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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.

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.


https://chez-risk.in/2023/04/05/why-are-children-forced-to-study-mathematics-at-gunpoint/

#Capitalism #Coercion #CompulsorySchooling #K12Education #Mathematics #MathematicsEducation #PoliceAbolition #PoliceViolence #Resistance #SocialSystems #Stability #STEMEducation

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

But what I see lacking in the ungrading literature is the undeniable fact that grading practices, and student attitudes towards grading practices for that matter, exist in a larger social context. It’s the context not only within which schools also exist, but which creates and requires pedagogical practices such as letter grades, mandatory attendance, comprehensive final exams and which ultimately specifies even the very subjects being taught.

The social context creates life-altering rewards for students with good grades and life-altering punishments for those who don’t measure up. It may even be this context that informs student thinking on the purpose of schooling and the significance of letter grades. This larger social context isn’t amenable to change on a pedagogically useful time-scale, which may be why the ungrading literature, as far as I can see, doesn’t really consider it in the design of particular grading practices in particular classrooms in pragmatic ways.

Ungraders may or may not be right about the harm letter grading does to the classroom learning atmosphere, but they are certainly right about the historically contingent status of the practice itself. Letter grades aren’t an immutably objective requirement for successful education. They’re just a tool that some people invented at some point to further their purposes. Since then evolving needs have revealed new capabilities in the tool and letter grading has come to serve many new purposes. But ultimately it was invented and adopted by people and we can abandon it as easily if it suits our purposes to do so.

Consistent with their habit of ignoring the political context in which letter grading exists there is a tendency among ungraders to see their pedagogical practices as creating safe bubbles for their students away from the antieducational but presently unchangeable system of letter grades. By implication, therefore, also away from the larger social context in which all of us, students, teachers, administrators, and schools themselves, exist. As Kohn puts it, the best ungrading practices allow “the prospect of final grades [to remain] as invisible as possible for as long as possible."5 Ungrading as reflected in the literature is fundamentally an accomodation to the larger social system rather than a challenge to it.

But the social context cries out to be challenged. Letter grades are used against students in many ways and in few if any ways that benefit them. If my goal is to educate my students, to help them learn something worth their time and to their benefit, well, this strikes me as incompatible with the pernicious effects of letter grading on my students. In this essay I propose a very partial solution to the question of the role of letter grades in this larger social context, but it’s not a general proposal.

In order to keep my thoughts and experiments as closely linked as possible to my own students’ best interests I resolved to only consider and propose modifications in the things I understand best, which turned out to be my own classroom. But I’m a tenured associate professor of mathematics at Whittier College, a small private liberal arts school in Southern California. This gives me a wide range of not so widely available options, which may make my thinking only narrowly applicable, maybe even only to me. I hope that perhaps my thoughts might inspire other teachers to find ways to address this problem, the problem of letter grading in a coercive society, in ways that make sense in their own disciplines, employment constraints, methodologies, and so on.

Classrooms aren’t bubbles


Instead of beginning with the relatively unexamined assumption that students are wrong to focus so intently on getting As, that it’s something problematic inside the students’ heads hindering learning, it might also be fruitful to assume that the students are right, that they know their own interests better than their teachers do, no matter whether they can articulate them in academic jargon or even at all.

Students clearly understand what they have at stake with respect to their grades.6 Everybody understands. Good grades may or may not correlate to a good education but they certainly afford vastly more opportunities than mediocre or bad grades do in terms of future education, jobs, income, health, and even wealth. These things shape people’s entire lives and the lives of generations of their families. It’s unrealistic to expect students to forget this omnipresent, evident, and absolutely life-essential fact.

The benefits that follow good grades are the carrot, such as it is, but there’s also a stick. In an immediate sense even a single F can mess up students’ financial aid, get them kicked out of school or the dorm, which may be their only housing option. It may trigger loan repayment obligations or worse. Later on bad grades and less education lead to worse jobs, which lead to less money, worse medical care, lowered life expectancy, and less personal control over one’s place in the world, often with heavy student debt adding to the pain.

Bad grades lead to a more precarious existence, in which bad luck or what might otherwise be small errors spiral up into terrible consequences like unemployment, loss of health insurance, hungry children, homelessness, and so on. Without independent wealth it’s life-threatening not to have a job, and the worse a job is the easier it is to lose it. It’s really unrealistic to expect students to forget this omnipresent and evident fact.

The context in which students go to college is coercive, then, and letter grades are part of the coercion. They go on your permanent record, don’t they? It’s hard to create a safe bubble in the classroom to keep grades invisible for as long as possible given the dire consequences attached to them. Bubbles can’t hide the real threat of impending unemployability and potential death from homelessness.7

As far as I can see, though, the ungrading community lacks an analysis of letter grading that confronts this social context. Their attention seems to me to be focused almost entirely on students’ mindsets insofar as they’re within a given teacher’s power to affect during a single course taught in a single classroom. This may well be an essential issue, but I don’t think it’s nearly as important as their larger-context anxieties. For this reason I don’t engage deeply in this paper with ungraders. I don’t think their work is harmful, and I haven’t read enough of it to know if it’s generally useful, but the problems ungraders set out to solve aren’t the problems I’m addressing here.

Who and what are letter grades good for?


Not for the students, but they’re useful to someone or they wouldn’t be ubiquitous. Grades don’t tell students much about their own work in a class, and they certainly don’t tell students more than I can tell them in a brief conversation at the end of the semester. But there are plenty of people, organizations, and other grade consumers who make a lot of assumptions about students, accurate or not, based on letter grades. If a class is a prerequisite the grade consumers might be the people who teach the classes it’s a prerequisite for. Institutions themselves also consume letter grades, which they use to assign or deny various rewards, like diplomas and scholarships. These are important cases and I discuss them below.

But grade consumers outside the institution, graduate schools, governments, financial institutions, employers, also extract a great deal of information about students from letter grades. This is not to say that the information they extract is accurate, but it is information, they do extract it, and they use it to make decisions which then affect students’ lives, sometimes drastically. Its objective accuracy, if there even is such a thing, is not necessarily correlated with its utility to grade consumers.8 They use this information to serve their purposes, but there’s no reason to assume they use it for the students’ benefit. If they do it’s a coincidence. I don’t know why letter grades are so embedded in their ranking and control systems, but they own the whole world, so they must know their business.

The pal in the corral


If you read about collegiate pedagogy you will inevitably encounter the so-called “sage on the stage,” a gloomy and highly non-normative stock character who drones on and on about dusty old irrelevant nonsense, never stopping to check if anyone cares or even if they’re listening. This fellow’s highly normative antithesis is known as the “guide on the side,” who expertly and lovingly facilitates the students’ innate natural desire to learn joyfully.

But if students’ anxiety about grades in fact originates outside the classroom, if it comes from that exact social context which pens students up in classrooms, processes, ranks, and sorts them for external purposes that are decidedly not in their best interests, then more than either a stage sage or a side guide the ungrading teacher risks becoming a pal in the corral, who isn’t exactly serving the students’ interests either. By the way, it may seem like an extreme way of phrasing it to say that college students are penned up in classrooms given the superficially voluntary nature of going to college. It’s not inaccurate, though. At least not in the sense that the choice not to go to college is a weighty one, made under duress with low information since no one can tell the future. It has life-changing consequences no matter which option people choose. If you have the means and opportunity to go to college and aren’t independently wealthy or without solid other plans for your future it’s a big risk not to go.

So whatever the purposes of the institutions that require us to assign letter grades, my claim here is the grades are currently used by grade consumers outside the institution to harm students. There are a couple commonly heard and fairly facile arguments against this claim. Many people with whom I discussed earlier versions of this paper brought up one or both of them. First, that competitive scholarships or grants awarded based on GPA are a use of grade ranking that helps students. This is only even plausible because college is ruinously expensive. Since it should be free as long as it’s so consequential and since As don’t hurt student scholarship chances, I don’t feel any need to respond to this phenomenon in my grading practice.

Another argument raised in favor of letter grades helping students is the argument from motivation. Without the chance of being publicly labeled as a lower class of student, the argument goes, these folks wouldn’t be able to motivate themselves to study. Unstated but often implied is that without people to do better than they’d have no reason to try to do well. I have so little sympathy for this position that I won’t waste anyone’s time arguing against it.

There’s no defensible pedagogical justification for letter grades but there are many defensible justifications, both pedagogical and ethical, for their abandonment. They don’t help students, and any helpful information they may convey can be conveyed through other means. They do help powerful grade consumers, who have no interest in students’ well-being, achieve their own purposes for the students. We wouldn’t have letter grades if grade consumers didn’t require them.9 The difference between an A and a B or a C is negligible if we’re only concerned with whether or not students have learned enough of the material, but it can be huge in their postgraduate life. If my purpose as a teacher is to teach rather than to sort my students into piles for the benefit of those who don’t have their interests in mind, why would I not give all of these students As? And if my job as a teacher, which is not coextensive with my purpose, somehow requires me to do this, well then, I’d like to hear someone say that out loud, which would also be a valuable outcome.

What is to be done?


As a college teacher I have a lot of freedom in how I assign grades. As far as I know as long as I follow the grading policy I create and put on my syllabus and as long as the policy isn’t prima facie insane,10 no one has substantial grounds for complaint – as far as I can see I’m protected by academic freedom.

One of my recent letter grading policies says that an A grade requires an aggregate score of at least 90% or in the top 10% of the class’s aggregate scores or either of these scores on the final exam alone. I have no idea why I chose these numbers. They’re completely arbitrary, although in line with cultural expectations. If I changed them to something similar, like 86% and 13% or whatever, it’d have to be equally acceptable. No one has ever asked me where these numbers come from, and I wouldn’t know if they did ask me. No matter what numbers I use the policy would make equal sense or nonsense and be equally defensible or indefensible. As far as I can see there isn’t and probably couldn’t be a rule even against giving all the students As all the time.

But, as always, the lack of a rule against something doesn’t mean it’s a good idea to do it, even though in this case it would in some real ways be good for students to only give As. But mathematical knowledge is famously cumulative, and it’s not doing anyone, student or not, much of a favor to give them an A in precalculus if they’re utterly unprepared for calculus.11 A specific quirk of my department is useful here. We require at least a C- to move on to the next class.

For me, at my institution then, the prerequisite problem can be solved by giving As to students who are ready to move on and Ds to the others. While D grades can have bad consequences for students they’re much less immediate than with Fs. The bad consequences of being unready for the next class are more immediate and more likely to happen. But this is easy for me to do within institutional constraints. Since the numbers are arbitrary there’s nothing wrong with making an aggregate percentage of 65% or higher12 worth an A and everyone else who participates in the course gets a D. When I first started thinking about these ideas I didn’t see any reason to give students Fs, but I had to revise this position. Space in classes is limited, and if my policy is to give no Fs then it’s likely that some students would enroll in the class and never show up again because a D serves their purposes.

I don’t object to this in principle, and I don’t even see it as taking unfair advantage, but it does use up a seat in the class that could be filled by a student who does want to learn the material. This is a problem because both my employer and my own limited time restrict the number of students I can enroll in each class. So this semester, which is the first time I’m trying this method openly, in the sense of putting it on my actual syllabus, I will assign F grades to students who don’t attempt at least a certain amount of the coursework and don’t earn at least 50% of the possible points. Here’s the actual language from my Fall 2022 College Algebra syllabus:
If you get 65% or more I’ll give you an A. If you get 50% or more but less than 65% I’ll give you a D. If you get less than 50% and you have turned in all homework and completed all tests I’ll give you a D. If you’re missing assignments and/or tests and get less than 50% I’ll give you an F.

My goal with this language is to give at least a D to students who use all their learning opportunities without penalizing them unduly if they don’t succeed in learning at least enough to move on to the next class. This move solves the prerequisite problem and the nonparticipation problem, but it doesn’t address the low information problem. In fact, it makes it worse by exchanging ten possible outcomes for only two (or three, if you include the possibility of an F for not participating, but I assume the students to whom that applies know why it applies to them). It’s not really an issue, though. While there is every reason to hide the numbers behind the grade from external grade consumers there’s no reason at all to hide them from the students.

The grade consumers don’t glean details from letter grades anyway. If they want more information than grades provide they ask for letters of recommendation. But since I continue running my classes as usual, with numerical scores on assignments as always,13 the students can always know where they stand from the numbers and from conversations with me, just like they always could. The information is still there, and completely available to the students who find it useful, but can easily be ignored by everyone else.

Other Social Commitments


So far I’ve been discussing the issue as if the only relevant parties are the students, me, and some external grade consumers. But my department and the college as a whole use letter grades for our own purposes also.14 All of these contexts create responsibilities. Whether I agree or disagree or don’t know how I feel about how my department or my college use letter grades is not the only consideration. In this kind of social context I have essentially the same power as any of my colleagues to work to change how letter grades are used locally. This makes it seem to me that unless I’m willing to work to advocate and effect change or there’s some immediately overriding moral consideration, neither of which is currently the case, I ought to be guided by the collective wisdom of my colleagues.

For example, my department gives various awards to graduating seniors, and some are based on GPA in the major. Some of the awards are named in honor of family members and come with endowed funding to provide money gifts. One is named for a dear, now deceased, colleague with whom I worked personally. These are weighty social commitments whose bonds and obligations I voluntarily accept. Such commitments aren’t to be fooled with frivolously.

Maybe ranking students at all is morally objectionable, but so is unduly violating deep community commitments. I can’t resolve this problem here — there will always be such problems interfacing with the coercive world and they can’t all be solved at once — my temporary solution is to note that percentage scores are as good or better than letter grades for ranking students. If my grading system unduly perturbs departmental or institutional commitments it’s easy enough to convert one to the other. I don’t have a strong feeling as to whether this is good or bad for students and for that reason it seems better to go on as before in the absence of clarity.

Nonprerequisite Courses


When I first started putting this argument together I felt like it implied that I should only give A grades in courses that weren’t prerequisites. That is, the only reason I saw at first for giving Ds was to not harm students and their future teachers by letting them move on to courses they weren’t prepared for. This conclusion seemed obviously wrong to me, but I couldn’t see where the problem was. I didn’t feel like I could defend that position publicly but also I didn’t have a way to explain, even to myself, why I felt this way.

But once I started thinking about the role of social commitments, the weight of the duty imposed on me by my collegial community, I realized that, whether or not I have a duty to rank students for the benefit of third party grade consumers, I do in fact have a duty to my department and to my college to certify that my students understand the subjects I teach them. As a department we set standards for our major and make collective decisions about whether students meet them. As a college we do the same for the degrees we grant. The conclusion, as before, is that at least until I’m willing to work to change my department’s or my college’s policies, which I’m not since I haven’t thought about them enough to have an opinion, I should and will continue to be guided by my colleagues’ collective wisdom.

This is not pass/fail grading


The plan I’m describing here exchanges ten possible grades for only two. In this one sense it’s similar to pass/fail grading, which Whittier College allows students to opt for unilaterally as long as they do it before some deadline. I think I might have the option to require students to take at least some of my classes on this basis, which is something that at least some ungraders see as a good resolution of their concerns about letter grades.15

I won’t do it, though. Not only does pass/fail grading as it’s practiced at my institution not solve the problem I’m trying to address, it actually makes it worse for the students in at least one specific way. If I give a letter-graded student a D they pass the class and get credit for it even though it lowers their GPA and can’t advance to successor classes. But if the student has opted for pass/fail and I give them a D the registrar automatically translates it to an F (or an NC), potentially triggering all the dire consequences outlined above.

I have no control over this at all. It’s an institutional policy. When I’m teaching as well as when I’m entering grades I can’t even tell which students are taking my class pass/fail. To avoid students falling inadvertently into this trap I will explain the situation thoroughly before the deadline so at least they can make an informed choice with respect to their grading options.16

Conclusion


In this paper I’ve presented this problem as if I, the teacher, am somehow outside the coercive social context that weaponizes letter grades against my students. But of course I’m not. No one is. Not only do I have it in my power to adjust my grading practice to shield students from some small part of the harm done by letter gradeas used by coercive power, but I have a moral duty to do so at the very least because I also benefit from that very coercion. College students aren’t directly forced into my classroom at gunpoint like students subject to compulsory attendance laws, but they’re not there on a purely voluntary basis either.17 Not only that, but the coercive society’s insatiable need for technicians keeps math classrooms reliably full enough for me to earn a living teaching in them.

I also, like so many of us do, have blood on my hands. Like so many of us I’m forced into complicity by my bodily needs, the bodily needs of the family to whose support I contribute. There is no purely ethical way to meet these needs in this world, the only world we have to live in right now. I have no way to be noncomplicit, so the resistance I describe in this paper isn’t some kind of neutral benevolence, and it’s not a contradiction-free political theory. It’s an attempt to address what I see as a moral duty to pay back some few of the benefits I’ve gained from coercion, to bite the hand that feeds me, to say out loud that although I’m forced into complicity with exploitation I’m not forced to be quiet about it, as if I approve of it. I do not approve. I didn’t ask for it and I will take all the steps I can see how to take in order to extract myself from it. This is one step.

Acknowledgments


I am indebted to a number of colleagues, friends, and family who read and commented on earlier versions of this paper. They’ve made it much better than it might have been. I’m especially indebted to Marcus Schultz-Bergin, whose close reading and detailed comments clarified a number of essential issues for me, and whose insight helped me understand what my actual topic was.

Bibliography

[Blum] Ungrading – Why Rating Students Undermines Learning (and What to Do Instead). Susan D. Blum. West Virginia University Press 2020.
[Gibbs] Let’s talk about grading. Laura Gibbs. in [Blum] pp. 91-104.

[Kohn] Foreword. Alfie Kohn. In [Blum] pp. xiii-xx.
  • See e.g. [Blum] for a comprehensive introduction to the literature.
  • [Kohn] p. xiii
  • [Blum] p. 12
  • There are no A+ grades and neither Ds nor Fs admit +/-.
  • [Kohn] p. xvi.
  • The undergraduates that I teach do, and plenty of kids I went to high school with certainly did.
  • Which may sound extreme, but I don’t think it is. Even if postgraduate life may not be as terrifying as some undergraduates imagine it is, it is terrifying, and the connections to school success aren’t exactly secrets.
  • Also interesting is the fact that students can use the information carrying capacity of grades for their own purposes as well, and not just to signal to Harvard Medical School that they should be admitted. From time to time over more than thirty years teaching college I have had students ask me to lower their grades to send messages to grade consumers the details of which I still consider confidential but which made (and make) complete sense to me.
  • Or at least we wouldn’t have them everywhere. Maybe some free people could find a use for them, but I can’t think of any.
  • By which I mean only that as long as it plausibly and in good faith supports the appropriate goals, e.g. teaching students some mathematics, it’s acceptable.
  • This issue is slightly more complex than I’m making it out to be here, since at least at Whittier College and probably at other institutions as well, not every student enrolled in precalculus intends to go on to calculus. This is too particular and tangential to discuss in detail here.
  • This, or even lower, is a normal cutoff for a C- in many college math classes. It seems low, but it’s possible to adjust the course content so that 65% of it prepares a student for the next cleass. It’s useful to make this number low since then not every student has to learn the same 65% of the material, which I think is pedagogically crucial in math classes.
  • Not that I think this is the ideal way to do things. It might not be. But at least for me it’s not a good idea to change too many variables in my classes at one time without solid reasons for doing so. Also it’s useful to me for keeping grades consistent across similar mistakes, which is extremely important pedagogically. Also I’m really comfortable with this system and as far as I can see it’s working pretty well.
  • I use the pronoun “our” rather than “their” deliberately to acknowledge and honor the fact that I am not just a math teacher in a classroom with students, I’m a math teacher in a math department in a college in a classroom with students.
  • See e.g. [Gibbs].
  • It’s possible, maybe even plausible, that this policy is a violation of my academic freedom in that it allows a passing grade that I assign to be changed to a failing grade without my knowledge or consent. Even though I am the professor and have sole responsibility for assigning grades I have no way to know whether I’m passing the student or not. There are no other circumstances I’m aware of in which the institution is allowed to change the substantial meaning of a grade I assign without some kind of process that all parties can participate in. This is not a battle I care to engage in at this time, but I will certainly keep thinking about it.
  • It’s not hyperbole to say that kids subject to compulsory attendance laws are forced into school at gunpoint. If the laws are enforced, and these days they’re enforced assiduously, they’re enforced by courts and police, which is to say that they’re enforced at gunpoint. Anyone who has raised a teenager who just would not go to school is very likely to have experienced the truth of this fact personally.


https://chez-risk.in/2022/10/28/how-im-grading-now-and-why/

#Anarchism #Grading #Ungrading