ABSTRACT
A hierarchy can be defined for any body of mathematical knowledge with an overall structure. In refuting the claim that mathematics has a unique hierarchical structure, attention has been restricted to the logical, that is deductive structure of mathematical theories. It is often claimed that the learning of mathematics is hierarchical, meaning that there are items of knowledge and skill which are necessary prerequisites to the learning of subsequent items of mathematical knowledge. There is an assumption concerning the nature and structure of mathematical knowledge which deserves examination because of its educational import. This is the assumption that mathematics can be analyzed into discrete knowledge components, the unstructured sum of which represents the discipline. The theories of mathematics, curriculum, pedagogy, ability and society are all similar, are they hierarchical or change orientated. The fact that the discipline of mathematics does not have a unique hierarchical structure, and cannot be represented as a collection of ‘molecular’ propositions, has significant educational implications.
