The conversation started via Twitter when Daniel and I were exchanging views on our different theoretical perspectives on learning, coupled with the implications that those beliefs might have for practices in education. Daniel brings a situated learning perspective to his work. Talking/tweeting with him about that raised some questions for me about the implications for identity and agency, particularly when we view learning as "becoming like" or "thinking like" the members of a particular "community of practice" (my language here is crude in an effort to be concise). I suggested an article from Rochelle Gutierrez that I felt captured some of my concerns, and our email exchange grew from there. See Daniel's blog for his response to the article. My post here is the email I wrote in response to his, with quotes from his email in bold...
I enjoyed reading your response to the article I shared with you...thanks for taking the time to send that along. Here are some brief reactions to your email:
"Math isn't like literature - it's important to see yourself in the books you're reading in English class, because that sends a message that school is a place for people like you, but times tables / cosines / integrals are the same for everyone..."
This was a very interesting statement. Our societal view of mathematics is one that treats it as objective and static and, therefore, influences a view of mathematical knowledge as homogenous (at least within different communities). On the contrary, my own personal epistemology (being heavily influenced by various constructivisms) creates ways for me to think about "mathematics" and "knowledge" much differently. One distinction I make is between "school math" (or what we take to be "the Discipline") and other forms of activity and knowing that I might still classify as mathematics/mathematical. I also try to recognize that we each have different nuanced ways of knowing; I attribute a unique way of knowing to an other...recognizing that I can never have access to their ways of thinking other than through the mental model that I, myself, create (see Steffe's "children's mathematics" and "mathematics of children"). I guess all of this is to say that I do treat mathematics education in much the same way I would think about literature (as it relates to identity formation). In schools, students measure themselves against what is valued/privileged. So, when they feel they aren't thinking/knowing the way they are supposed to know, they begin to feel that they are not mathematical. One remedy might be to provide conditions where dominant mathematics (school math) can flow from the the intuition and activity of individuals. In my mind, this most closely resembles the current narative around CCSS, Realistic Mathematics Education, NCTM's Principles to Actions, etc. The goal here, though, is still to get students to replicate dominant mathematics (to "think like" or "become like"....the standards, the discipline, the teacher's ways of knowing those things). I like to imagine other possibilities as well, ones where the goal is merely to provide conditions for the expansion of "children's mathematics" and where we feel confident naming that activity/knowledge as mathematics.
Maybe this is tangentially(?) related: http://www.doingmathematics.com/blog1/knowing-alongside
"Although if it isn't, and every cultural group has their own mathematics, then what should be taught in math class? Should standards / curriculum depend on classroom demographics?"
Maybe this is partially hinted at above? We might also step back for a moment to consider the purpose of education? of math education? Must we name things to be learned? What are the benefits? What are the consequences? What ideology does it rest on?
The idea of naming things to be learned seems to still be predicated on the belief that school is about "filling" people with knowledge in "preparation" for their future. What would be different if we seriously considered Dewey's belief that "education is not preparation for life; education is life itself"?
"I'm taking an ASL class this summer, and I'm going to have to develop some sense of who I am as an ASL speaker. As I join the community, that changes me, but it changes the community as well."
I'd be curious to know more about your perspective here...in particular about how the community changes because of your participation in it. As I try to make connections to schools and math education, it is easy for me to see how the community changes the individual. I have a harder time seeing places where the mathematical community and the schooling institution allow themselves to be changed by the participants.
Thanks, as always, for the conversation and for making me think! I hope you're enjoying it as much as I am.