| In addition to the synthetic approach, algebraic approaches are inherent in the use of transformations, coordinates, and vectors to study geometry. This study investigated secondary students' use of algebraic thinking: the use of symbols and algebraic relations, the use of different forms of representations, and the use of patterns and generalizations in geometry and their related conceptual difficulties.; This qualitative study took place during the first semester in two midwestern high schools. One geometry class was selected from each high school, and an algebra test and a van Hiele test (Usiskin, 1982), were administered to the students for selecting three of them from each high school. The focus students were interviewed four times each, their classrooms observed for two months, and artifacts such as tests, quizzes and homework were collected. The teachers from these two classes were also interviewed twice.; The constant comparative method and the grounded theory were used in the analysis of the data. The theoretical perspectives in this study were the theory of reification (Sfard, 1991), the theory of representation and representation systems (Goldin, 2002), the theory of thinking as communicating (Sfard, 2001), the emergent perspective (Cobb & Yackel, 1996), and the theory of knowledge connectedness (Anderson, 1990). The results showed that the students used algebraic thinking in solving problems in geometry, but they had several difficulties as well, including: understanding the nature of a variable, writing an equation/expression, recalling and using formulae, understanding the use of different forms of representations, finding generalizations from patterns. Sometimes a geometrical concept/idea was the source of their error and sometimes it was an algebraic concept. In addition, it was found that students' use of algebraic thinking was related to their teacher's use of the same in their classes. Also, van Hiele levels do not necessarily give a complete picture of students' thinking in geometry. |
