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Pedagogical conceptions of geometry
Professional development of teacher
Case study and classroom observation were adopted in this study which described the pedagogical conception of two junior high school mathematics teachers when they taught geometry. According to the content of 7 grade’s mathematics curriculum, this research process was divided into the pilot study which took the relations of numbers and patterns as the theme, and first and second stage studies took geometric plane figures and transformation of geometric figures as the themes respectively. The author used questionnaires, interviews and classroom observations to collect the empirical data, to analyze and interpret the pedagogical thinking and teaching practices when they taught different kinds of classes. The results revealed that two teachers displayed similar and different pedagogical conceptions of geometry, and they had different pedagogical thinking and teaching practices in different kinds of classes. Among them, teachers’ former learning experience, grips of students learning conditions and understanding of curriculum materials were the main factors that influenced teachers’ pedagogical thinking. Although the teacher’s pedagogical thinking and classroom activities were fair coincidence, but the low efforts of students’ learning and the indigestibility of materials would make her pedagogical thinking and teaching practices slightly disagree. The main difference between two teachers’ teaching practices in geometric units was the manipulative activities. One of them considered manipulative activities and geometric concepts should be equally emphasized, therefore she used the concrete objects to help students to construct visual imagery of geometric figures. Another used the examples of live or handmade instructional aids to discourse the abstract geometric concepts to help students to construct the same visual imagery. In addition, they would also reflect their classroom activities and students’ learning conditions. They also discussed with colleagues about how to teach geometric concepts, so as to advance their teaching quality. Finally, the results of this research might help junior high school in-service teachers to understand the connotations, differences and influential factors of pedagogical thinking and teaching practices. On the basis of these results the junior high school mathematics teachers could design more proper geometric learning activities to students, and helped them to figure out their own pedagogical conceptions of geometry, furthermore to facilitate their professional development of teaching.
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