An Analysis of Development of Sociomathematical Norms in One First-Grade Classroom
Paul Cobb, Kay McClain
The analysis reported in this paper contributes to the effort to understand how mathematics teachers might proactively support their students' mathematical learning by documenting one first-grade teacher's role in guiding the development of sociomathematical norms in her classroom. We highlight the learning opportunities that arose for both the teacher and her students during this process. The analysis therefore serves to clarify what teachers might actually do to support the emergence of the type of mathematical disposition advocated in reform documents. In addition, the analysis describes the decision-making processes that were involved in setting the teacher's agenda. This aspect of the paper focuses on the teacher's interactions as part of a research team whose dual focus was to support both the students' mathematical learning and their development of mathematical autonomy. The analysis was informed by and builds on Yackel and Cobb's (1996) discussion of sociomathematical norms.
Building on Informal Knowledge Through Instruction in a Complex Content Domain: Partitioning, Units, and Understanding Multiplication of Fractions
Nancy K. Mack
Six fifth-grade students came to instruction with informal knowledge related to partitioning. This knowledge initially focused on partitioning "units of measure one" into a specific number of parts. Students were able to build on their informal knowledge to reconceptualize and partition units to solve problems involving multiplication of fractions in ways that were meaningful to them. Students built their knowledge by developing mental processes related to focusing on fractional amounts and to partitioning units in different ways. Students also frequently returned to their initial focus on the number of parts and to ideas embedded in equal-sharing situations.
From Preservice Mathematics Teacher Education to Beginning Teaching: A Study in Recontextualizing
This article describes a two-year longitudinal study that tracked seven students through a one-year, full-time, university-based secondary mathematics method course and into their first year of teaching in the Western Cape province of South Africa. The purpose of the study was to describe the recontextualizing from the mathematics method course by these beginning teachers. Qualitative analysis of the teacher education course, of students' positioning in relation to this course, and later of their positioning in relation to teachers and learners in schools, was conducted. The results showed that beginning teachers drew in two ways from the method course: they reproduced a small number of discrete tasks that had been introduced to them there, and they also deployed a professional argot--a way of talking about teaching and learning mathematics. This recontextualizing was shaped by the beginning teachers' educational biographies and school contexts, but most particularly by access to recognition and realization rules.