Diagrammatic reasoning and hypostatic abstraction in statistics education

Peirce's notions of diagrammatic reasoning and hypostatic abstraction are relevant to educational research in areas where diagrams and abstraction play an important role. In this paper, I analyze an example from statistics education in which diagrammatic reasoning created opportunities for hypostatic abstraction. For instance, where students initially characterized data points as being 'spread out,' they later said, 'the spread is large.' This is a prototypical example of hypostatic abstraction - taking a predicate as a new object that can have predicates itself. More generally, the notion of diagrammatic reasoning proved helpful to identify the key learning processes involved in learning to reason about statistical concepts.