Overcoming visual obstacles with the aid of the Supposer

This paper presents research about the effect of intensive work with diagrams on high school students' use of diagrams in geometry. It identifies three obstacles, culled from previous research, which students must overcome when examining and interpreting diagrams: Diagrams are particular; common usage confuses certain standard diagrams with the classes of objects to which they belong; and a single diagram can be viewed and described in different ways. The paper outlines the resources of the Geometric Supposer, a set of microcomputer software tools which were designed to aid students in overcoming these obstacles. The bulk of the paper presents evidence from students' papers and classroom comments indicating that over the course of a year's work students using the Supposer became more facile in their use of diagrams and were able to overcome each of the three obstacles.The preparation of this paper was supported in part by the National Academy of Education's Spencer Fellowship program.