The Study On The Teaching And Learning Calculus In Middle Schools

Derivative and its applications is one part content of calculus, and it also is the part of content of "the Ordinary High School Mathematics Curriculum Standard (Experiment) " which has been reformed in introduction of concepts and arrangement of teaching content. I think it is necessary to explore how to design teaching, especially using what angle of view. This article studies the basic mathematic thoughts and the content structure of derivative and its applications. It also theoretically studies the aims and tasks of studying in the middle school mathematics curriculum of some developed countries and the curriculum value of studying in elementary calculus. Simultaneously, it studies the teaching and learning in derivative and its applications on the groundwork of experiments. It shows that(1) the thoughts involved in calculus are necessary for social civics in information age and provide impetus in mathematics development. Calculus has a wide range of applications in other areas. (2)Students shoud be armed with the basic theory of limits .(3)It goes through three psychological levels in the cognitive structure of comprehension of derivate for students. Fist, derivate of "specifically practical significance" . to Second ,derivate of "rate of change" .The third level is to distinguish the point derivate and the concept of derivate. Based on the above survey and analysis, some teaching advices have been made on specific content:(1)In teaching derivative and its applications, it is advised to water down the formal definition, stand out the essence of definitions.(2) avoiding degeneration which is made that let students only memorize formulas and conclusions in calculus teaching. (3) Strengthening teaching of mathematics thoughts. (4) Attending the thoughts of algorithm and integrating of information technology. (5) Enhancing infiltration of mathematics culture. (6) Dealing with the relation between calculus and elementary math. (7) Strengthening the anatomy of ordinary mistakes in elementary calculus studying, intensifying animadvert of thinking. So students can have deeply comprehension on calculus.