When Do Gifted High School Students Use Geometry to Solve Geometry Problems?

Abstract

This article describes the following phenomenon: Gifted high school students trained in solving Olympiad-style mathematics problems experienced conflict between their conceptions of effectiveness and elegance (the EEC). This phenomenon was observed while analyzing clinical task-based interviews that were conducted with three members of the Israeli team participating in the International Mathematics Olympiad. We illustrate how the conflict between the students’ conceptions of effectiveness and elegance is reflected in their geometrical problem solving, and analyze didactical and epistemological roots of the phenomenon.