Teaching Strategies To Promote Students' Understanding Of Geometric Proof

Chinese mathematics education has attracted a lot of international attention due to its unique characteristics. Therefore, we should not only make great efforts to study concepts of mathematics education from the western countries, but also review our experience on mathematics teaching and build up theories of mathematical education in our own educational context.Plane geometry is the main content in secondary mathematics teaching, and is also the key to foster students’ logical thinking. However, in view of strong logic in geometry proof, many students are afraid to learn geometry, and often disarray the internal logic. Most previous researches on geometry have focused on the cognition of geometric figures, understanding of geometric poof ways, the comparison between geometric cognitive differences of different students, reasons of difficulties of learning geometry and strategies etc.. Also there are some researches studied the geometry classroom teaching from the perspective of video cases. The main purpose is to package the video case study for front-line teachers’ learning. However, there are few researches which are to study teachers how to promote students’ understanding of geometry proof from the perspective of the day-to-day classroom teaching.According to the above situation, this study focused on three geometry lessons of a master mathematics teacher in one junior high school from the perspective of classroom observation. In our study, we carefully analyzed the case teacher’s strategies of promoting students’understanding of geometry proof.We analyzed the three lessons from the following four dimensions:the nature of classroom tasks; teacher’ roles; the social culture of the classroom; mathematical tools as a learning support. Then the research developed four coding systems under these dimensions:the coding of the cognitive level of the mathematical tasks; the coding of discourse analysis between the teacher and the students; the coding of the types of problems; the coding of classroom teacher-student interaction types to capture a variety of classroom teaching strategies of promoting students’ understanding of geometric proof. Based on the four coding systems, the author encoded the text and the video of classroom teaching, and analyzed teaching strategies through quantitative and qualitative analysis.The results showed that the case teacher used different strategies in the following four aspects to promote students’ understanding of geometric proof.(1) From the perspective of the nature of the classroom tasks, the teacher always used a procedural variation to arrange the high level of classroom learning tasks. More importantly, all the high level classroom tasks had maintained the high-level cognitive demand in the implementation process.(2) From the perspective of the teacher’ roles, the case teacher carefully arranged the dialogue with her students. The teacher-students dialogue contained mathematical thinking, and there was much more deductive reasoning. The teacher mainly raised reasoning problems and interpretative problems. The former problems were able to foster students’ logical reasoning ability, the latter could stimulate students to reflect and make the students’ logical thinking more closely. Dialogue and problems facilitated students’ understanding of geometry proof from different ways.(3) From the perspective of the social culture of the classroom, the teacher used teacher-class interaction as the main classroom activities. Meanwhile, the case teacher paid close attention to the teacher-student individual interaction as much as she can. Teacher-class interaction could create a good learning atmosphere for the classroom of geometric proof. Teacher-student individual interaction could encourage introverted students to think positively. Cross-interaction combining teacher-class interaction and teacher-student individual interaction together could inspire the individuals and all to be able to promote each other.(4) From the perspective of the mathematical tools to support learning, the applications of the teaching tools such as the small blackboard, colored chalk, ruler and compasses not only could save teaching time, but also highlighted the key points and demonstrated the way of drawing figures. Therefore, the application of these tools was conducive to students’ understanding of the methods and knowledge and contributing to students’ understanding of geometry proof.This study also proved Chinese mathematics teaching had its own characteristics from the perspective of the classroom observation. Moreover, it was able to produce meaningful learning and provided an example for the formation of China’s localization theory of mathematical education.