Investigating Statistical Unusualness in the Context of a Resampling Activity: Students Exploring Connections between Sampling Distributions and Statistical Inference

Reasoning proportionally about collections of a sample statistic’s values is central to developing a coherent understanding of statistical inference. This paper discusses key developments that unfolded in a classroom teaching experiment designed to support students constructing such understanding. Instruction engaged students in activities that focused their attention on the variability among outcomes of randomly drawn samples. There occurred a critical shift in students’ attention and discourse away from individual sample outcomes and toward the distribution of a collection of sample outcomes. This shift supported further developments concerning how to compare entire distributions of sample outcomes as a basis for conceptualizing a notion of statistical unusualness. We characterize aspects of these developments in relation to students’ classroom engagement.