University ofHaifa Learning Through Teaching: The Case of Symmetry

A study was carried out within the framework of an undergraduate course in teaching skills and strategies. An experimental part of the course was designed to provide an opportunity for the students to learn a mathematical topic through teaching it to eighth grade pupils in a Learning Through Teaching (LTT) enviromnent. Symmetry was chosen as the focal mathematical topic for the experiment. This paper focuses on the development of the students ' understanding of line synunetry. The findings show that the implemented LTT enviromnent served as a vehicle for the student teachers to learn mathematics. In spite of the difficulties they encountered during the study, the students expressed positive dispositions towards symmetry and its role in mathematics. Our study stems from the conviction that symmetry can be helpful both for understanding various mathematical concepts and for solving mathematical problems. We also believe that symmetry has the potential to foster a rich and powerful learning, teaching, and learning-to-teach environment. The study reported in this paper is _part of a larger research project aimed at exploring the concept of symmetry as a tool for the professional development of mathematics teachers (Leikin, 1997). The students who took part in the study were student teachers enrolled in an undergraduate course on general teaching skills and strategies. For the purpose of this study, students were required to learn the concept of symmetry in order to be able to teach it. The development of the students ' content and pedagogical knowledge (Shulman, 1986) was observed, documented, and analysed. This paper focuses on the development of students' knowledge of the concept of line symmetry and their dispositions towards symmetry. Backgroun