12 th International Congress on Mathematical Education Program Name XX-YY-zz (pp. abcde-fghij) 8 July – 15 July, 2012, COEX, Seoul, Korea (This part is for LOC use only. Please do not change this part.) abcde PRE-SERVICE TEACHERS’ USE OF SYMMETRY OF QUADRATIC GRAPHS IN PROBLEM SOLVING Weng Kin Ho, Foo Him Ho, and Dindyal Jaguthsing National Institute of Education, Nanyang Technological University wengkin.ho@nie.edu.sg, foohim.ho@nie.edu.sg, jaguthsing.dindyal@nie.edu.sg This paper reports on the performance of pre-service mathematics teachers with regards to the use of symmetry in problem solving. The current study reveals that pre-service teachers do not make use of symmetry as their main problem-solving tool, even in situations where symmetry is the obvious notion to consider. In addition, a quantitative comparison of the effectiveness of problem solving among approaches (those relying on symmetry versus those relying on other conventional methods) is reported herein. This formal comparison validates the opinion that active usage of symmetry in problem solving significantly enhances the chance of solving non-routine problems. Keywords : Problem solving, Symmetry, Quadratic graphs, Pre-service teachers INTRODUCTION In Singapore schools, the notion of symmetry is first introduced in the lower primary syllabus where children of age 9 years old are expected to locate and draw lines of symmetry of a given figure, such as a square. In the upper primary, students built upon this knowledge in their study of angles, for instance, it is expected of a Primary 4 student to obtain the size of the acute angle made by the diagonal of a square with its side as half that of the right angle, i.e., 45°. Moving up to the secondary level, symmetry is invoked primarily in connection with geometrical properties of congruent figures as well as the graphs of quadratic functions. It is clear that symmetry in itself is not a fundamental concept in the Singapore Mathematics Syllabus; at least not as important as mensuration concepts, such as area and volume, just to name one example. However, symmetry has long been hailed as one of the most powerful and commonly-used problem-solving tools by mathematicians (Weyl, 1952; Pólya, 1981; Schoenfeld, 1985; Hilton & Pedersen; 1986; Dreyfus & Eisenberg, 1990).The aforementioned discussion about symmetry compels us to raise the following questions: (1) Does the lack of emphasis on symmetry in the current Singapore Mathematics Syllabus significantly handicap the students’ and teachers’ problem solving ability in mathematics? (2) To what extent is symmetry perceived as one of the heuristics or cognitive resources in problem solving, and how often is it invoked? Incidentally, the lack of emphasis of symmetry in the Israeli national mathematics curriculum was reported, and its effects studied in detail, by Leikin, Berman, and Zaslavsky (2000) as well as Leikin (2003). These studies reported that the concept of symmetry is taught only in connection with the graphs of quadratic functions in the Israeli mathematics syllabus, and this