Construing a collection of values of a sample statistic as a distribution is central to<br>developing a coherent understanding of statistical inference. This paper discusses key developments that<br>unfolded over three consecutive lessons in a classroom teaching experiment designed to support a group of<br>high school students in developing such a construal. Instruction began by engaging students in activities<br>that focused their attention on the variability among values of a common sample statistic. There occurred a<br>critical shift in students' attention and discourse away from individual values of the statistic and toward a<br>collection of such values as a basis for inferring the value of a population parameter. This was followed by<br>their comparisons of such collections and by the emergence and application of a rule for deciding whether<br>two such collections were similar. In the repeated application of their decision rule students structured these<br>collections as distributions. We characterize aspects of these developments in relation to students'<br>classroom engagement, and we explore evidence in students' written work that points to how instruction<br>shaped their conceptions.
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