Based On The Similarity Principle Of Middle School History Teaching Design Research Of The Concept Of Derivative

Influenced by the new curriculum reform, the content of the text book for mathematics inhigh school has gone through a series of changes. Besides knowledge and skills, more emphasishas been laid on students’ experience of the generation of knowledge and students’ attitudinaldevelopment during the process of learning. New disciplinary standards consider derivativeimportant because of its relevance with life actualities. Meanwhile, more emphasis is paid on theunderstanding of the concepet of derivative.As a means to know the process of the accumulationof the knowledge of mathematics, a modal dealing with mathematics history is introduced into thehigh school selective text book. Therefore, teachers and researchers should pay more attention topassing over the concept of derivative to students through a study of the history of the conceptitself. Guided by the principles of historical similarities, the thesis deals with the followingresearch agendas:(1) Giving an outline of the development of the conception of derivative in relation with theproblems of an infinitesimal, tangent line and velocity. Based on the three problems, the writeragain organize the development progress, and give some of my own ideas.(2) Generalizing the characteristics in the mathematicians’ understanding of the problems ofchange rate, tangent line and instantaneous velocity, as well as their mathematic thinking andmethods.(3) Designing a triple of questionnaires to survey students’ understanding of concept ofderivative, while predictions of students’ obstacles in cognition is put in consideration.An analysis of the questionnaires shows that the principles of historical similarities do atwork, thus a further prediction is made that it would be more effective if teachers carry out theteaching following the thinking pattern of mathematicians. Based on the survey results, theresearcher designs the teaching plan which includes a history of the development of the concept ofderivative, a combination of real life problems and mathematic questions. The thesis hopes torender some help to high school mathematics teachers for reference.