Reasoning in the Presence of Variability

James K. Hammerman and Andee Rubin

TERC, 2067 Massachusetts Ave., Cambridge, MA

Jim_Hammerman@terc.edu; Andee_Rubin@terc.edu

Do not circulate without written consent from the authors.

Abstract

This paper describes several ways that learners use new software tools to reduce cognitive complexity in analyzing data, and suggests the beginnings of a framework for understanding these techniques. The approaches we address include normalizing differences in group size by using proportions; reducing the detail of data variability by grouping it using numerical bins or cut points; and attending to general trends in data while ignoring variability around those trends. This framework is built on our observations of middle- and high-school teachers in a professional development seminar, as well as of students in these teachers’ classrooms and in a 13-week sixth grade teaching experiment.