1 Reasoning in the Presence of Variability1

Abstract

Do not circulate without written consent from the authors. 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. Overview Teachers often come to professional development programs thinking that statistics is about mean, median, and mode. They know how to calculate these statistics, though they don’t often have robust images about what they mean or how they’re used. When they begin working with computer data analysis tools to explore real data sets, they are able to see and manipulate the data