When I was an undergraduate and a graduate student, I used to hate taking classes. Classes were generally mind-numbingly boring. When I was doing graduate coursework, I played a game of hangman during class in which I got to put in a new body part every time a certain number of minutes passed. It wasn’t that I hated education. I loved getting the kind of gold stars school gives you, certainly, but I also loved working, thinking, and solving problems. Homework was never boring. It was sometimes aggravating, and I remember wishing that one of my professors would be jailed for the semester because his homework frustrated me so. But I have always enjoyed working on problems, whether those problems were mathematical or theoretical.
So, honestly, it’s a little surprising now that I just signed up for my second course of the new year. I started the year with #moocmooc, and I can’t even remember why I signed up. I had started reading Hybrid Pedagogy and some of the ideas were getting me fired up. Suddenly I was in a course, but one where I got to skip all of the boring parts. Instead, I got to have some amazing conversations about pedagogy, open learning, and the educational system. Now I’m signed up for #etmooc (Hi #etmooc-ers!) because it is clear to me that if I want to liberate people with and through mathematics on a big scale, I’m going to have to figure out how to make intense, disruptive, and connected learning happen through technology.
In a #digped discussion that was part of #moocmooc last week, the idea of a course as a container was discussed. You can read this Storify to get a feel for part of the discussion. I think that most of my courses are actually routes on a map. In them, guide my students to some pre-defined learning outcomes, and I tend to take students on paths that I have walked before, in the hopes that I can be the best guide possible. I’m helping them to explore a terrain and create a map of that terrain, and I do that by guiding them along the path I laid out and pointing out particular features of the landscape. Honestly I have always hated the kind of course I teach, and I feel guilty when I teach it, because I know I’m teaching the wrong way.
Like many mathematicians, I privilege mathematics as problem-solving over mathematics as quantitative literacy. I started my life as a teacher firmly in the constructivist movement, taking as my bible the NCTM standards of 1989. But I’ve been teaching in some form now for over 25 years. I understand the job of teaching much less now that I did then, since it is a complex job, and everything I learn shows me anew how impossible the task is and how inept I am at it. In those 25 years, again and again I have learned that most students don’t actually want constructivism, at least not a pure form of constructivism. Most students want to be helped and guided. Students want some assurance that they are doing the right thing, and learning the right thing.
I have been reading “Why Doesn’t This Feel Empowering? Working through the Repressive Myths of Critical Pedagogy” by Elizabeth Ellsworth. It’s a thick paper and I’m not through even close to the whole thing, but I’m struck by this quote: “Strategies such as student empowerment and dialogue give the illusion of equality while in fact leaving the authoritarian nature of the teacher/student relationship entact” (p. 306). I feel this way about problem-based learning and constructivism in my classroom — they give the illusion of allowing the student to construct meaning, but really reinforce the power structure that allows me to dominate the class and inculcate my students. Constructivism appears to stand against the rote, oppressive recitation of mathematics as Betty Johnston calls it:
To learn every day that it is normal that mathematical knowledge is externally given and monitored, that patterns reflect no reality, that a quest for a certain kind of understanding hinders success, that everyday practices are quantified and regulated by a vast array of indices, is to experience mathematics as a profoundly decontextualized discourse that could refer to anything and for most people refers to nothing. It is to experience mathematization as the ordered daily training in the normality of heteronomy.
But constructivist classrooms are just putting a small bandaid on the overriding oppressive and compulsory nature of mathematics education. I can’t change dynamics in my classroom by flipping a problem-based learning switch. Students simply experience that as more oppression. And when I try to push in onto them as a style of teaching and learning that they hate because it is is “good for them,” then that’s me violating the trust that the students place in me.
Basically I’m damned if I do and damned if I don’t — I can’t teach rote recitation in good conscience, but neither can I teach a constructivist problem-based curriculum without my student’s consent. So what do I do? I think the type of course I need to teach more is like an incendiary device than a map, but one that’s delivered with love and connection, and one in which I give the students a map, point out the landmine on the map, and as them to go over and step on it. I need to find a way disrupt both the students and myself, because we are all wrong about what we can and should do with mathematics. I need to get them to give voice to the righteous and unspeakable rage and shame that they have bound up with mathematics. We need to blow up the whole project of mathematics learning together, and then maybe I can find a way to listen to them and we can all start asking and answering the right questions. That brings me (finally) back around to the role of technology, which I see as giving my students power to create new narratives publicly, narratives that have the potential to disrupt education beyond the confines of my class.
Ellsworth, E. (1989). Why Doesn’t This Feel Empowering? Working through the Repressive Myths of Critical Pedagogy. Harvard Educational Review, 59(3), 297.