Undergraduate Students' Use of Primitive Notions When Reasoning About Variability

Abstract

Previous research has shown that students form fragmented understandings about variability even after instruction and that these primitive notions function as obstacles to a robust understanding of variability. To investigate the effect of disruptions to students\" primitive notions of variability, we examined undergraduate students\" reasoning about variability when distributions of quantitative datasets to be compared (a) have equal ranges, (b) do not include extreme values, and (c) have approximately the same number of different values. We designed homework questions and collected student responses to these questions from a large number of students attending an introductory statistics course. We also reorganized these questions into interview tasks and conducted task-based interviews with students. The results showed that students either did not address variability in these narrowly framed situations or provided limited, ambiguous, or inconsistent responses. The findings suggest that students typically think about variability in terms of range\"s colloquial meaning and how different the values are from each other. Students\" reasoning was often contingent upon the particular and more prevalent characteristics of the distributions on which they were asked to work. Future work should explicate ways to utilize students\" available conceptions of variability in teaching the concept\"s normative meaning.