Teachers Using GeoGebra to Visualize and Verify Conjectures About Trapezoids

This paper describes outcomes from a project conducted at a small US university where 23 secondary school mathematics teachers participated in the study. Based on sketches created in a dynamic geometry software (DGS) and written responses to an assignment related to developing the trapezoid area formula, we explored how teachers used DGS when visualizing and verifying geometrical conjectures. We found that teachers used a combination of four strategies—eye-balling, measurement, constructions, and written statements—in their DGS sketches. Some teachers used DGS as paint software and their DGS files did not pass the dragging test. Teachers’ misconceptions became obvious while they were visualizing conjectures in the software, which were mediated by the skill for use of technology. Also, some used shortcuts that disagreed with conjectures and distorted their solutions, thus employing practices that could be damaging in teaching situations. These results and the methodological approach used in this study will be of interest to mathematics teacher educators, facilitators of professional development programs, and mathematics teachers.