I recently reviewed a document which as been circulating and generating much criticism. It’s called A Pathway to Equitable Math Instruction – Dismantling Racism in Mathematics Instruction. It can be downloaded here, although few will dare to read it because it it is over eighty pages long.
I became aware of it through a tweet by Lawrence Krauss,
This was quickly followed by a reply from Hemant Mehta who publishes the Friendly Atheist blog:
Which made me think I had better read the thing. And I did.
Thankfully, it is formatted as a workbook with lots of blank pages for the aspiring teacher to fill out. It is segmented as a 10-month plan which would allow the reader to implement these strategies gradually over the course of a school year. The question is whether they should bother.
The answer is definitely no! That is not to say that I disagree with everything inside, only that the document, taken as a whole is an irredeemable waste of time. The few pieces of useful advice should already be known to any teacher who would come across this document and so anything good it brings to the table is not new, and anything new it brings to the table is not good.
By way of background, I spent 12 years tutoring high school students as a side hustle. I can confirm that many, many people find math extremely challenging. I’ve had a lot of time to think about why and can attest this really has nothing to do with their race.
We know why math is hard. You can easily imagine why when you think about what the subject entails. Where does our math come from? It was developed gradually over a period of 2000+ years by individuals who, at the time when they lived, would have been among the smartest humans alive. Their work was assembled across countries, languages and generations. It was refined, edited, simplified, streamlined, and eventually assembled into an order where we presume to teach it to average ordinary humans before they are old enough to vote. The sheer quantity of material is reflected in the pacing of a math class. After middle school, it’s basically a new topic every single class for six years straight, with only the occasional pause for a test. And it all builds on earlier material like a snowball.
The whole subject is interconnected. I tell all of my students early on that the most important thing to remember is that you are not allowed to forget anything taught to you in math ever. Topics you assumed were over and done with reappear years later without warming. And the teacher assumes you know them. That means that if something is missing in your math education early on (you had a bad teacher, you had an illness that caused you to miss chunks of a school year, you were an accomplished athlete and the school allowed you to miss classes frequently, or any other number of perfectly reasonable challenges) then this handicap persists and amplifies over time. Someone who doesn’t master the basics of solving a linear equation at age 13 or 14 is in for at least four years of consistent misery because that skill is constantly in use and the teacher doesn’t have the time to pause to re-explain it to you.
Why can I say that this document is useless. Because for all of the challenges I have just listed about learning math which are patently obvious to anyone who as attempted to teach the subject… the authors of this document don’t seem to be aware of any of them.
How this manifests in the real world
Early on, almost every child comes up with the following brilliant observation: When am I ever going to use this? This is pointless.
The truth is that almost everything you care about in real life relies on people who excel at mathematics. The phone that runs your life, the video game console that allows you to have fun over the internet, the GPS satellites that keep you from getting lost, the government agency that needs to ensure that enough vaccine doses get to the right place as quickly as possible. Hell, my watch has enough computing power in it to run all of the moon landings, and break every Nazi WWII code at the same time, and it’s been manufactured with enough precision and durability that I haven’t turned it off in over three years and it’s still running. To assume that math doesn’t play an important role in your life is to just assume that new technology appears on the scene delivered by fairies and storks.
So the complaint evolves. But I can just use a calculator… I can pay someone to do my taxes. So without pausing to admit that their first objection was wrong, it mutates into a kind of bargaining. Even if I don’t learn math, the world will have a sufficient stockpile of nerds to hold the modern world together and I can just do some other job. You are allowed to get off the math bus. The only drawback is that because of the snowball nature of the material, once you’re off you’re almost certainly off forever.
As a society, we have generally allowed this. Math has an opt-out clause. If you are willing to publicly confess yourself as “not a math person”, then we will nod along and lower our expectations of you. That in and of itself isn’t necessarily bad. We thrive as a species through division of labour. Society needs writers, lawyers, journalists, doctors, engineers, programmers, chefs, artists and all the rest of it.
The challenge is that the concepts have a way of sneaking back into your life in unexpected ways. Most recently we’ve been assaulted with numbers in the form of COVID-19 statistics. How do I make sense of case numbers per day? Vaccine effectiveness rates? Risks of various activities? What if I have spent most of my life hiding from numbers, relying on others to do my math for me? Will I know how to question my trusted news source to have someone on staff to learn that math for me? Or should I just listen a politician who says something isn’t a big deal? Innumeracy can become a lifelong handicap.
But anyone reading this document is left with a powerful message: math and science, along with the thinking and values that underpin it, are white things. The way you interact with society, the skills and knowledge that you are likely to pursue in your life is determined by your skin colour. Students from certain races have brains that are fundamentally different in some way, and need to be accommodated so that they are able to pay lip service to the value of math and science and they can learn about it, but without being expected to acquire the same skills.
Coincidentally, before composing this piece, I listened to an interview on the Canadian science program, Quirks and Quarks about a scientist tasked with firing a ray gun to blow up rocks on Mars. If there were anything liable to get kids interested in science, it would be that. But the thrust of this anti-racism document is that teachers are to make the assumption that they can tell whether or not students would be suited to that based on the colour of their skin. There is a term for this: The Soft Bigotry of Low Expectations. And the confusing wishy washy language that pervades modern “anti-racism” is perfectly applied to take this quiet racism and disguise it with political spin.
So the race portion of the document is simply bullshit. But the question remains: how do you fix the problem?
Could you just cut out some of the material and let the whole process slow down? There are two major practical problems. The first is that math is fundamentally intertwined with science, mostly physics but to a lesser extent chemistry. So if you delay teaching math, you also have to hold back certain concepts in science.
The other problem is competition. These skills have tremendous value in the marketplace. All the money you want to handle and all the technology you depend on is built by people who are comfortable with math. So if you’re going to say that students in X district are going to know less math by the end of high school then students in Y district, it’s pretty obvious what’s going to happen. And you can’t solve it by just making it a national mandate. Cause universities and companies will all of a sudden become more interested in students from other countries. It’s a prototypical arms race (as described brilliantly in The Selfish Gene.)
There’s no way to improve math education by dumbing it down, making it easier or spreading it out over more time.
Making it better
Here are the couple of possibly useful ideas contained in the document, even though they aren’t new and don’t have anything to do with racism, anti-racism or white supremacy nonsense. Being an engaging teacher is challenging, particularly when your field presents difficult subject matter that needs to be delivered on a tight schedule. Are there other ways of injecting knowledge besides lesson-homework-test-rinse-repeat? Of course there are, but they are generally more time consuming.
Math concepts generally follow a pattern. We explore a new concept, try to understand what’s going on. From there we generalize to make rules, laws or useful shortcuts. The hard work is in the useful shortcuts. Understanding division in terms of pizza slices and members of a sports team is easy. The algorithm for long-division when you divide by decimals is complex and abstract. “Understanding” division is nice, being able to do division is better. And if there’s a better way of becoming proficient at it other than rote repetition, no one has yet come up with it. Could there be an animation or a song or a piece of visual art that makes learning that algorithm less grating? Maybe. But if you’re asking individual teachers in workbooks to try and come up with it, then that doesn’t scale to the likely millions of teachers currently working.
Would it help to engage students to more about the human stories behind the people who invented these concepts? Maybe? Should it matter the skin colour of these people? No.
Remember that math has values embedded in it. We want to get the right answer because we value precision. We want robust techniques that scale to more complicated problems if numbers get large or are replaced with long decimals. Math isn’t the way it is because a math-pope says it is. It’s because people (across languages, countries and centuries) have adopted techniques because they work. We value showing work, not because math is about “getting the right answer”, but in the real world when you are doing math not for a teacher that has the answer key, your answer should have embedded within it, the justification for why we should accept your answer is true. Showing work is about communicating clearly, effectively and persuasively
Currently we do have some new opportunities presented. Recreational content created by YouTubers can have extraordinarily high production value with great visuals and animation to make concepts easier to understand. And because of the way the internet works, once they’re out there, all classrooms in principle have access to them.
If you want to become a better math teacher, there are ways to do it. None of them revolve around paying closer attention to the skin colour of the students in a class. If they don’t know something, teach them. If they forgot something, remind them. If they don’t understand, find another way to explain it more clearly. But math belongs to humans all over the world and has nothing to do with nationality or skin colour.