Courses as Maps or Incendiary Devices

math atheistWhen 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.

Johnston, B. (1995). Mathematics: An abstracted discourse. In P. Rogers & G. Kaiser (Eds.), Equity in Mathematics Education: Influences of Feminism and Culture (pp. 226–234). Routledge.

10 thoughts on “Courses as Maps or Incendiary Devices

  1. Jeff Merrell says:

    Ditto what Bonnie said. But also – just a note appreciating your reflections and ability to craft a damn nice blog post. Looking forward to reading more. And curious (because I am exploring similar) as to whether you find some answers or insights to the questions you pose here as you engage with Hybrid Ped and #etmooc. Cheers…

  2. Steve says:

    Really fantastic post, Angela. LOVE IT. My favorite part:

    “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[k] them to go over and step on it.”

    The idea of *just enough* structure to catalyze the reaction is a powerful concept. How often do we smother the natural learning process by putting a lid on the experience, oblivious of what “meaning” means to the student. Too often:)

    I wrote a post about this awhile back. My context is vocational training so it’s not *exactly* the same but I think there’s some parity between education and training. Both are preparing folks for something. To be ready.

  3. Carolyn Durley says:

    Hi Angela,

    This post captures for me so poignantly conflicts I have been experiencing in my teaching (I teach Bio). You hit the nail on the head with your description of a “course” as a container. I have been feeling this so keenly of late and too the limitations of it. The course has: been run before by 1000’s, a pre-determined finish line, rewards for how close to the course students stick & rules to stick as closely as possible to what has been laid out for them. Yikes!! It seems that when you see something, you really see it and can not go back to pretending you never saw it. This idea weighs on my daily and I am still going in circles to find a safe, clear way out.
    I love your mention of a course that is more “an incendiary device than a map”, this describes it for me and how I have been feeling. But as you mention, how do this and maintain the trust that underlies strong relationships? What a great challenge.

    I love though that you end pointing in the direction of hope “giving my students power to create new narratives publicly, narratives that have the potential to disrupt education beyond the confines of my class.” Yes onward we go!


  4. Angela Vierling-Claassen says:

    Thanks for the excellent comments, everyone! Steve, that balance of just enough seems impossible since the right balance I think is going to be different for all learners. I really like your post since it reminded me that I can’t do it and that’s OK. But I can keep working toward making thinks better.

    Carolyn, it is so great to meet a kindred spirit in STEM! I also have the problem of doubting my whole enterprise every day I teach, and it can run me ragged a big. Focusing on the connections with students really helps rather than if I’m doing something reasonable in the first place!

  5. Sean Michael Morris (@slamteacher) says:

    Terrific post. So glad you came away from #moocmooc and our #digped discussion this way.

    I have just one thought, and that is about how quiet incendiary devices can really be. The act of, as Steve says above, “just enough structure” is often an incredibly subtle play in the classroom or online. I am currently teaching in this quietly incendiary way, and every day I wonder if I’m doing anything (exploding anything, disrupting anything) at all… Because I feel like I’m doing so little (teaching, leading, instructing). I wonder if maybe it is in being silent that we allow the real explosions to occur?

    • Angela Vierling-Claassen says:

      Sean — Thanks, #moocmooc was awesome, and I’m very happy that I did it. I think the lesson of being quiet and is one that I struggle to learn. I always want to do too much, because it covers my anxiety and makes me feel productive/important. I do this everywhere, not just in teaching! My goal this semester is to really focus on my connections with students, because that is so key for me, and it doesn’t require a song and dance, it just requires paying attention and being open. I do think that a teacher being silent can be one of the most powerful things because our silence can provide a space for students to claim space and power. Honestly silence is not my strong suit, but maybe I need to start working on it!

  6. catherinecronin says:

    Hi Angela – I found your blog via #etmooc today and I’m so happy I did! I’m struck by many things you explore in your post, especially the power dynamics in the classroom and how these underpin all that we do. We may ask and invite our students to participate in new ways in the classroom, but the unequal power relations remain — unacknowledged and unreflected though they may be. Seeing and naming this, and seeking ways to interact authentically with our students (as learners ourselves) is our essential work. And you have written about this beautifully here.

    Your description of constructivist learning in the classroom rings true in many ways — highlighting the sensitive issues of trust and power. Connectivist approaches may offer some possibilities. Howard Rheingold discussed some of the ways that he helps students to navigate the “strange new world” of the connectivist classroom in a G+ post yesterday. Howard’s philosophy of working with and empowering learners to become self-directed (as we have experienced in MOOCS) is inspiring.

    Delighted to be connected with you via Twitter and your blog — I’ll share the link with a few wonderful educators here in Ireland as well 🙂

  7. Bryan Meyer says:

    I am so glad that I have stumbled across your blog. From what I have read, it seems we share many interests in critically examining issues of equity, identity, agency, power, and ethics in the math classroom.

    Lots for me to think about from your post:
    What is mathematics? How does our definition limit what can be done in the classroom?
    Is teaching with specific outcomes in mind inherently oppressive?
    How are you defining problem-based learning? Are there other ways? What are the benefits of each?
    Why do certain students not like the approach? Are those reasons cause for change?

    Thanks for getting me thinking!

    • Angela Vierling-Claassen says:

      Yay! It’s great to hear from you. Yes, I so have all of those questions. I think I could spend a long time just stopped at what is mathematics? I would love to better understand ways of non oppressive math education that really feel non-oppressive to students. I think there is so much good in problem-based learning in the spectrum from just good problems to real student control but I also see students for whom it is just more drudgery and meaninglessness, and my good intentions don’t always turn it around!

      Great to meet you and I’m headed off to check out some of your blog!

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