A Study Of "Open-Approach" Method In Class Mathematics Teaching

Abstract: Open-aducation is to return to the nature of study, which emphasizes the procedure of study, unties students'thinking, and regards students'value. Nowadays, the focuses of mathematics aducation in china are how to combine the pupils'creativity with their "two basics", and how to promote pupils'all-sided development. "Open-ended"problem solving is a way to meet to the goal. But the kind of problem is one of the factors, in fact, the whole mathematics aducation should be to expand the space of study and develop pupils'thinking. So, the study of "open-approach"method is coming into being. This paper includes two main parts: the study of theory and the study of pratice. The two aspects stimulate each other, on one hand, the theory is the base of pratice, and on the other hand, pratice explains the theory better. After comparing and analyzing the related literatures on the metacognition from home and abroad, and basing on the theory of situated cognition, the paper suggests the frame of the study of "open-approach"method, discusses it's learning environments, microcosmic mechanism, teaching designs and procedure, offer strategy to teachers. The specimen include 16 teachers and 245 students of 5 classes in foreign language school attached to Guangxi Normal University.In ten months, from the seedtime to the end, we use many survey means such as questionnaire, inteview, observation and examination paper. All the datas are analysed by SPSS11.0. According to the junior mathematics teaching, we provide the designs about "open-approach"method and the means of investigation of teaching procedure in 3 different classes. It is most important of such a study to promote the devolpment of both teachers and students. By designing open humanize enviroment and open problem enviroment , the "open-approach"method help students to delve into learning and cooperate with others. During the course of proplem solving, students with different ability gain corresponding development and defferent experience of study and feeling. The "open-approach"method is not only one teaching pattern, but also a kind of teaching idea and concept. It's connotation includes open goal, open context, open procedure, open teaching method, open relationship between teacher and students, open teaching eviroment and open evaluation. Its intrinsicme enviroment chanism includes situation, variety, diversity, difference and selection. In such a class, the students'psychological chanism includes interest, self-determination, curiosity, competitive sensation, winning feeling and responsibility. Its extrinsic chanism includes communication, interaction and participation. The paper also offers 11 points to design open-approach method and some macroscopic and microcosmic strategy about it. Accoding to the defferent open-degree of students'activity, the method is divided into two layers: open-conduced type and open-independent type. The results of the study suggest that the study of practise suits the study of theory well, and the strategys are effective. It's a challenge for teachers to carry out open-approach method. If only teachers convert the close teaching concept into the open one, attach importance to students'selt-determination, master teaching strategy,and advance their innovative consciousness, then all of them can practise open-approch method step by step. So, it's feasible to carry out open-approch method in routine mathematics lessons. Furthermore, the convertion of teachers'concepts and activities can strengthen students'conscious initiative of learning. The teachers will make progress by cooperating and communicating with each other and by acquiring guide from professor. Especially, the teaching cases with theory instrution will lead the way to get it best. The favorable cognition situation and intrinsicme enviroment chanism of open-approach method motivate students'psychological chanism; stuents break through their drawback and generate strong desire of self-represence, arouse their passion of study. Especially, the open problem enviroment supply more space for student to study, find and solve problem by self-determination. Students with different ability can take part in the lesson and gain corresponding development. It also improves their interest, deepens their comprehension, enhances their innovative consciousness. Furthermore, high quality of ideology of students is coming into being during the course of "diversifying and converging". They have learned how to think and summarize what they had used, which include various and precise mathematics method. In such a class, study is more effective by cooperation than by individual. Students cooperate within group or in class. They hope to communicate their ideas with their companion. They approve that it's more efficient by teamwork, competition and communication. They can comprehen knowledge well by debating different ideas. Pay more attention please, it's most necessary to set apart enough individual time to students to think.Those students with more knowledge and stronger ability are more adaptive in the open class. They feel more satisfied. Those with less knowledge and shorter abiblty feel more difficult and depressive, but they also culture their desire to study in the challenging enviroment. Teachers should try to promote different students to cooperate and communicate. This paper predicts students'development in the future by short-term practice. It is not the end but the begin. Coming along the development of such a study, the "open-approach"method will attain better vitality by absorbing more essence.