Mathematical Communication In Middle School Mathematics Teaching

This thesis is mainly about some problems concerning the mathematical communication during the classroom teaching. It studies the meaning and mechanism of mathematical communication theoretically by way of sorting out the documents, then by adopting the way of doing a survey, gets a general idea about the actual practice of mathematical communication activity during the classroom teaching in Middle School, draws some valuable conclusions, and gives some reasonable suggestion on how to develop mathematical communication activities effectively.Firstly, the thesis fixes a position for mathematical communication after arranging the origin and development of the concept of mathematical communication, that is, it is a kind of activity, and then gives us the definition of mathematical communication: mathematical communication is a kind of activity in which the agent, during the course of mathematical teaching and learning, receives and expresses the cognition, feel, and experience about the mathematical knowledge (containing concept, relation, regulation, and application, etc) with mathematical language and method of thinking, by way of listening, speaking, reading and writing. Next, it indicates that mathematical language is an important instrument for developing the mathematical communication activity, and based on the predecessors' achievements, reclassifies the mathematical language: character language, symbol language, figure language, chart language and logic language. It analyses the general course of mathematical communication, and explains the process of mathematical communication, which consists of outward communication and inward communication. The former is the information transmission between the subject and the object. Its form of reflection contains listening, speaking, reading, and writing, etc. The latter, on one side, decomposes and encodes (classification) the outside input of information, and at the same time, draws (activate, search) themode of the inside cognition structure, then identifies the mode in order to decide in which way to solve the outside input, by answering or making a new mode. The whole process is stored as a new mode for further use. The thesis constructs the theory about the development of mathematical communication in the following six theoretical bases: information processing, social constructionalism, teaching and students, learning transference, meaningful study and the metacognition. Then it classifies the mathematical communication in the following five points of view: the content of mathematical communication, the level of communication, the environment of communication, the passage of communication, and the form of communication. By way of doing a survey, it analyses the mainly existed teaching links in the classroom teaching in Middle school, and gets the percentage of the components of mathematical communication in different teaching links. According to the order from the high percentage to the low percentage, the components are: the teaching of the new knowledge, the discussion between teacher and students, the classroom questioning, the guidance after class, the correcting of students' papers, the brief summary after class, and the mathematical reading. It also does a preliminary research on significance of mathematical communication, that is, it helps the students to develop the self-study ability, to improve their mathematical quality, and it also helps the teacher to adopt the criticism-and-reflection teaching. The data of the survey indicates that teachers think highly of the mathematical communication activities during the classroom teaching; in present mathematical communication acting is not satisfying. The suggestion is that the teachers should continue to further develop the teaching method of using mathematical language.Secondly, this thesis mainly tacks about three kinds of mathematical communication activity in three different aspects: the questioning in mathematical reading, and the mathematical diary. The classroomquestioning is a commo...