Combatting shallow learning in a tutor for geometry problem solving

Abstract

The PACT Geometry tutor has been designed, with guidance from mathematics educators, to be an integrated part of a complete, new-standards-oriented course for high-school geometry. We conducted a formative evaluation of the third “geometric properties” lesson and saw significant student learning gains. We also found that students were better able to provide numerical answers to problems than to articulate the reasons that are presumably involved in finding these answers. This suggests that students may provide answers using superficial (and possibly unreliable) visual associations rather than reason logically from definitions and conjectures. To combat this type of shallow learning, we are developing a new version of the tutor’s third lesson, aimed at getting students to reason more deliberately with definitions and theorems as they work on geometry problems. In the new version, students are required to state a reason for their answers, which they can select from a Glossary of geometry definitions and theorems. We will conduct an experiment to test whether providing tutoring on reasoning will transfer to better performance on answer giving.