Students' Understanging Of Dihedral Angle And Dihedral Angle Plane Angle Concept

It is a micro study of the learning and teaching of mathematical concepts. The learning of mathematical concepts is such an activity to generalize the essential attribute of a certain kind of mathematical objects abstractly and is an activity progress to apperceive experience continuously. It is also a construction process attained though revising and processing objects by learners. In this process, the author studies the students' presentation of their activity to generalize the essential attribute of the concept of dihedral angle and dihedral angle's plane angle abstractly and the concept image.Students have different characteristics in presentation of the two concepts image and there is significant difference between the female and male. However, there is no significant difference between the first-year and the second-year students of senior high school. In the process of cognition of the two concepts, this study reveals the students' feasibility of the two concepts cognition and measuring the angle of line and line , line and plane and the dihedral angle at different learning stages; meanwhile, this study reveals the abstract generalization of essential attribution of dihedral angle and measurement of dihedral angle of students. Furthermore, according to the Modern Cognition Development, the author also studies the learning of the two concepts from the aspects as the concept image and concept definitions, the connections and network of concepts, the use and system of concepts and so on. The interviewees who have experienced the concept formation have richer concept image and more systematic and complicated concept network while the interviewees who haven't experienced the formation of concepts is lack of concept image, and their concept network is simple and out of order. The concept network structures between teachers and students are very different. The teachers' concept network structure of the two concepts and their teaching strategies have influence on the forming of students' concept network. The concept image of students affect the use of concepts. The students' understanding of the concepts reaches a certain stage and then their using of the concepts will reach the corresponding level,The major factors affecting the learning of the two concepts are past experience, visual backgrounds, the prototype and variation of concepts, examples and counterexample, related and unrelated characteristics of the prototypes. In the study, the two main errors appeared in the two concept learning are "procedure error" and "reasonable error". Under the guidance of modern cognition perspective and with the precondition of predicting students' "the nearest development zone" and cognitive errors, the study designs the corresponding teaching strategies in the terms of...