On page 99, I am a conversation analyst. The top of the page features two of Schegloff’s transcripts illustrating two different sorts of repair initiation: the kind of thing you might say if I asked a question and you didn’t understand, followed by what you’d say if *you* asked *me* a question and didn’t understand my answer. I bring up these patterns to highlight their absence in my own field work. Schegloff’s examples come from everyday conversation, but I conducted research in mathematics classrooms, and teachers and students do not ask for repetition and clarification in such a democratic way. In one classroom, I saw a teacher orchestrating class participation such that students would provide corrections to their classmates’ mistakes. In another, I observed what happens when the statement you didn’t understand is not spoken aloud but written in chalk on a blackboard. And in both cases, I realized that “understanding mathematics” was equated with “finding the right answer,” as all conjecture, supposition, incomplete learning and conceptual knowledge were eclipsed by the authority of the teacher and the textbook.
Now, in general, I am not a conversation analyst. This is simply the methodology that I selected for that chapter, which dealt with the question, *How do sequences of classroom interaction realize ideologies of mathematical knowledge?* Elsewhere, I considered the utility of mathematical notation alongside other communicative systems such as language and gesture, as well as the ways that students think about “math person” as a kind of identity that may be more or less in conflict with other aspects of their self-concept. These areas of inquiry required different methodologies: multimodal interaction analysis, narrative analysis, ethnography. And yet, in every case, the data led me to similar conclusions: it’s often difficult for students to see themselves as successful mathematics learners. Educators know this—we all do—but my point is that their difficulty is wrapped up in particular practices of talk and interaction. Put into practice, this knowledge may suggest ways to make mathematics instruction more equitable.
Daniel Ginsberg. 2015. “Multimodal Semiotics of Mathematics Teaching and Learning.” Ph.d diss., Georgetown University. <https://www.academia.edu/19577481/Multimodal_Semiotics_of_Mathematics_Teaching_and_Learning>
Daniel Ginsberg is a Professional Fellow at the AAA.