Although research has been done on students' conceptions of centers (averages, means, medians), there has not been a corresponding line of research into students' conceptions of variability or spread. In this paper we describe several exploratory studies designed to investigate school students' conceptions of variability. A sampling task that was a variation of an item on the 1996 National Assessment of Educational Progress (NAEP) was given to 324 students in Grades 4 - 6, 9, and 12 from Oregon, Tasmania, and New South Wales. Three different versions of the task were presented in a Before, and in an After setting. The Before and After students did the task both before and after carrying out a simulation of the task. Responses to the sampling task were categorized according to their centers (Low, Five, High) and spreads (Narrow, Reasonable, Wide). Results show a steady growth across grades on the center criteria but no clear corresponding improvement on the spread criteria. There was considerable improvement on the task among the students who repeated it after the simulation. Students' growth on the center criteria may be due to the emphasis that instruction places on centers in school mathematics. Similarly, the lack of clear growth on spreads and variability, and the inability of many students to integrate the two concepts (centers and spreads) on this task, may be due to instructional neglect of variability concepts.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education