Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students' Engagement and Thinking in the Context of Instruction Involving Repeated Sampling

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