Students’ reasoning about uncertainty while making informal statistical inferences in an Integrated Pedagogic Approach.

Reasoning about uncertainty is a key and challenging element in informal statistical inferential reasoning. We designed and implemented an “Integrated Pedagogic Approach” to help students understand the relationship between sample and population in making informal statistical inferences. In this case study we analyze two sixth grade students’ reasoning about uncertainty during their first encounters with making informal statistical inferences based on random samples taken from a hidden TinkerPlots2 Sampler. We identified four main stages in the students’ reasoning about uncertainty: Account for, examine, control, and quantify uncertainty. In addition, two types of uncertainties – contextual and a statistical –shaped the students’ reasoning about uncertainty and played a major role in their transitions from stage to stage. Implications for research and practice are also discussed.