CONCEPTIONS OF DISTRIBUTION HELD BY<br>MIDDLE SCHOOL STUDENTS AND PRESERVICE TEACHERS

This paper examines how preservice teachers and middle school students reason about distributions as they consider graphs of two data sets having identical means but different spreads. Results show that while both subject groups reasoned about the task using the aspects of average and variation, relatively more preservice teachers than middle school students combined both aspects to constitute an emerging form of distributional reasoning in their responses. Moreover, these emergent distributional reasoners were more likely to see the data sets as fundamentally different despite the identical means used in the task.