Middle School Students’ Statistical Reasoning About Distribution in Their Statistical Modeling Processes

Statistical reasoning about a population through samples can be achieved by modeling the relationship between population and sample. One way to do this is to model real data situations in a technology-integrated environment. With this view, we aimed to investigate how middle school students formed distributions and examined their statistical modeling processes through the informal reasoning process within the Reasoning with Informal Statistical Models and Modeling (RISM) framework. The case study reported in this paper focuses on how the conjecture and data models students designed throughout three activities evolved and how their inclusion of a fundamentally probabilistic mechanism matured. Findings show the students approached the distribution probabilistically with their inferences during the modeling process and grasped the statistical concepts they would encounter at a more advanced level. Therefore, we claim that students shifted from understanding empirical distributions to understanding theoretical distributions.