I am trying to make a commitment to myself to "write rough" here more often. My hyper-analytic personality leads me to think and rethink things so much that I rarely get to a mental space in which I feel like I can write with any clarity. So, this might be rough.

I attended the Creating Balance conference up in San Francisco last weekend, where Rochelle Gutierrez gave a talk about "Teaching Mathematics as a Subversive Activity." Her talk hit close to home for me but, even given it's closeness, still has left me thinking and rethinking her words this past week.

I appreciated many things about her talk, but mostly the critical way in which she addressed the sort of taken-for-granted discourses, or structures, in mathematics education that politicize the issue. Things like success, proficiency, achievement, and even what counts as mathematics largely have a singular meaning. As she writes,
"What counts as knowledge, how we come to 'know' things, and who is privileged in the process are all part and parcel of issues of power."
Mathematics education deals primarily with the dominant view of mathematics, the "discipline." With such a singular view we fail to recognize that, as Dr. Gutierrez points out, "mathematics needs people as much as people need mathematics." She writes,
"Most often, the goal in mathematics teaching is to try to get the student to become a legitimate participant in the community of mathematicians, thereby subsuming their identity within the currently sanctioned way of communicating in the field."
"Yet, when students offer a different view, they are seen as having deficient, underdeveloped, or misconstrued understandings of mathematics."
Dr. Gutierrez describes this as the "deficit model" which I see as very similar to Friere's "banking model." Attending to dominant mathematics can sometimes mean losing oneself at the expense of adopting another's way of knowing. As Dr. Gutierrez reminded us during her speech, teachers of mathematics are "identity workers." When we define mathematics narrowly and we impose that mathematics, we fail to recognize the mathematics of the individual, the student, the child. These are issues of identity (is my thinking mathematical?), of equity (who gets to participate in mathematics?), and of power (who benefits as a result of this?).
The point where the two axes intersect is a space Dr. Gutierrez has named "Nepantla." Borrowed from the work of Gloria Anzaldua, Nepantla is an Aztec term that refers to "el lugar no lugar" (neither here nor there). It was best described, I think, by Dr. Gutierrez to simultaneously mean "both" and "neither." I think it succinctly captures the paradox and tension I have felt in my research on student agency and identity. The discourses and structures in society require that we attend to dominant mathematics (access and achievement), yet I know there is an alternative in which moving away from dominant mathematics allows us to attend to the mathematics of students/people (identity and power). We can't do both but we also can't do neither. So, as teachers, we live in Nepantla...we live in tension.

It is from this space of Nepantla that new options, new knowledge emerge. To retreat to safety, to settle in the current ways of doing things because no clear alternative is present, is to choose to live in "desconocimiento" (a distancing, ignorant space in which we refuse tension). The alternative is to choose tension, to live in the messy space of Nepantla. Dr. Gutierrez describes curriculum as "both a mirror and a window." A mirror because it allows the student to recognize oneself in the work they do, but a window because it also allows them a new perspective on the world. I don't know that it's attainable, but I think we must choose to pursue the unrealizable philosophical ideal and live in messiness because to settle is to distance ourselves from knowing mathematics with our students.
Last night, "60 Minutes" ran a segment on Khan Academy and the influence it is having in improving mathematics education. Here is the letter I sent them today: