What I see is not quite the way it really is: students’ emergent reasoning about sampling variability

Currently, instruction pays little attention to the development of students’ sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and interview responses from four students to describe their emergent reasoning about sampling variability. Their reasoning is analyzed using our adaptations of a statistical inference framework and a mental processes framework. Our findings suggest that these students are beginning to develop understanding of sampling variability concepts from probabilistic and generalization perspectives and to articulate the evidence used from the data. We conjecture that these students’ understanding of sampling variability is aided by the development in instruction of the three mental processes of visualization, analysis, and verbal description.