A Framework for Coordinating Whole Class and Small Group Justification Norms

Susan Nickerson

San Diego State University

Snickers@sunstroke.sdsu.edu

The research presented here is part of a larger effort to coordinate analyses of individual student justifications, small group reasoning, and whole class patterns of justification in an Algebra I classroom. The focus is on how students’ ways of justifying differed in small groups when compared to their whole-class discussions and furthermore how the presence of technology affected these ways of justifying. I report particularly on the degree to which students constructed personal ways of judging and changes in their use of imagery in justification.

Researchers and the teacher designed a technology-intensive unit to support students’ development of meaning of graphs of linear equations in a classroom teaching experiment (Cobb, 2000). The analysis is based on a framework described by Cobb (2000) that takes students’ individual reasoning as a unit of analysis while simultaneously viewing that reasoning as an act of participation in communal practices.

Analysis of small group and whole class justification norms when coupled with articulation of mathematical practices indicated that, at the beginning of the teaching experiment, authority resided with the teacher and computer. As the class developed in ways of reasoning, they began to use the imagery developed through their experience with the software, and hence developed more robust personal ways of judging.

Reference

Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly and R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education. Hillsdale, N.J.: Lawrence Erlbaum. 307-326.