Fast Kids, Slow Kids, Lazy Kids: Framing the Mismatch Problem in Mathematics Teachers' Conversations

Abstract

This article examines the social nature of teachers' conceptions by showing how teachers frame the “mismatch” of students' perceived abilities and the intended school curriculum through conversational category systems. This study compares the conversations of 2 groups of high school mathematics teachers addressing the Mismatch Problem when implementing equity-geared reforms. Although East High teachers challenged conceptions that were not aligned with a reform, South High teachers reworked a reform mandate to align with their existing conceptions. This research found that the teachers' conversational category systems modeled problems of practice; communicated assumptions about students, subject, and teaching; and were ultimately reflected in the curriculum. Because East High teachers supported greater numbers of students' success in advanced mathematics, this study considers the relation between teachers' understandings of student learning and the success of equity-geared math reforms. In addition, this study contributes to the understanding of how teacher conceptions of students are negotiated and reified in context, specifically through interactions with colleagues and experiences with school reform.

ACKNOWLEDGMENTS

The study was supported by a Spencer Dissertation Fellowship. The dissertation received the 2003 AERA Division K Outstanding Dissertation Award and the Outstanding Dissertation Award from University of California-Berkeley's Graduate School of Education.

I thank Rogers Hall, Judith Warren Little, Alan Schoenfeld, Anne Haas Dyson, and Susan Jurow for their assistance and support in the early stages of this analysis. More recently, I have benefited from conversations and correspondence with Manka Varghese, Jennifer Stone, Bret Norris, Yasmin Kafai, Janet Kolodner, and several thoughtful anonymous reviewers of this journal. Any errors that remain are my own.

Notes

¹All proper names of schools and participants are pseudonyms

²The social organization of schools as it relates to categories of students has been explored previously. For example, McDermott (1993) argued that schools are organized to help categories such as learning disabled“acquire” students; Eckert (1989) examined the social spaces that separate jocksfrom burnoutsin high schools.

³Judith Warren Little, Principal Investigator. Funded by the Office of Educational Research and Improvement, and the Spencer and MacArthur Foundations.

⁴Student population sizes are rounded to the nearest multiple of 50.

¹The concept ofpedagogical reasoninghas been discussed by others who studied teacher knowledge (McDiarmid & Ball, 1989; Wilson, Shulman, & Richert, 1987). What distinguishes my use of this con-struct is that I am investigating pedagogical reasoning as it emerges in teachers'everyday conversations.

⁶“Check-in” has a certain routine structure in the Algebra Group In this routine, members would state where they were in the common curriculum and what activities they had been doing with their classes. Any questions or issues that arose since the last meeting then followed.

⁷“Perimeter lab gear” refers to an activity that involves finding the perimeters of two-dimensional rectilinear polygons built with algebra tiles (Piccioto & Wah, 1994). The tiles provide a geometric representation of variable expressions. The perimeter activity provides a geometric representation for combining like terms.

⁸Carrie is using language and ideas from complex instruction (Cohen, 1994; Cohen & Lotan, 1997). Complex instruction is a key component of East High's detracking work. See Horn (2006) for more details.

⁹The group makes frequent references to the 8th grade, which constitutes a kind of existence proof for their detracking work. Up until 2 years prior to this meeting, East High School was an 8 though 12 grade school. The math teachers, over the course of a decade, created a detracked 8th grade curriculum.

¹⁰This practice of inserting imagined classroom dialogue into conversations is explored more in Horn (2002)

¹¹Noah's own biography belies deterministic classification of students' abilities. He was a student who had been routed out of the mainstream into an alternative high school where, according to his own account, he did not learn much math. He eventually went to a community college, discovered a love for math, and graduated as a Phi Beta Kappa math major from a prestigious university.