Stepwise discovery of mathematical knowledge in GeoGebra

Abstract

We describe an enhancement to GeoGebra, a well-known dynamic geometry software tool that calculates the significant geometric properties of a planar construction.
In a previous experimental version of GeoGebra, "GeoGebra Discovery," the Discover command determined geometric properties such as parallelism or perpendicularity of lines, equality of segment lengths, and collinearity or concyclicity of points. This work introduces a further improvement of the Discover command, the "stepwise discovery" mode, which supports real time, dynamic identification of true statements and geometric properties as each new point is added to the construction. Our contribution explains how the stepwise discovery mode can be helpful in teaching planar geometry at the secondary level or in the researcher's work.