I have always taken my teaching very seriously. Mainly because I believe that I am not just teaching my students mathematics, but general skills that will make them successful in life, regardless of whether that future life involves mathematics. This is why I think it’s important to teach them, among other things, the value of “productive struggle” (my new favorite buzz words), effective communication, and collaborative work. I strongly believe that these skills help students learn mathematics better, but they are still useful even without the mathematics. In fact, the mathematics provides a very good context for learning these skills. I also feel very strongly about creating an inclusive atmosphere in the classroom, and hopefully as a result increasing representation of minorities and women (who are still largely underrepresented in mathematics classrooms), and I believe the teaching goals I just outlined are also helpful in creating this atmosphere. But there is something I thought very little about until recently, because I bought into the myth that it doesn’t exist: mathematics in its socio-political context. This is something I just started thinking about with a very talented group of faculty during the Park City Math Institute a few weeks ago.

How many times have we heard “mathematics is universal”? Or thought “I’m glad I don’t have to deal with that” when our colleagues from social science departments talk about the difficulties in creating a safe and respectful environment in their classrooms, while not censoring students’ various opinions? I am certainly guilty of all that. Mathematics is completely separate from values and ideologies, I thought. This is why it was particularly eye-opening when we started reading about critical education theory and critical pedagogy. This started with the work of Brazilian educator Paulo Freire, with his book Pedagogy of the Oppressed. In particular, Freire believed that there was no such thing as “neutral” education, and in particular that the structures of oppression were present in much of the educational system. He worked on increasing literacy in rural areas, as his viewpoint was that people could not be active participants in society or be agents for change is they were not literate and well-educated. The main thing we worked on at PCMI is understanding this in the context of mathematics in higher education. This was very tough, for many reasons.

First of all, I myself was guilty of thinking that mathematics had nothing to do with oppression and power structures. On the other hand, it is pretty obvious that people who are innumerate, in today’s society, are very much at a disadvantage, and are much more susceptible to manipulation and outright oppression. I have also been very uncomfortable, for many years, with the power dynamics in my own classrooms: many of my first-generation and minority students are quiet and insecure, my white male students are much more likely to dominate the discussion. I work very hard to make participation and agency much more even, but I don’t think I thought about these things in this particular context.

One of the main things Freire criticizes, which I agree with wholeheartedly, is what he calls the “banking model” of traditional education. Basically, he thinks that students are treated like empty vessels that need to be filled with the instructor’s knowledge, and only are required to regurgitate this knowledge back. The model he proposes is a student-centered one, in which the student is empowered to take charge of their own learning, and turning the instructor into a facilitator instead of a “banker”. This is very close to the ideals of Inquiry Based Learning (my favorite way of teaching) and other student-centered approaches that have been gaining some momentum. The most exciting part of this, to me, is that in this larger context, where it’s not just important that the student learn mathematics, but also the skills to make them an active participant in their own society and a possible agent for change, student-centered approaches are not just “fashionable” ways to teach but absolutely crucial to the effort.

And this brings me to another issue. Just because a class is student-centered in theory, it does not mean that it is structured in a way that empowers students or that makes them capable of resisting oppression and changing power structures. The best example, of course, is the infamous Robert L. Moore. He was one of the biggest supporters of IBL methods, and in some ways one of the most successful. He taught and mentored some famously successful mathematicians (like R.H. Bing and Mary Ellen Rudin), and is to this day revered by his former students (and others) as the greatest mathematics teacher ever. However, it is also well-known that most of his students “auditioned” to get into his courses, and he would only take the very best. He was also racist and misogynist (although that is not that special for a white man born in the late 19th century in Texas). My point is that although he did teach in a student-centered way, and to all accounts was incredibly successful at it, he did not use this as a way to empower individuals against oppression. If anything, he perpetuated stereotypes and inequality in which privileged students were helped, and everyone else forgotten. Dave Kung gave a beautifully eloquent talk on these ideas at the most recent Legacy of R.L. Moore conference in Texas, and it should be required viewing for everyone interested in diversity and equality in mathematics. He also proposed, somewhat controversially, but to a standing ovation, that the conference needs to change its name.

I have been thinking of removing references to R.L. Moore from my syllabi altogether. But I like to give my students a reason for why we are doing things differently from what they’re used to. It is hard to convince people who are used to the banking methods to somehow become active participants in their learning without explaining carefully why this is important. This is why I am interested in reading more about critical education theory, and perhaps coming up with a more compelling and more empowering argument for my IBL methods.

I was talking to my mother recently about the PCMI readings, and was surprised to find out that she had read all of these books and articles. Of course, I shouldn’t have been surprised, as she was a Social Psychology professor in Venezuela in the 1970’s, and that is the height of Freirian approaches to teaching. She told me about a book titled Teaching as a Subversive Activity which came out at around the same time, by Neil Postman and Charles Weingartner. First of all, what an awesome title, right? When I googled the title (as one does) I found this Wikipedia page on Inquiry education. How serendipitous that my crisis of conscience related to the Moore method as the birth place of IBL would lead me to another source for inquiry education, but one whose values are more aligned with mine. All of the principles outlined in the Postman and Weingartner book (for students and for teachers) are exactly what I have worked with all these years. However, the REASONS for doing this are different. The point is not to make the “rich” richer (in this banking model or in the IBL model), but to give EVERYONE access, power, agency, and the skills to make them active participants in society.

This is definitely something I will be thinking about for years to come, and there is at least much reading and practicing what I preach yet to do. But I am excited and re-energized, I have a new framework in which to think about my teaching, and I believe I will be serving my students (all of my students) much better. So here’s to a teaching revolution, and to hoping that many others will follow. We can change the world, people, even if (or maybe especially if) we’re teaching math.

Oh, you mean that all mathematicians don’t have to read Freire as part of their training? Just me? But yeah to all of what you said.

For a mathematical version of some of the same ideas, you might check out “Radical Equations” by Bob Moses. I can say more, but really just go read the book. The focus is on high school algebra, but the message is a lot the same. Algebra, and more generally a good education, is a civil rights issue, and he gets communities organized around it.

And thanks for your honest comments about RL Moore. I’ve ben really bothered by the honor and reverence with which he’s treated in the IBL community ever since I saw videos of him talking and teaching. He may have had some good ideas, but they were not his ideas alone. And frankly the guy was a jerk. He doesn’t deserve to have a conference named after him. I have long said that I would go to an IBL conference, but will not in a million years go to something with Moore’s name attached. It may be silly, but the stuff I heard come out of his mouth seriously makes me queasy.

In terms of justifying the different approach and “productive struggle” to your students, have you looked at Carol Dweck’s work on mindset? There’s definitely research that says that you learn from struggle & mistakes and that you don’t learn from getting stuff right and doing busy work. Jo Boaler cites a lot of this stuff in her book, which I don’t have with me right now…

Great post! Thanks for introducing me to the work of Postman and Weingartner.

Bienvenida a ese mundo comprometido con la justicia y la igualdad a partir de las diferencias, que es o debe ser la docencia. Cada estudiantedeja una huella en una y debemos siempre dejar una huella en cada uno/a de ello/as. Crecer en su propia valía como ser humano y descubrir que pensr es hermoso en cualquier espacio de la vida.

Un abrazo

This is an excellent article with ideas that the mathematical community needs to hear. Here are a few comments:

0. I second Michelle’s comments about Bob Moses, Carol Dweck, and Jo Boaler in her comment. All good stuff. Last year I wrote an AMS Notices article about the connections between Dweck’s research on Mindset and active learning pedagogy in postsecondary mathematics, which you might be interested in: http://www.ams.org/notices/201401/rnoti-p72.pdf

1. I first read Freire’s article “The Banking System of Education” as a college sophomore in an English composition course; it’s an amazing essay.

2. My favorite discussion of R.L. Moore, which lays it all out honestly, is a chapter in the book “Loving and Hating Mathematics: Challenging the Myths of Mathematical Life” by Hersh and John-Steiner. I feel that all mathematics teachers and students should read (at least) selections of this book — it fits very well with Critical Pedagogy.

3. Another book that touches on all of these issues is Ken Bain’s “What the Best College Teachers Do.” While not about mathematics specifically, it is very relevant to this discussion.

Another good book that I read, outside of mathematics, but still applies is “Why Teach?” by Mark Edmundson. May not add too much “new content” to education theory, but it was a refreshing read.

The biggest challenge I find in college level education is having to re-teach subjects that were poorly covered in high school. Since only some students come from a very good background, I can’t simply leave the other half of my class behind because “they had a poor high school experience” whether it was their fault, their instructors, or the constantly changing focus in the curriculum. I’ve been falling back on the “banking” method, mostly due to the fact half my students don’t need to “inquire” on some of the material since it would be remedial for them. This has been an ongoing challenge across the board for the freshman mathematics classes, where we all attempt to “catch” people up as best we can…