Using students' informal notions of variability to develop an understanding of formal measures of variability.

This paper describes some preliminary results from a classroom teaching experiment at the college level, in which students were guided through activities to reveal and develop their notions of variability. Starting with their intuitions about variability, students were asked to speculate about the distributions of different variables, focusing on the informal ideas of whether they expected the variables to have larger or smaller variability. The class activities then guided students from their intuitions about variability as meaning "lots of different values" and overall range, to a dual understanding of variability as both range and clustering in the middle. A final goal of the teaching experiment was to help students make the transition from their initial ideas of variability to the ideas that variability has many dimensions, that formal measures (e.g., range, interquartile range, and standard deviation) all measure different aspects of variability, and that these measures are more useful or appropriate (e.g., to use in comparing groups) depending on the characteristics of the data. The use of assessment items to evaluate student learning will also be described.