Described is the notion of multiple alternative representations of mathematical reasoning, particularly as they relate to algebraic notation and the potential of computers to change representations. Features of a desirable notation for algebraic problem solving are described. This is followed by a description of the RAND Corporation's intelligent algebra tutor and the specific tools it contains that support multiple representations: a boxes-and-weights tool and goal commands. These tools supply students with important learning opportunities. Finally, comments are made about continuing research in this area, and the importance of testing different representational systems in real educational contexts. In addition, theoretical work must be directed toward deriving a general classification scheme for representations. (MNS)