The co-emergence of aggregate and modelling reasoning1

Abstract

This article examines how two processes - reasoning with statistical modelling of a real phenomenon and aggregate reasoning - can co-emerge. We focus in this case study on the emergent reasoning of two fifth graders (aged 10) involved in statistical data analysis, informal inference, and modelling activities using TinkerPlotsTM. We describe nine phases of the students' articulations of aggregate and modelling reasoning as they explored a small sample, constructed a model and generated random samples from this model to examine its validity. These phases are distinguished by the students' views toward data, variability, and models. We discuss implications and limitations of the results. Despite the idiosyncrasy of the case, the lessons are important because they open a new direction for research about reasoning with data and models.