Talking Past One Another and Getting on the Same Page: Communication in Mathematics Teaching and Learning

Interpersonal interactions between teachers and students are a site where students may encounter negative experiences with mathematics; they are also a site where students can experience mathematics in empowering and positive ways. The aim of this study is to understand the work of communicating mathematics in ways that empower, rather than marginalize, students of color and girls. It explores communication in one-on-one interactions about mathematics to understand and conceptualize moments when teachers and students “talk past one another” and the work of “getting on the same page.” Grounded in a conception of teaching as interactive, this work takes as axiomatic the brilliance of students of color and girls, which informs the following assumptions: students are intelligent and capable of doing mathematics, they have a desire to learn and succeed, and they are actively trying to do so. With these assumptions in place, this dissertation explores the research questions: In episodes of one-on-one communication between a teacher and a student about mathematics, (1) What do teachers and students do during moments when they are likely talking past one another? (2) What common sources contribute to these moments of talking past one another? (3) What do teachers and students do as they work through moments of talking past one another? To understand talking past one another and getting on the same page, I employ qualitative methods together with tools from discourse analysis to examine video data of one-on-one interactions between teachers and students. The two-phase analysis began with discourse analysis procedures of focal analysis and preoccupational analysis (Sfard, 2001). I used these procedures to create tables and interaction flow charts, conducting a line-by-line analysis of 12 focal episodes. In the second phase, I used open coding together with a practice-based lens, to develop themes related to sources of talking past one another and getting on the same page. The analysis points to three core findings. First, talking past one another was ubiquitous—most episodes showed evidence this occurred throughout the interaction. Talking past one another is therefore normal and expected in teacher–student interactions. Second, certain types of language were more consequential for the work of getting on the same page: action language, comparison and directional language, qualifying language, and implicitly referenced objects. The inconsistent or unclear use of language led to talking past one another when teacher and student were operating in different contexts wherein the same word has different meanings. Third, one of the most important resources for communicating is what I refer to metaphorically as “space to think.” Space to think includes physical space, material space (e.g., paper), and temporal space. Less space for students to think complicated the work of getting on the same page; more space for students to think made the work of getting on the same page less challenging. In the final chapter, I discuss how this research offers new insights into processes of teaching and learning, how language functions in mathematics, the sensibility of student thinking, the importance of space to think, and the ubiquity of talking past one another. I discuss how these findings provide implications for teachers and teacher educators to develop capacity for working to get on the same page with students. I conclude with a discussion of new questions raised by this study and future directions for research.PhDEducational StudiesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/172740/1/hickmala_1.pd