High school mathematics teachers' content knowledge of the logical structure of proof deriving from figural-concept interaction in geometry

Abstract

The present study aims to examine high school mathematics teachers' content knowledge of the logical structure of proof in geometry. For this purpose, three scenarios were established based on errors in proof deriving from the figural-concept interactions. Based on these scenarios, clinical interviews were held with five mathematics teachers, who were working at different high schools, who used proof actively in their classrooms, and who had varying experiences. the obtained data from the interviews were analyzed descriptively under three categories. the results of the study revealed that the teachers did not have sufficient content knowledge to cope with proof errors deriving from figural-concept interactions in geometry. the teachers generally failed to base the information they obtained from figures on an axiom or theorem, to avoid sweeping generalizations based on geometric figures, and making accurate changes in figures when contradictions emerged as a result of valid reasoning processes. It is recommended that discussions be held on the justifications underlying the propositions constituting the proof and mistakes in geometric proof at the undergraduate level of education.