Daniel Chazan and Michal Yerushalmy
When evaluating the effect of an educational innovation, it is important to test for the goals that the innovation has set out to accomplish. In the Supposer approach to teaching geometry (described below), in addition to teaching the content of high school geometry, teachers try to inculcate in their students mathematical and scientific inquiry skills, beliefs, and attitudes that are helpful in solving inquiry problems. These skills develop in students throughout a year-long course. We would like to be able to assess the success of this approach in teaching students to be good inquirers. The task is an extremely difficult one.
We begin this chapter with a short description of the approach we favor for teaching high school geometry. We then provide a rough outline, which we developed with a group of teachers, of the types of higher-order skills (as well as beliefs and attitudes) involved in exploring an inquiry problem. Having provided this background, we concentrate on students' verifying, conjecturing, and generalizing skills. We first present a research instrument designed to compare generalizations created by students. After presenting this paper-and-pencil test, we present a more thorough analysis of the verifying, conjecturing, and generalizing skills used by competent explorers of inquiry problems. This analysis derives from sessions with classroom teachers as well as considerations suggested by the research