We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expression (in the form of the Gergonne…

The development of conceptual understanding in arithmetic is a gradual process and children may make use of a concept in some situations before others. Previous research has demonstrated that when children are given arithmetic problems with an inverse relationship they can infer that the initial and final quantities are the same. However, we do…

This paper draws on earlier work on ideas that underpin the collection and use of evidence in science in schools. It establishes that different types of practical work share the same procedural underpinnings. It then takes the work of Toulmin on argumentation to suggest that the idea of the "public claim" can be used to forge a link…