Informal statistical models and modeling

Abstract

ABSTRACT Growing scholarship on the pedagogical applications of statistical modeling is currently taking place to create adaptations of this practice to introduce novices to statistics. These are intended to promote novices’ reasoning, and are typically void of formal mathematical procedures and calculations. In this article, we define the potential product that novices can create as they engage in such informal implementations, Informal Statistical Models (ISM), as purposeful representations – with both deterministic and stochastic components – of how observed variability in data is generated. This definition reflects the potential connection between informal constructs that novices and young students can create and the formal view of statistical models, thereby suggesting how informal insights may be later cultivated into more mature understandings. We illustrate the usefulness of this definition by providing an in-depth account of the reasoning that a pair of sixth-grade students employed through their informal statistical modeling process. The findings illustrate a four-episode sequence where students created and developed an initial deterministic model before extending it with an informal stochastic component. This shows how starting with deterministic models can be a valuable precursor to develop initial ISMs.