Resistances to Mathematical Knowledge

Resistances to Mathematical Knowledge

[Note: this short paper was intended as the first draft of a chapter for a Free/Open/Libre

textbook on queer math methods, intended for use in an elementary or high school

math methods classroom.   This work is licensed CC-BY-SA, and contributions to it are

welcome, and will be collated, attributed, and added to the website.   You’re also free

to remix this work, provided you credit me for the original work.]

 

Susannne Luhmann (1998) discussed how traditional education is about transmission of knowledge and modeled after pederasty, where, as Jane Gallop (1982) suggested “[a] greater man penetrates a lesser man with his knowledge” (Gallop, p. 63, cited on Luhmann, p. 148). In mathematics education, we talk a lot about sharing intellectual authority with students and building up students’ abilities to engage in mathematical conversation. The agency for making this change in the classroom, however, is given to the teacher – we talk about professional development, changing textbooks, coming up with better teaching methods, increasing teachers mathematical knowledge. Math methods texts generally devote most of the text to presenting mathematical content and how it supposedly should best be taught. Luhmann warned us that the transmission model “returns like the repressed in the prevalent preoccupation of teachers with methods, or the how-to of teaching… [and] some (fantasmic) investments in the role of the teacher in the learning process” (p. 148).

 

I was assisting in a classroom the other day and a student asked for help in a rather dry and uninteresting word problem. He said “I don’t know the answer.” I asked him to read the problem out loud, and he said he had a sore throat and shouldn’t be talking. (He had literally lost his voice! in this classroom!) So I read the problem to him, and asked him to draw a picture. He refused. So I drew a diagram for him, and asked him to look at it. He leaned back, refused to look at the paper, and said “I don’t know the answer. I told you, I don’t know the answer” and repeated it a dozen times in a sing-song voice.   A few days later, he saw a math problem on the board and went up adn wrote the phrase “Yo Momma!” underneath the problem.  This reminds me of what Luhmann has to say about ignorance as a resistance to knowledge:

 

…Felman (1987) pointed out that ignorance, or forgetting, is tied to repression, as “the imperative to forget … Ignorance … is not a passive state of absence, a simple lack of information; it is an active dynamic of negation, and active refusal of information” (p.79). Rather than posing ignorance and knowledge in an exclusionary opposition, in psychoanalytic thinking, ignorance constitutes knowledge. Ignorance is not the opposite to knowledge but an opposition to knowing. Instead of a lack of information, ignorance is a form of psychic resistance, a desire not to know, which perhaps can be described as a position of “I do not want to learn anything else, because I already know too much. Teaching, so Felman concludes, is engaging with these resistances to knowledge more than correcting a lack of knowledge… [ignorance] is indicative of the incapacity– or the unwillingness– to acknowledge one’s own implication in the material studied.” (p. 150).

 

So, clearly the student was resistant to working on the problems. But was he resistant to mathematical knowledge itself? And if so, what is the implication in the material studied that he was afraid to acknowledge?

 

What I want to propose here is that mathematics, as a cultural tool, always comes to us gendered, raced, and classed. The math that the student was being asked to learn in class is a story of European conquest, of appropriation and erasure of the work of many cultures. The history of European mathematics is also mostly about the upper classes, about those with the luxury to sit around and work on mathematical problems rather than having to work in the fields or for basic survival needs. And the stories that get told are, as a poster Heather Mendick saw in one of the schools she worked in, about “the men of mathematics” – math gets recoded as masculine. So it’s been coded as white, masculine, and upper-class. Or more specifically, a white, upper class masculinity; a far cry from a black, working class masculinity. When a working-class black kid is being asked by an upper middle class white man to learn these tools, is it any wonder the black kid is going to resist?

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