This paper reports two prospective teachers' and a mathematician's ways of identifying similar triangle and hexagons through the analysis of routines, a characteristic of geometric discourse. The findings show that visual recognition was a common approach for the mathematician as wells as the two prospective teachers. However, when asked for justification, their routines of identifying similar polygons diverged. The paper also discusses the implication of classroom discourse practices to enhance prospective teachers' communication and reasoning skills while learning geometric concepts such as similarity.
This document was originally published in PMENA-37: Proceedings Thirty-Seventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education by Psychology of Mathematics Education - North American Chapter. Copyright restrictions may apply.
Available at: http://works.bepress.com/sasha_wang/21/