Thinking on the Practical Plan of "the Monotonicity of Function"

This study emphasized on practice of “the monotony of function”. The author had made a practical plan and comment on seven phases of conceptual understanding of “the monotony of function”. Through the process of teaching model, the student had better understanding of dynamic mathematics in symbolic mathematical format and representation. Results showed there was an urgent need to blend educational principle into practice. Key words: the monotony of; function; teaching situation; conceptual formation; action research Background ―The Monotonicity of Function ‖ is not only an important mathematical concept in senior high school, but also an important character of function in mathematics. It plays an essential role in the middle school mathematics. At present, when teaching ―the monotony of function‖, the teacher usually explains the definition verbally in middle school. Although the teacher may enlighten the students, there is a lack of active management of the students. There is especially a lack of constructive thinking of them. Essentially, the students lack ―the constructive process ‖ in their minds. By using this teaching method, some students may carry out meaningful learning; however, most students can only achieve to the mechanical learning level such as memorizing meaning and imitating exercise. In fact, many teachers desire to know how to apply the exploration method to the learning process of ―the Monotone of Function ‖ because this method can make students experience the process of constructive thinking. Teachers tried to solve this problem and some of them did carry out experiments, but the result is not satisfactory. Teachers feel it is difficult to cope with the exploration method. The Basic Understandings of Teaching “the Monotony of Function” Before learning this function content knowledge, the students have already learned many simple functions, such as linear function, quadratic function, inverse proportion function and so force. The students have known the variable definition