Representing Functional Relationships
The study of permutations and combinations of Cuisenaire rods has proved to be a rich source of mathematical tasks motivating abstraction through algebraic symbol systems as well as mathematical generalisation.
In this article I take a rod permutation problem and show how teachers can use this task to support generalisation by employing a new formalism and diagramming convention that records the functional relationships between patterns of Cuisenaire rods.
This convention was suggested by William Lawvere and Stephen Schanuel as an “external and internal diagram” for mappings between typed sets. (Conceptual Mathematics,1997,2004)