ABSTRACT
The dynamic linking of mathematical representations through computer circuitry is a new and promising development in mathematics education. A representation system consists of a mathematical system linked by a well-defined mapping to another mathematical system or to a nonmathematical situation. Structural syntactic features prescribe the well-formed entities of a notational system; action rules describe allowable actions on such well-formed entities. In the context of a given representation act, it may be useful to specify the medium in which a notational system is instantiated, the equivalence classes of marks or inscriptions that define its characters, and so forth. Cognitive concerns are addressed through explicit incorporation of mental representations in the theoretical framework. Expectation that the software under development may affect dramatic improvement would seem to be the basis for such an optimistic prognosis. The representation-linking software currently under development certainly represents a significant move toward referential teaching of algebra.
