempers risk even while creating it. It’s an error to look for single effects from tools as complex as the mandatory schooling system.
- This is an audacious claim and it requires a great deal of evidence and argument to make it plausible, which I’m working on producing, but it’s nevertheless correct.
- I know I do this a lot, and I apologize because I know how frustrating I find it when other people do it. My problem is that there’s too much to explain at once and if I wait till I can do it systematically I’ll never get anything done.
- It’s also a sufficient explanation for continually changing fashions in elementary math education, although there are plenty of other sufficient conditions, e.g. the publish or perish system of academic advancement. Fashions in education, like many of capital’s processes, are highly overdetermined.
- By “propositional knowledge” I mean facts that are analytic consequences of definitions and syllogisms. That mathematical knowledge is not of this kind is a difficult argument to make and I can’t make it in this essay. So for instance an algorithm for solving a class of equations, like completing the square, is similar to propositional knowledge, and any given application of it to solve a specific equation probably is mostly propositional knowledge, but the general context in which the algorithm exists is not. This context consists of social relations among mathematicians as a human community, aesthetic and historical judgments regarding which questions are interesting and which arguments are valid, struggles for intra- and intercommunity power, debates over the appropriacy of axioms, and every other aspect of human communities necessary for the creation and maintenance of a body of human knowledge.
- Which quite likely is a sufficient explanation for the fact that algebra is universally required of K12 students despite the fact that it’s absolutely useless in any normal human context. No one remembers the quadratic formula because the quadratic formula is useless, which is entirely consistent with its discovery and promotion by elite Bablyonian technocrats who had links to coercive state power and therefore many motives in common with contemporary mathematicians under capitalism. In contrast, many people know the Pythagorean theorem whether or not they know what it’s called. It’s the source of any number of folk methods for squaring up corners. The Pythagorean theorem has an existence in folk culture that the quadratic formula has never had and could never have. It’s qualitatively very different from the Pythagorean theorem in this respect.
- The notion that capital relies on such a process of identifying, diverting, and thereby repurposing universal human instincts to serve the needs of capital is one of the most important historical explanatory tools in the area, along with tool theory.
- This is the subject of a different essay. Think perhaps of a question like this: A tree grows two feet per year. A kid hammers a nail into the trunk six feet from the ground. How many years until the nail is ten feet from the ground? The correct answer is, well, dependent on how one thinks about tree growth. Abstractly, the answer may arguably be two years, but at least one problem with this solution is that in the actual real world trees grow from the tip rather than from the base. A nail in a trunk six feet above the ground will be six feet above the ground for as long as the tree stands. Also consider word problems where person A can do a task in X hours and person B can do it in Y hours and one is asked to find how long it will take them working together, which rely on the assumption that work rates are additive, that is, that workers are fungible cogs, an assumption only even plausible from capital’s point of view whose utility to capital is obvious. I need to write at least a whole essay on this phenomenon, but this is what I’m talking about here.
- I can’t overemphasize the extent to which I’m not arguing from any intrinsic bad qualities of mathematics. Mathematics as a human, social activity predates capitalism and predates the coercive state. Mathematical concepts and styles of reasoning have an extensive folk literature, oral as well as written. The human joy in thinking mathematically is yet another quality discovered and exploited by capitalism. In that regard it’s similar to the human joy in sexuality, another not intrinsically bad thing which can be diverted and repurposed in infinitely many very, very bad ways.
- It’s worth noting here that this point doesn’t require a conspiracy, where capitalists directly order math teachers to magnify their enthusiasms to have this effect. Math teachers do it each for their own individual reasons and capital, noting this tendency on a sociological level, has evolved to take advantage of the protection it offers. No conspiracy beyond ordinary sociological emergence is necessary to explain the phenomenon.
- I don’t know how this works now, but with respect to wasted lives, when I was in junior high school in the 1970s kids disappeared as the result of behavioral noncompliance all the time. Kids who wouldn’t shut up, sit still, respect authority, remain asexual, respect property, and so on, would just vanish, never to return. This process mostly stopped in high school, because the more primitively rebellious kids had been weeded out. In high school it was the cops who did the weeding out. The result is a bunch of well-trained college students who know how to sit quietly in calculus class.
- It’s possible that this is a rationalization, but I don’t think it is. Until I gain some clarity on it, though, I’m not going to do anything about it, so it’s unavoidable in the sense that I haven’t thought of a better option yet.
- I am in the process of writing a paper explaining this, although I won’t be able to finish it until I’m done assessing how well it works. Here’s the current version as of this writing. I’m interested in your thoughts if you have any.
- Hence my sketchy and passively voiced summary.
- Here’s a proof by contradiction of that claim. If they’re neutral they’d be evidence that capital doesn’t control every aspect of human life and therefore support the stability of capital in the face of critics who claim otherwise, of which there are many, so not neutral. Thus they don’t exist.
- I wrote an essay about this recently, but it needs some work.