I was never one of the students for whom mathematics came naturally. If I worked really hard and did twice as much practice as the worst "good" math students in my classes, then I was able to keep up. But I never experienced math the way so many of you describe your experiences of it. Don't get me wrong — I've always envied you. But I always seemed to need many more hours of privacy and "think time" and lots of step-by-step review of my own notes and rewriting what seemed to me to have happened in class. Slowly the ideas and understanding would grind their way into my body and mind, punctuated by multiple nights of dream-time reorganization of my learning efforts, until I could clumsily work along with the rest of you top students.
Carlos Castaneda makes a distinction between "stalkers" and "dreamers" — those who learn by pursuing their learning like hunters, finding and identifying and following their learning clues like predators hunting their prey, patiently tracking ideas through the jungle until their arrow meets the target and it becomes theirs. And then there are the "dreamers" — like me — who stumble along in mortal terror and confusion until we become one with the mud and the mystery.
"Wallowing" is a better description of how my primary learning state in mathematics proceeds. Day after day, I'm confused, mute, and incapable, unaware that I'm holding my breath like a deer in the "fight or flight" state, and praying that the teacher will not discover the secret shame that my body and my unconscious mind are desperately trying to conceal — the fact that I don't learn mathematics the way you are trying to teach me, the way you yourself learn mathematics. I wallow and I continue to wallow until the mysterious alchemy of osmotic transfer has occurred, until I have absorbed the mathematics as the mathematics have absorbed me.
I've always worried that my sense-making-reason-making-understanding mechanisms are defective because they don't accept the inputs being provided as the sole ingredients required for my learning. My body-mind cannot seem to identify them as nutrition. Sometimes it reacts to them as if they were pathogens I must be protected against. And that reaction triggers the fight-or-flight response, and I find myself once again holding very, very still to avoid your displeasure, disappointment, and frustration — and your discovery.
This is the curious thing for me about walking among you these days — I am a non-native speaker of this language of mathematics and mathematics teaching that we share. You speak to me as if I too grew up with this language, played with it from infancy, organizing my toys and numbers and ideas in my nest as you did. You speak to me as if I too were a native speaker, as if numbers were my first language. The other day Kate tweeted that her mom teases her that, when she starts teaching in the Southern Hemisphere, she may begin to swirl in the opposite direction from the way she has always operated up here, that, say, she will go from being someone who is naturally brilliant at learning and teaching mathematics to someone who is suddenly "good at poetry and relationships." When I heard that, I found myself wondering if I would experience the same thing if I moved that far south, but in reverse — if I would suddenly become someone who is naturally fluent in mathematics and does not speak it with a funny accent.
As a learner, I listen, I tinker, I do, I experiment, I reverse my thinking, I try to find a pattern, plus I take copious notes along the way so I can use them later to wallow in the material privately until I begin to feel the signs of absorption. I know that I will need time and space to live with my confusion, to wrestle with it, to struggle, and to hand off the baton of responsibility to my subconscious mind to rearrange the learning while my conscious mind and body take a break. Like the student volunteers in Robert Stickgold's sleep research lab at Harvard, playing a downhill skiing simulation video game before napping and playing again to assess their improved results, I need time and space for my unconscious mind to reorganize my daily fragments of learning. I need time and space to sink down into that primal, mysterious, adaptive soup before I will be able to notice that I am holding my breath once again in a fight-or-flight reaction.
Only then will I be able to breathe again and relax.
I don't know why learning mathematics is this way for me. I only know that it is. And I that gives me the confidence to say out loud that, as a learner, it simply doesn't work for me to be told to relax or to follow someone else's investigative process. It isn't always sufficient for someone like me to be invited into your curiosity about the purpose of mathematics—no matter how engaging your digital media representations are. Likewise, it isn't always sufficient for someone like me to be invited to pave a pathway to confidence through mastery of a checklist of concepts or procedures.
What does give me confidence — as well as engagement and determination — is being trusted and granted the autonomy to trust my own learning process and my own deeper wisdom about my own learning.
Of course, the tricky thing about cultivating autonomy, though, is that autonomy is by definition an all-or-nothing proposition. As a teacher, you can't grant autonomy cautiously or halfway, and you can't assume you know what another person needs in order to feel autonomous in their learning activity. If there is one thing I have learned from twenty-plus years of meditation practice and teaching, it is this:
You can't control somebody else's autonomy. You can only cease to interfere with their learning process.This is why reframing strategies — such as games and game-like activity structures — can be such powerful additions to the learning environment. They free learners to choose a different focus for their conscious attention — something other than their ability to understand or not understand the learning target. For the especially shut-down or anxious learners, such reframing activities give our conscious minds a displacement activity (finding the treasure, completing a turn in a game) that keeps it busy and out of our hair while our unconscious minds and bodies can help us organize and reorganize the material before us into understanding.
Reframing strategies are also valuable in encouraging autonomy in capable and curious students, providing variety and texture to their experience as well. But most importantly, by engaging everyone in the room in their own personal and collective pursuit and experience of flow, they help to create the social and emotional conditions under which students can experience lasting and meaningful engagement.
What I am arguing here is that a key to developing a sense of autonomy in our math classrooms is to harness reframing strategies that support the greatest number of students in experiencing the flow state while doing mathematics as much of the time as is possible.
By blending these strategies with those that cultivate a sense of purpose (such as Dan Meyer's digital media + "Any Questions?"), and with those that, like SBG, clean up the tense and often fraught expectations and communication of mastery, I believe we can dramatically boost the percentage of students in the room who feel autonomous and taste a sense of flow while doing mathematics.
And that, it seems to me, should be the goal we are targeting.