I’ve written two times on this blog about Andrew Hacker, the Queens College political science professor who keeps getting in the NY Times and has spent his career questioning the establishment and trying to push contrarian views on lots of stuff (race, gender, politics, money inequality, high education, and now math). I think a short summary of all his writing would be: “you think we’re making progress? Ha! Look at how bad things are! Here are some ideas on how to fix the things you thought were okay but are terrible.”

Over the past few years Hacker has taken on math in America. I don’t think anyone in the world thinks that the state of math education in America is the best it could be; that’s why we’re always doing reforms like Common Core standards (which I have written that I love). And Hacker wants to reform it too. But instead of coming up with new ways for students to approach problems and conceptualize content, he wants to get rid of the content and focus on numeracy. Summary of his view: “Say no to algebra.”

I’ve been in a tizzy all week because of his latest op-ed titled “The Wrong Way to Teach Math.” And my tizzy is because I have always held the guy to be a crazy cartoon villain in my head, and now I find that I agree with him on something (because we are both human and neither of us are cartoon heroes or villains and there is such a thing as nuance):

What citizens do need is to be comfortable reading graphs and charts and adept at calculating simple figures in their heads. Ours has become a quantitative century, and we must master its language. Decimals and ratios are now as crucial as nouns and verbs.

This is not a new concept and I hope Hacker nods to John Allen Paulos’ classic book Innumeracy and ensuing titles in his book, but I fear he won’t because Paulos is a mathematician and apparently Hacker hates us, per an article on slate:

Math professors, consumed by their esoteric, super-specialized research, simply don’t care very much about the typical undergraduate, Hacker contends. At universities with graduate programs, tenure-track faculty members teach only 10 percent of introductory math classes. At undergraduate colleges, tenure-track professors handle 42 percent of introductory classes. Graduate students and adjuncts shoulder the vast majority of the load, and they aren’t inspiring many students to continue their math education. In 2013, only 1 percent of all bachelor’s degrees awarded were in math.

Yep, that’s us, uninspiring teaching drones when it should be super-specialized researchers teaching undergraduates algebra. Side note: the skills to excel at research and the skills to excel at teaching do not seem to have a correlation, yet non-academics expect researchers to focus on teaching (link to an article about 4-4 bill in North Carolina).

Keith Devlin gets to the heart of something in his reaction piece for HuffPo, which is that Hacker is, like many people, confusing “school math” with “math.” Here “school math” is essentially a bag of math facts and tricks, like , rather than “math” which is conceptual understanding like that old Pythagorean theorem post (update on that in another post). NPR did an even more confusing thing in the first example of that article:

Hear that change jingling in my pocket? Good. I have two little questions for you.

- I have a quarter, a dime and a nickel. How much money DO I have?
- I have three coins. How much money COULD I have?
The first question is a basic arithmetic problem with one and only one right answer. You might find it on a multiple-choice test.

The second is an open-ended question with a number of different possible correct answers. It would lend itself to a wide-ranging debate over the details: Are these all American coins? Are any of them counterfeit? Do you have any bills?

Frankly, it’s a lot more interesting than the first.

So again, question 1 is “school math” and question 2 is on its way to “math.”

Keeping in line with Devlin’s notation, I think this is the issue:

- Most people think “math” is “school math,” which is a list of tricks to win strange games that they will never encounter again, but they are forced to memorize the rules of these games. Stuff like memorizing the quadratic formula, or algorithms for subtraction/multiplication/long division.
- Scientists, engineers, mathematicians, other friends of math think that “math” is using logical deduction and inferences, given a list of rules, to win a game. By which I mean, to win any game. Even “real-life” games like “how do I get
*n*articles written by the deadline with*m*length and*x*interviews” or “how can I figure out how far to cut this length of wood to support this truss on a theatre set” or “how many people do I need to interview before we’re satisfied/how many people should we have on our interview committee?” - Hacker thinks “school math” is dumb, doesn’t really understand what “math” is, and is a proponent of numeracy. Everyone is a proponent of numeracy, it’s like being a proponent of literacy, you aren’t really propon-ing anything controversial. I am concerned that he may see numeracy as similar to “school math” instead of “math,” and teach people how to read pie charts and bar graphs but not give them the tools to read any infographic (histograms etc.), which is an abstraction of particular charts and graphs.

So my point 3 back there should tell you how I feel about “math” (also the name of my blog, also how I choose to spend my time, also anything that comes out of my mouth.) Practicing math forces us to use logic, discipline, and rigor, which are things we all need in daily life. That slate article says that “reading fiction builds empathy” as a counterpoint to math, which drives me nuts.

I was so worked up about this I sent a letter to the editor of the New York Times, which they obviously didn’t publish because… who cares? (A: me, and probably you). So here’s the unpublished letter:

Math education isn’t an either/or proposition: people need to understand numbers as well as what algebra teaches us. Hacker says students will never use algebra in their lives, but does not hold the rest of high school curriculum to this standard: how many of us dissect frogs, write book reports, or analyze historical documents in our everyday lives? Most people work within a specified set of parameters and rules, whether that’s the maximum number of customers or what forms need to be filled out for whom. We also need to use logic and convince others of our conclusions: for instance, listing the reasons why one deserves a raise, making sure to eliminate questionable arguments. We often repeat tasks and find a fastest algorithm for them, which we then apply to related tasks: making change for a dollar, making change for a ten. Discipline, communication, and abstraction: this is what math is for, and this is what algebra teaches us.

On a happy ending note, here’s an old article that was a response to Hacker’s first op-ed, by a woman who overcame her math anxiety to learn algebra.

Apologies if you have mentioned this before, but I think the best reply to Hacker is Paul Lockhart’s essay, “A Mathematician’s Lament” (published long before any of Hacker’s algebra rants):

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

That op-ed you mentioned at the end is fantastic. In re the role of research mathematicians vs teaching, I totally agree that research professors shouldn’t be teaching college algebra. But more broadly, it seems there’s no stable equilibrium between “all research” and “no research” depending on who’s in charge. I wrote a long thing with some thoughts on it: https://medium.com/@jeremyjkun/the-competing-incentives-of-academic-research-in-mathematics-6d7b9436d46b