The Coordination of Distributional Thinking

My aim is to trace the thinking-in-change (Noss & Hoyles, 1996) during the co-ordination of two epistemologically distinct faces of distribution. By co-ordination here, I refer to the connection between a data-centric perspective on distribution, which identifies distribution as an aggregated set of actual outputs, and a modelling perspective on distribution, which views distribution as a set of possible outcomes and associated probabilities. The coordination requires that the learner connects in both directions the data that forms a distribution of results to make up the modelling distribution. The dual connection is, I believe, at the heart of informal inference.