This paper examines a range of studies done on the "Geometric Supposer" software and its use since the mid-1980s. It describes how the "Geometric Supposer" is a response to the call for reform by the mathematics community to create classroom environments that allow students to construct their own knowledge. This approach to learning mathematics is called "guided inquiry" and is described and contrasted with current practice. Research findings about students and teachers from studies using the "Geometric Supposer" are presented. Findings are reported about mathematical behaviors, attitudes, geometry content, learning behaviors, and teaching behaviors. Key issues and dilemmas that arise in the course of using the software with a pedagogy of guided inquiry are also identified. Since the "Supposer" exemplifies mathematics education as called for in the prescriptions for change by the National Council of Teachers of Mathematics and the Mathematical Sciences Education Board, the paper argues that what has been learned from six years of "Supposer" experience can serve as a guide for thinking about mathematics education reform beyond geometry. (MDH)