The Rise and Run of a Procedural Approach in Discussions about Slope

• In Event: Reexamining the Links Between Curriculum and Instruction for Latina/o Mathematics Learners

Abstract

Objectives
This paper examines the development of mathematical discourse about rate, slope, and linear functions in a bilingual ninth grade algebra class, examining how linguistically diverse students appropriated mathematical discourse about important algebra concepts. I use multilevel analysis to show that, although the teacher introduced rate and its relation to slope with a conceptual focus, both the teacher and her students shifted to a focus on procedures for computing slopes such as “rise over run.”

Theoretical Framework
Rooted in a sociocultural approach to mathematics teaching and learning (Forman, 1996; Moschkovich, 2002, 2004), I examine the transformation of participation in mathematical discourses across time, and the appropriation of socially shared tools for thinking. In the classroom setting, mathematical discourse practices are shaped by many factors, including the selection and implementation of curriculum materials and pedagogical tasks (Brenner, 1998; Stein, Grover, & Henningsen, 1996).

Data & Analysis
I examine a bilingual algebra class taught by an experienced teacher. The teacher used the Interactive Mathematics Program ([IMP] Fendel, Resek, & Alper, 1996) in both Spanish and English, as well as supplemental handouts and worksheets. Following Moschkovich and Brenner’s (2000) naturalistic paradigm for examining mathematical thinking, the study included six weeks of video recorded classroom observations supplemented by a series of out-of-class group problem solving discussions.

The multilevel analysis focuses first on how the teacher and students used mathematical discourse to reason about rate of change in relation to slope. I also examine factors that shaped mathematical discourse, such as the selection of tasks for discussion, and the ways that students took up and transformed activities across the stages of task implementation.

Findings and Discussion
In general, the mathematical discourse about rate and slope shifted from a conceptual focus to a procedural or calculational focus. This shift was reflected in the selection of curricular tasks across three weeks, the sequence of activities within individual lessons, and the teacher’s and students’ use of mathematical discourse during selected lessons. In the paper, I use excerpts of talk and samples of student work to show that the students appropriated a procedural approach to slope, while they did not consistently use a conceptual interpretation of slope as rate of change.

Scholarly Significance
The evolution in mathematical discourse documented here illustrates challenges faced by teachers of linguistically diverse students to maintain a focus on conceptual development. The documented shift may have many possible explanations, including accountability pressure at the school level, time constraints, and balancing the needs of students with widely variable prior school experience. This analysis adds to a body of work on opportunities and challenges for teaching reform mathematics in linguistically diverse settings.

Author

• William Carl Zahner, Boston University