Investigating Prospective Mathematics Teachers’ Strategies to Generate Definitions of Special Quadrilaterals

Strategies to Generate Definitions

Abstract

The purpose of this study was to address the ways in which prospective mathematics teachers (PSTs), who enrolled in different years of a teacher education program at a public university in Turkey, generated definitions of special quadrilaterals. By addressing the strategies that the PSTs employed while generating definitions, this study aimed to investigate to what extent the participating teachers could distinguish the necessary and sufficient conditions for each special quadrilateral. Analyzing the details of the characteristics of definitions generated and the strategies employed by the PSTs who had different years of experience in a teacher education program was essential to further delve into the complex defining processes and to better conceptualize the types of struggles that the PSTs experienced at the beginning and near the end of the program. A questionnaire was administered to 57 senior and 57 freshman prospective teachers and six prospective teachers from each grade level further participated in the individual interviews. The results indicated that both senior and freshman PSTs struggled to generate more than one definition for each special quadrilateral, especially for a kite and isosceles trapezoid. Furthermore, the strategies that the participants employed differed among the PSTs in different years of the program and indeed illustrated their different ways of reasoning skills.