A logical perspective on cuisenaire and bar modelling

Abstract

A novel approach is proposed to the analysis of the expressive powers of Concrete, Pictorial and Abstract representations of arithmetic . Drawing on the theory of formal mathematical logic, it is shown that precisely defined syntaxes and semantics can be introduced for Cuisenaire rods and part - whole bar models. By interpreting sentences expressed in these representations as sentences in the first - order theory of arithmetic, it is possible to rigorously study the potential and limits of these representations. It is shown that different appr oaches to bar modelling vary depending on the semantic content given to geometric bar length, and the implications of this observation are studied to reveal the relative power of these representations for expression of word problems and their subsequent so lution within the representation.