**I.**

If you’re just joining us: I wrote this, some people liked it, others did not. Sunil Singh, whose post I was critiquing, understandably didn’t like what I had to say.

(He also didn’t like *how *I said it. Admittedly, I was a bit obnoxious. But Sunil’s rhetoric was not kind either and, dammit, sometimes two wrongs *do *make a right. Happy to deescalate the rhetoric, though.)

As I see it, Sunil’s core argument in his post goes like this:

- People, in general, hate math
- It’s math education’s fault
- The problem is that math education has deviated from the purposes and values of math (as identified by Francis Su)
- Math needs to take back math education — in particular, mathematicians need to direct math education

I wanted to make sure I was understanding the argument correctly — it seems to check out with Sunil.

Now, the goal here is to reconstruct Sunil’s argument in a way that he would recognize — maybe, if we do a really good job, in a way that he would recognize as even clearer than his own version.

Towards that, let’s try to clarify: what exactly would it mean for mathematicians to “take back” math education? This gets clearer from Sunil’s examples of where math education has gone wrong. He calls out homework as a major problem (“homework is on life support”). He wants to get rid of grades. He wants to radically change assessment. He thinks math education has been infected by financial and political forces. He says math education is not operating in the best interest of children.

The point being that it’s not only classroom teaching that is making children hate math — it’s everything, the whole system. Mathematicians need to be in charge of *all this*.

And who are these “mathematicians”? Am *I *a mathematician? The problem, as Matt Enlow points out, is that while the term “mathematician” can mean “someone who gets paid to do mathematics” or “someone who has received an unusual amount of training in mathematics,” it can also mean “a lover of mathematics, someone committed to the discipline.” (The exact same difficulty surrounds words like “artist” or “educator.”)

Sunil Singh isn’t a professional working mathematician, so let’s assume that he means to use “mathematician” broadly.

His argument, all together, therefore goes like this: *If mathematicians — people who love and truly get mathematics — had control of math education, there’s no way it would look the way it does. There would be no homework. There would be none of this testing to decide who is worthy or unworthy of more math. There would be no grades. The universal values of mathematics would be the focus of education: play, justice, truth, beauty and love. Students would have a chance to learn math that truly interests them, not the garbage we throw at them in algebra classes. They’d learn the “dream team” of beautiful math, not a hierarchy of topics on this inevitable, dreary march to nowhere. *

This, as I understand it, is Sunil’s argument.

**II.**

I disagree with basically all of it.

Not because the status quo in math education is ideal to me. I don’t like grades, I think they’re overall bad for learning. I think the math curriculum is over-stuffed and deserves a healthy pruning. Our current testing regime in the US is nuts, and my experience with NY’s Regents exams have all been frustrating.

But here’s the thing about mathematicians and math education: you don’t have to sit and wonder what a math education designed by people who love and truly get math would look like. It’s not some mystery. University math departments are designed and filled *exclusively* with people who love math so much that they’ve signed up for a lifetime of studying and teaching it.

You know what’s coming next, right? Because university math courses are, on the whole, taught far more poorly than k-12 math courses. Where were all the mathematicians when they were designing entrance exams to decide which Calculus section you get to sign up for? Where is the play and exploration in Abstract Algebra classes? Why is the dominant pedagogy notes and lecture? What on Earth is the deal with a class like Math 55?

And it’s also not some sort of mystery what professional lovers of math advocate for when it comes to k-12 education. They call for more rigor, they worry that their students are coming with weaker skills than they used to, they criticize textbooks for having ever-so-fuzzy definitions, and, not to put too fine a point on it, they aren’t exactly lining outside of the statehouse asking k-12 educators to ditch all that algebra.

The way I see things, Singh’s mistake is in thinking that math education is some deviation from the desires of mathematicians and lovers of mathematics. I mean, yes, k-12 math education absolutely is a deviation from a particular vision of math that Singh articulates. But if you look at university teaching and if you look at the rigor, precision, and gate-keeping that mathematicians frequently call for in k-12 education, you can see that this isn’t a deviation; it’s a reflection of what a major segment of the math-loving population wants out of math education.

Singh’s piece was written as a polemic against math education. This is entirely unfair, though, as math education and math culture are codependent. The issues with math education are equally issues facing the broader mathematical community.

Mathematicians and lovers of mathematics love to hate on math education and its deviations. But it’s the lovers of mathematics who have set up the system that we have. They protect it and extend it into higher education. It’s painful to see that some of the problems we have in math education can even *spring** *from that love — from a desire to protect mathematics, or a desire to spread mathematics.

And realizing all of this is a way to realize that Singh’s diagnosis is incorrect. The problems with math education come from the competing desires that non-mathematicians along with mathematicians want from k-12 classrooms. Mathematicians may want students to be exposed to the beauty of math, but they equally want to find the gifted few who can enroll in their college classes, and they want those students to be well-prepared. Lovers of mathematics want to make sure that the discipline — which they love — is well-understood and used by the populace. And they want to make sure that engineers, doctors, accountants, NSA hackers, software designers, everyone is given a solid grounding in math. And, like the rest of us, they want to think that everyone gets a fair shot at any of those jobs.

You can’t improve math education without understanding what exactly is going on. Singh’s vision of mathematics isn’t universal among lovers of math, even among those who really know and *get it. *(Unless we say no *true *lover of math would disagree with Singh’s vision, which is totally cheating.)

We’ll never improve math education in our current system by trying to blow it up, and I think that would only make things worse. I have a great respect for those who operate outside of the world of math education who try to spread their love of the field more widely. But here in the world of math education, we’re all trying to figure out how to help kids deal with the mess that mathematicians and everyone else have left us.

And, actually, we’re making some progress. So ease up on the attack on math education.

Jesus. This is gorgeous. Rock on with your bad self.

LikeLiked by 1 person

I can think of few cruler things to inflict on K-12 students than my own University Mathematics experience.

It seems a bunch of us online folks are fond of thinking about the mathematicians we like from TED talks and accessible books – Strogatz, Devlin, Ellenberg, Fry – and forget that these wonderful messengers are the exception among professional mathematicians, not the rule. And even then, we don’t really know anything about their pedagogical tendencies.

Thanks to both you and Sunil for getting all of us to think more deeply about the issues and potential correctives. These conversations are important and have certainly challenged my own thinking.

LikeLiked by 1 person

Sometimes I think that one of the hallmarks of being a mathematician is thinking you could do anything better than the people who are currently doing it. Took me a while to get over that, so I could be projecting.

One of the reasons I appreciate my department so much is that it’s filled with mathematicians who get that teaching math is different and just as hard as doing math. Some of them have written an inquiry based abstract algebra book, for example. (And linear algebra, and calculus…) At a typical university you get your job by just being good at research, and it is almost an accident if you are a good teacher, or even what passes for one in a university math department. (“He is a good teacher, and pauses regularly to ask if the students understand,” I have read in a teaching recommendation letter.)

Developing an appreciation for how complicated the problem of math education is and acknowledging that the people working on it are bright and hard working is a good start.

LikeLiked by 1 person

As far as math professors go, I think I had some great ones. And yet, my experience from undergrad is that I’m not very good at math despite being a math (and cs) major. Only later to understand that I’m just not very good at *college* math, proving abstract things and the like. Nor does that kind of math interest me very much. I love math, but I don’t love college math. (Thought my anecdote would be interesting)

LikeLiked by 2 people

This post resonates with me, especially your comment in your previous post that pedagogy is a source of mathematical innovation. I think it’s easy to fall into the trap of viewing K-12 math teachers as “second rate mathematicians” while thinking only the PhD mathematicians know enough math to curate what’s worth teaching. But I wish there was more research into how math education impact the mathematical community as a whole. Because I think it does. And it’s not just that pedagogy drives innovation. Math is a way of organizing, processing, and communicating ideas. It’s just as much about *how* we say something as it is about *what* we’re saying. A proof may be true, but it’s the conclusion combined with the proof that we call mathematics.

So here’s my question: how has the way math has been taught over the years influenced the way mathematicians have organized, thought about, and communicated mathematics? To the extent math has taken shape as a result of human traditions, how have trends and ideas in pedagogy shaped and influenced these traditions?

It just seems like you can’t relegate math ed without ignoring forces that have helped math itself take shape

LikeLike

Thanks for the comments everybody — and especially the stories about college math experiences, which I share.

I want to add that I don’t mean to say that the REAL problem is university math educators. I only bring up post-secondary educators because I think it’s a counterexample to Singh’s diagnosis. If the problem were a problem of enthusiasm for mathematics, or a love of mathematics, or getting the values and purposes of math then university educators should be the solution. From Singh’s point of view, you shouldn’t expect people who really “get” math to replicate all the issues that he sees in k-12 education. But we do, so he’s wrong.

So I really don’t want to be guilty of playing a blame game. University educators, like k-12 educators, are mostly doing their best with a tricky system. But that system is reinforced by many lovers of math, precisely BECAUSE they love math, and so I think Singh’s take is not correct.

LikeLike