Research On The Teaching Design Of High School Derivative Based On The History Of Mathematics

The birth of calculus is regarded as a mathematical achievements which is an epoch-making product.Calculus provides an important method and means for functions and variables. Since the21 st century,calculus teaching has entered a new time,and the calculus is introduced into the high school mathematics course in the nations of the world.In China,the ministry of education promulgated "the ordinary high school mathematics curriculum standard(experiment)" in2003.The calculus is included in the curriculum standard as one of the elective course.However,the high school mathematics curriculum standard in the course design in our country did not follow the content of limit,derivative, integral calculus traditional scheduling order, but rather when there is no limit on the basis of learning in general, the derivative as a special limit(increment ratio limit) to deal with, reflect directly through the derivative thought and the nature of the concrete examples(such as instantaneous speed) to guide students to recognize and understand the concepts of derivative.HPM mainly studies how to promote education of mathematics in the mathematical history,which is the main component of mathematics education research.The current mathematics education researchers are aware of the importance of history of mathematics in mathematics education.Not only it can promote students' classroom learning efficiency, but also can increase the students' mathematics history and mathematics cultural knowledge, which is the effective practice of the new curriculum standard.In this paper, based on the theory of HPM, I will probe into the history of mathematics teaching design of the derivative in the high school. Derivative is an important part of the calculus.First of all,I analyzes the historical development of calculus, the brewing period of nearly half a century that from Newton, Leibniz created calculus to 18 th century mathematicians until Cauchy and others who committed to the development of process that calculus to strict.Secondly,I investigated two groups students,who are the grade three students in high school and science freshman in the university.Through this investigation,I study that whether the design of the course under the new curriculum standard is good for the students to understand the idea of calculus deeply.To understand the problem of teachers in the teaching of calculus content and how to design reasonable teaching cases,I also interviewed the teachers who come from the high school and university.Last but not least,according to the investigation and study,I design two teaching cases for the concept of derivative and implement in the classroom.Then I analysis the result of the implementation.The two teaching designs which integrated into the history of mathematics can be as references for the middle school teachers.