Conceptual issues in understanding the inner logic of statistical inference: Insights from two teaching experiments

We report on a sequence of two classroom teaching experiments that investigated high school students' understandings as they explored connections among the ideas comprising the inner logic of statistical inference-ideas involving a core image of sampling as a repeatable process, and the organization of its outcomes into a distribution of sample statistics as a basis for making inferences. Students' responses to post-instruction test questions indicate that despite understanding various individual components of inference-a sample, a population, and a distribution of a sample statistic-their abilities to coordinate and compose these into a coherent and well-connected scheme of ideas were usually tenuous. We argue that the coordination and composition required to assemble these component ideas into a coherent scheme is a major source of difficulty in developing a deep understanding of inference.