I was a postdoc in the Stanford math department for five years, from 1998 to 2003. I had a very pleasant time there, and had many pleasant interactions with my fellow department members; I’m glad that I ultimately left academia, but that’s purely because of me being a misfit.
Part of that being a misfit is that I didn’t spend nearly as much time as I should have actually doing math. I spent some of my time helping raise my daughter and playing video games (the latter not at work, of course; for the former, Miranda actually did hang out in my office a lot during the first two years of her life), and reading random books. I was still reading a fair amount of sociology of science books at the time; I dimly recall having fairly pleasant conversations about the topic with my fellow department members over lunch, but conversations with a modernist flavor that’s familiar to any reader of We Have Never Been Modern. This was fairly soon after the Sokal affair; that paper fit neatly into a narrative that was in the air, where mathematicians and hard scientists write papers full of gibberish that is incomprehensible to outsiders because that’s the only way to express our deep understanding of complex truths, while humanists and soft scientists write papers full of gibberish that is incomprehensible to outsiders in an attempt to cover up the vacuousness of what they’re saying. Those conversations weren’t generally mean, or as lacking in respect as I’m making them out to be here, but there was an asymmetry in the undertone.
The other thing that I spent a lot of time (far too much time, if you’re a postdoc in a research-focused school—teaching really isn’t what schools like Stanford are about) is thinking about teaching, which led to me running my courses in eccentric ways. The department was actually quite accepting of my eccentricity—I don’t know if anybody noticed the one time that I gave three quarters of my students an A in an intro course instead of weeding most of them out, but if anybody noticed, nobody brought it up to me—and while I was clearly an outlier within the department, my recollection was that I generally had pleasant conversations on teaching with other department members. (They were happy to let me stick around teaching calculus for a couple of years after my first postdoc expired, which I’m very grateful for.)
And there was a fair amount of surprisingly broad conversation about math teaching in the air. California had recently published a new set of standards (you can still see many of them on the California Content Standards page, look for the ones with the late-1990’s dates); and the math standards in particular had led to a fair amount of contention. I was curious about this (mostly because of my own interests, but also because they might be shaping the schools that my daughter would eventually enter), so I read through the various different standards; as I recall, the math standards seemed to me to be the most innocuous (standard skills-based stuff, noticeably but not offensively overstuffed), while the science ones were starting to get offensively overstuffed, the social studies were outright jingoistic, and if I wanted to design a curriculum to make somebody hate reading and writing, I’m not sure I could have done a better job than the English standards. Though maybe I’m being a bit hypocritical saying this, given my sniping above: I don’t have any expertise in childhood education, so I’m not the right person to criticize!
I think what was going on with the math standards was that they tapped into a real cultural discomfort with math teaching. The general context of the math wars was whether math teaching should focus on having kids be able to accurately carry out algorithms or whether they should focus on having kids develop a holistic understanding of concepts. Neither side thought that the other goal was bad: everybody would agree that algorithms should ideally lead to understanding of the concepts underlying them, while if you claim to have a holistic understanding of multiplication but can’t calculate seventeen times thirty-six, you’re just deluding yourself. But there was quite a lot of heat as to which side you could start on.
From my point of view, the heat was actually mostly in one direction: the algorithms folks were engaging in shameless fear-mongering about the conceptual approach. If I recall correctly, there was one local lady who went around to various local school board meetings telling people how, if their schools took a conceptual approach to teaching mathematics, then colleges wouldn’t accept their kids, which she based on some almost completely trumped-up claims about discussions with admissions departments. My take on this, on the other hand, was that the algorithms approach had been ruling the scene since basically forever, and it had a remarkable capacity for producing people who are actually traumatized by mathematics. That is not a term that I use lightly, and I recognize that, as forms of trauma go, math education trauma is relatively benign; it is, however, the case that, when I tell people that I’m a mathematician, the response is quite regularly for the person I’m speaking to to tell me unprompted how they’re a failure at mathematics. (With many variants; a quite common one is for people to say when they felt that they stopped being good at mathematics, e.g. “I was good at mathematics through calculus, but then linear algebra kicked my butt.”) I don’t believe any other field of study gets nearly the same tenor of response, and the situation is fucked up enough that, from the time I showed up in California until the time when Miranda was maybe in third grade, I actively avoided telling people I met outside of Stanford that I was a mathematician. (And of course now it doesn’t generally come up because I don’t work as a mathematician.) So, from my perspective, the results of the algorithmic approach towards teaching mathematics were Not Good, and it was high time to try something else.
The reason why I bring this up in a context of a discussion of the Stanford math department is that at least two members of the Stanford math department were involved in the production of the California state standards. My memory says three members, but when I look at the standard itself, the names that I recognize are James Milgram and Gunnar Carlsson, so I guess it was only two. The core of their involvement was before I showed up in the department (the standards have a 1997 date, and I was still in grad school then); and, in general, I think the idea of professional mathematicians being involved in the production of standards is a laudable idea, because they have specialized knowledge that will inform what is valuable for students to know, including subtle linkages between different areas.
It’s not, of course, the only specialized knowledge that is useful when writing a standard for teaching mathematics. I would like actual math teachers to be heavily involved in the production of such documents, as well as education professors who are up to date on the research for what educational approaches currently seem to give the best approach. And my impression (based admittedly on scanty evidence) is that this did not happen on the California math standards: that there was quite a lot of politicization in the composition of who participated in the committee and what voices were listened to, based on philosophical beliefs on what approach would work that weren’t supported by research.
I interacted with Gunnar Carlsson not infrequently during my time at Stanford (and worked part-time at a startup he cofounded during a few months when I wasn’t teaching), and all my memories of that interaction were pleasant: in particular, I’m sure his motives for devoting considerable amounts of time to the California math standards were public-spirited, trying to lend the help of his professional expertise without a particular didactic axe to grind. I spent much less time interacting with James Milgram; I’m sure his motives were also public-spirited, but I’m fairly sure that he did have an axe to grind, an axe that wasn’t backed up by his professional expertise.
Which brings us to the person whose name gives the title to this blog post, Jo Boaler. I assume we met during some sort of new faculty event in 1998; and we talked several times about math teaching over the years. I really enjoyed those conversations (and reading her first book), and found them very useful in thinking through some of the approaches I was trying to take in my course design. When I went further along that path, trying to turn what I was thinking about into an attempt to gather substantial data, she helped me with methodological advice and convinced a couple of her grad students to donate time to me interviewing some of the students who were taking my class. And I’m embarrassed that I didn’t do a real job of following through on that; though less embarrassed than I would be, because it was only by doing that that I started to realize just how much work it is to turn observations into real data that you can begin to draw conclusions from. (Mathematicians have it much easier in that respect in the relatively cut-and-dry nature of our proofs; though of course mathematics has its own significant difficulties because that cut-and-dried nature means that we’ve been able to dig very deep over the centuries into areas where our approach works.)
She mentioned conversations that she had had with Milgram. I dropped into his office once or twice because of that (and rarely ran into him in other contexts around the department, we traveled in different circles there); I don’t recall probing too deeply, but those conversations were consistent with Jo’s description of his behavior. I got the impression that my approach towards mathematics teaching was quite different to Milgram’s approach, that our opinions of mathematics teachers were also quite different, and that there wasn’t much point in having further conversations in that area.
I lost touch with Jo Boaler after my first three years at Stanford—she was busy, I was going in different directions. And of course, I’ve been out of academia for more than nine years by now. I was pleased to see her name show up recently in my twitter feed; I was sad to learn that the reason for that appearance was that she was starting a social media offensive campaign against Milgram (and Wayne Bishop, a math professor from elsewhere). According to Jo’s report of the situation, Milgram and Bishop have been trying to destroy her professional career; if a quarter of what Jo says there is accurate, then Milgram and Bishop’s behavior is, at the least, shameful.
Of course, I’m an outsider, so I can’t talk about the nuances of what happened first hand. But what Jo describes is consistent with what I saw: a strong ideological dislike for certain didactic approaches which translates into a lack of respect for people who aren’t aligned with scientists laying down the truth from high: a lack of respect for people who come to other conclusions, a lack of respect for professors who work in other fields, a lack of respect for people who are actually doing the day-to-day work of the teaching that is under discussion! There are strong structural undercurrents pulling in those directions in math departments all over the country (along with reinforcing undercurrents: Jo doesn’t call out gender issues in her web page, but they’re all over the place in science departments, and for that matter in Silicon Valley in general, as I’ve seen repeatedly in my post-Stanford career); a lot of the time, people work to fight those undercurrents and at least maintain a basic level of professional respect, but not always.
So: maybe Milgram and Bishop are right. But to believe that, I’ll have to believe that I should take the word of a couple of people who have never published peer-reviewed mathematics education research over somebody who has built a career on that, over the word of multiple departments that have given Jo Boaler research appointments over the years, over the word of a committee set up to investigate exactly that question. And you can make a consistent worldview out of that, if it’s the direction you choose to go in: it’s a world view that leads to statements like the one Bishop apparently made that schools of educations should be “nuked”. (That sort of lack of respect for math ed research by people who haven’t done any math ed research is depressingly common, though most people who hold such a view are more polite about it than that.)
It’s not a worldview that I hold, though. And I’m very glad Jo Boaler is showing the strength to fight against it.