The only thing worse than our pervasive cultural misbeliefs about numeracy is when mathematicians give them cover.
Here’s an example, with author omitted. (These gags are ubiquitous and I’m not trying to “cancel” anyone!)
I am a trained mathematician right up until I have to calculate a restaurant tip. (In reply to the below)
I am a trained microbiogist right up until a cookie falls on the ground.
— Susanna L Harris (@SusannaLHarris) September 30, 2019
And while I know these are tongue-in-cheek funny jokes (so please don’t @ me), I have to ask: Who laughs? Who’s supposed to laugh? And what happens when they do?
I suggest three things.
- This gag is dangerous when it activates in its listeners a soft anti-intellectualism. (And in particular stokes antipathy toward mathematics and numeracy.)
- But, in the mouths of mathematicians, it also comes from a place of valid frustration over public misunderstanding of what our discipline is about.
- And, it is Okay™️ for anyone to stumble over mental arithmetic — but not to pretend that that skill is without value, especially since that pretense often comes from privilege.
You might only have gotten one of these three, but #MathTwitter felt strongly otherwise:
Resisting the urge to rant RE: the "I'm a mathematician who can't do simple arithmetic" meme. Do I:
— Matt Salomone (@matthematician) October 1, 2019
So let’s dive in, shall we?
“I Can’t” As Anti-Intellectualism
The anti-intellectual tradition in American popular culture is an old one. Richard Hofstadter in the linked book, written in the 1960s, sees the phenomenon as a consequence of the U.S. educational system’s successful democratization of knowledge. The more available education was, the more devalued its currency may have become — and the average American had fewer excuses to remain uneducated. In this way, anti-intellectualism became a projection of one’s own shame onto elites and experts:
[T]hey found it easier to reject what they could not have than to admit the lack of it as a deficiency in themselves.
The result is a uniquely American strain of Know-Nothingism for which it is easy to find parallels in today’s public discourse that are so eerie, I suspect Hofstadter may have had a time machine. He wrote in 1963! that:
[t]he citizen cannot cease to need or to be at the mercy of experts, but he can achieve a kind of revenge by ridiculing the wild-eyed professor, the irresponsible brain truster, or the mad scientist, and by applauding the politicians as they pursue the subversive teacher, the suspect scientist, or the allegedly treacherous foreign-policy adviser. There has always been in our national experience a type of mind which elevates hatred to a kind of creed; for this mind, group hatreds take a place in politics similar to the class struggle in some other modern societies.
English literacy in the U.S. is all but universal now, and you will find few holdouts who take pride in making light of one’s lack of basic language, grammar, and spelling skills. Apart from this joker, of course:
Me: Spelling bee champion in fifth grade
Also me: Can't use a UNIX shell without 'alias claer clear' https://t.co/5E0WDiSUGc
— Matt Salomone (@matthematician) September 10, 2019
But mathematics and numeracy skills are a whole different story. Far from universal, basic numeracy skills in the U.S. are increasingly concentrated in fewer and fewer hands. The OECD’s Survey of Adult Skills included a test of basic numeracy for the first time in 2013, and among the twenty-five developed countries in which the survey was administered, U.S. adults ranked 23rd — surmounting only Italy and Spain.
And, as the labor market and the Big Data economy has created a wealth of new, well-compensated jobs for data professionals working in fields like business intelligence, predictive analytics, and data science, the net effect is that numeracy is in danger of becoming an elite skill. The one percent of the most numerate now wield more economic and political power over the ninety-nine percent who are less numerate than ever before. That’s a problem, especially when numberphiles are no less likely — in fact, more likely! — to deploy numbers to mislead, misinform, and motivate their biases.
Is it any wonder, then, that I can’t do math has become the new shibboleth of the populist anti-intellectual? The phrase is almost invariably deployed to either
- Deflect potential shame from a more numerate interlocutor. (This is what every mathematician and math educator experiences every time they tell a new acquaintance what they do for a living. Some, by now, have given up and tell people they drive trucks.) Or,
- Create solidarity among one’s peers, using this disclaimer as a signal of my “average person”-ness. (I’m not like Them — I’m one of You!)
It is that second usage that is, I suspect, most common – and most pernicious. As Hofstadter points out in the 1960s, we are invariably at the mercy of experts. And and Cathy O’Neil has memorably pointed out in the 2010s, the experts about whose ways and whose reach we have the least understanding are the “quants,” the professionals who collect, design, and analyze vast quantities of data on us that impact every facet of our lives (and, impact less privileged folks disproportionately more). In O’Neil’s view, being one of You, opting out of one’s obligation to be numerate at minimum as a defense against exploitation, comes at a steep social cost that perpetuates historical inequities.
So why do mathematicians – who are often the first to decry the culture’s antipathy toward all things mathematical – join the chorus, declaiming their own basic arithmetic skills?
One reason is exactly because it is a soft bid for solidarity with their audience. “It’s okay; I might be a mathematician but I’m not like that mean Mr. Horton who called you out in third grade for not knowing your times tables.” And I’m sure they don’t mean in those moments to normalize anti-intellectual or anti-numerate sentiments for their audience. But there’s a second reason that mathematicians as a group might want to diminish the importance of basic arithmetic and mental computation skills.
Mathematics Is Not (Only) About Numbers
"Many persons who have not studied mathematics confuse it with arithmetic and consider it a dry and arid science. Actually, however, this science requires great fantasy."
— Sophia Kovalevsky
— Brendan W. Sullivan (@professorbrenda) October 2, 2019
Every social movement has its radical elements. (I’m barely restraining a good square-root pun here.)
Only extreme positions and extreme methods, they reason, are capable of shifting the Overton window in the direction of the change their larger movement wants. I’m thinking here about the contributions of people like Huey Newton and Malcolm X to the movement for civil rights, or the ways that some people justify disruptive protests and property damage in movements for environmental or social justice. There will always be those who will reach for a mile to move the public an inch.
Mathematicians who tout their lack of mental arithmetic skills, likewise, serve as radical exemplars of a cause: the cause of educating the wider culture about the nature of mathematics itself. Namely, that mathematics is vastly more than arithmetic and its kin subjects; it is an expansive way of thinking and reasoning, analytically and logically, with rigorous self-consistency and fastidious attention to detail. It is a discipline in which many of its practitioners find enormous beauty, taste seemingly transcendent truths, and playfully explore the limits of their imaginations. For them, mathematics is a true expression of human flourishing. And they don’t understand why the rest of the world doesn’t see it that way.
Or maybe they do understand, and that is the very source of their frustration.
Many students, after all, do experience school mathematics as the “dry and arid science” Kovalevskaya describes. Hemmed in as it is by a narrow arithmetic-geometry-algebra-calculus curriculum, and taught (especially in the early grades) by teachers who themselves harbor deep anxiety, trepidation, and skepticism of the value of the subject, it’s no surprise that the mathematics encountered in a great many school classrooms leaves little room for the kinds of playful, appreciative, beauty-seeking practices that professional mathematicians enjoy. The few students who are fortunate enough to have teachers and/or parents who nurture those practices with them — such as by playing with logical games or puzzles that often have very little to do with numbers or arithmetic at all — are more likely to persist and be successful in mathematics and science later in their educational life.
Worse yet, professional mathematicians do not generally find their colleagues in the academy to hold any less blinkered a view of the nature of our discipline. It is becoming increasingly possible in modern higher education for students to complete bachelor’s degrees having never had an experience of what “real” mathematical thought and practice looks like. There are probably several structural reasons why this is more the case now than it was fifty years ago; in my view they are, from most to least culpable:
- Enrollment booms in higher education without commensurate increases in hiring of tenure-track PhD mathematicians. More students than ever are being taught by contingent faculty, many of whom have not themselves had a flourishing experience with mathematics in their own education and professional lives. [Edit: Thread clarifying my point here.]
- Ineffective pedagogical choices in many math classrooms, particularly at the college level. Related to the previous point, we have many college math instructors whose own orientation to the subject is “dry and arid,” and (likely because their own teachers did as well) rely on didactic instructional methods. Lectures. “My job is to teach the subject, not the students,” they say, and when the subject is seen as a static superstructure of received facts, it makes sense to treat teaching as an exercise in the transplant of those facts. Give students room to play or explore, and they might arrive at the “wrong” conclusions.
- Differences in the meaning of grades between math instructors and … well, the rest of the academy. D/F/W rates have long been stalking horses for college administrators to pressure math departments to make reforms. Math faculty receive this as pressure to lower their standards, or face marginalization in the liberal education marketplace. And math requirements have begun to fall by the wayside in higher education. But there is blame on all sides in this: math faculty culture continues to see our field as an intellectual gatekeeper for higher education. We see high attrition as a synonym for high standards. We are among the last fields to think critically about designing our courses for significant learning, our syllabi around student outcomes and not just content, and our assessment practices to recognize mastery-over-time and not just performance. Reports of our demise are still premature, but if it happens, we cannot say that we have not contributed to hastening it.
- Intransigence in K-12 curriculum that continues to focus almost exclusively on preparing students for calculus. It asks them to run a long sprint through the woods without ever giving them the opportunity to pause and admire the scenery. The Common Core State Standards’ Standards for Mathematical Practice may be the first high-profile effort to make the nature of mathematical thought explicit for K-12 educators and their students, but the narrow focus and density of the content standards make this a nearly-impossible thing to dwell on in the primary and secondary classroom itself.
There is a kind of codependent relationship between mathematicians and the university when it comes to teaching. We may want to make authentic mathematical discovery a part of every student’s education, but in the face of an academy that (rightly) sees innumeracy as a crisis and (wrongly) mathematics as its solution, we are at times too content to accept whatever role we are permitted to have in general education. And if we cannot introduce the wider student population to the true meaning of mathematics in our college curriculum, we can at least push back on this injustice by pointing out that our own deficits in basic arithmetic skill do not impair our ability to practice “true” mathematics. It may be passive-aggressive, but it keeps food on our tables.
Yet, while we as highly-educated people with (what were at some point in history) prestigious and stable careers can seemingly “get away” with deficient number skills, we ought to keep in mind that that is not true outside our bubbles. That brings me to my last point.
Numeracy is an Equity Issue
Quantitative literacy intersects with equity and social justice in more ways than ever. With numerical data being collected and stored at a breakneck pace, our lives are at the mercy of a tidal wave of numbers on a daily basis.
But, not all of our lives are affected equally. Cathy O’Neil’s book Weapons of Math Destruction has given perhaps the most popular oxygen to public skepticism about automation, algorithms, and Big Data. She argues that many data-powered algorithms, from credit scores to college admissions, far from being objective forces for equity, offer no more transparency or accountability than human decisions do, and in fact replicate social biases.
Algorithms don’t make things fair if you just blithely, blindly apply algorithms. They repeat our past practices, our patterns. They automate the status quo. That would be great if we had a perfect world, but we don’t.
To be innumerate in today’s world is to forsake an important defense mechanism against commercial, political, and financial exploitation. More privileged people, who enjoy more structural defenses against this kind of exploitation, can afford to lay this shield aside. But to normalize that behavior is to uphold an unequal status quo.
It takes a certain basic arithmetic skill, for example, to comprehend the scope of income inequality in our economy well enough to organize against it. It takes a certain basic arithmetic skill to grasp the corrosive effects of ever-more-regressive tax rates. To understand why usurious loans are never a good idea. To advance from wage employment to salary. These might not be critical issues for people in higher social strata, but to pretend they are unimportant is to narrow the pipeline into the middle class.
Paying the Bill
So, innumeracy exacts a high social cost in the United States, and that’s a bill that is coming due more and more each day. But does that mean all of us need to be able to calculate a tip on that bill off the tops of our heads? Is mental arithmetic really that important? Do we all need to go back to our times tables and speed tests?
No. Of course everyone will stumble over simple arithmetic computations done on the fly, because there are always moments when our rapid-thinking, relational cognition makes mistakes. The purposeful, effortful thinking required to do accurate mental arithmetic is always less likely to be used. And, as Daniel Kahneman writes in Thinking, Fast and Slow, that means we are less likely to assign importance to it.
People tend to assess the relative importance of issues by the ease with which they are retrieved from memory.
And mental arithmetic per se is admittedly less important nowadays, given the sheer ubiquity of computers and the instant ability nearly all of us have to use that technology at any given moment.
But for a public whose tendency is to conflate mental arithmetic, numeracy, and mathematical skill, throwing out the bathwater casts out the baby. When we devalue mental arithmetic, we risk — in their eyes — devaluing both numeracy writ large and the discipline of mathematics we hold so dear.
That’s why, despite my both-sides-iness in this post, I contend that projecting an image of innumeracy, even in jest, does more social harm than good. As long as a culture persists that is fearful, suspicious, and dismissive of all things numerical and mathematical, gags like these only add fuel to that fire.
We cannot stand on the deck of a ship and brag to a drowning person that we never learned to swim.