ABSTRACT
Statistics is the science of modeling the world through the theory-driven interpretation of data (Burrill & Romberg, chapter 2, this volume; Schwartz, Goldman, Vye, Barron, and the Cognition and Technology Group at Vanderbilt, chapter 9, this volume; Shaughnessy, 1992). Models of chance and uncertainty provide powerful cognitive tools that can help in understanding uncertain phenomena. In this chapter, we consider the development of children's models of chance and uncertainty by considering their performance along five distinct, albeit related, components of a classical model of statistics: (a) the distinction between certainty and uncertainty, (b) the nature of experimental trials, (c) the relationship between individual outcomes (events) and patterns of outcomes (distributions), (d) the structure of events (e.g., how the sample space relates to outcomes), and (e) the treatment of residuals (i.e., deviations between predictions and results). After discussing these five dimensions, we summarize and interpret the model-based performance of three groups as they solved problems involving classical randomization devices such as spinners and dice. The three groups included second graders (age 7-8), fourth/fifth graders (age 9-11), and adults. We compare groups by considering their interpretations of each of these five components of a classical model of chance. We conclude by discussing some of the benefits of adopting a modeling stance for integrating the teaching and learning of statistics.
