Research On Instructional Design Of Derivative Concept From The Perspective Of HPM

In recent years,with the continuous advancement of the new curriculum reform,the derivative concept has become increasingly important in the college entrance examination.The concept of derivative is not only one of the core concepts of calculus,but also a bridge connecting high school and college knowledge.The concept of derivative is very abstract,which is one of the difficult concepts for students to understand.Therefore,how to let the students understand the concept of derivative and how to let the students know the essence of derivative has become one of the difficult problems perplexing teachers.HPM is the study of the history and culture of mathematics,and its educational value is widely recognized in China.HPM concept provides a new direction for derivative concept teaching.There are many researches on the derivative concept under the HPM concept,but few teachers do classroom practice research.In terms of the teaching practice of derivative concept under the concept of HPM,teachers' difficulties are mainly reflected in the following aspects:1.HPM cannot help improve scores;2.Some teachers agree with the concept of HPM and are interested in the practice of derivative concept,but have no materials at hand,so they have to give up;3.Derivative concept course content is tight,there is no time to use the history of mathematics;4.The understanding of the history of mathematics is not enough,mistakenly think that the use of mathematics history in teaching is simply to tell the story of Newton and Leibniz.This study is to solve the above problems to provide methods and reference cases.The research contents of this study include four aspects:1.Collecting historical data of derivative concepts,selecting appropriate historical data and appropriate application methods of mathematical history according to the teaching objectives of derivative concepts;2.Combing teacher feedback,curriculum standard requirements and textbook content to create an operable teaching design case of derivative concept based on the history of mathematics and adapted to the HPM perspective of students in the school;3.A comparative study of two liberal arts classes in Yunnan A senior high school was conducted according to the new teaching design cases;4.Questionnaire survey and interview are conducted to understand the achievement of teaching objectives and students' views on HPM teaching and teachers' views on HPM teaching are also understood through interviews.The research results include three aspects:1.HPM lesson examples can improve students' understanding of the concept of derivatives and achieve teaching goals.In terms of the rate of change,students understand that the instantaneous rate of change is the essence of the derivative;in terms of the geometric meaning of the derivative,students understand that the tangent is the limit position of the secant,and that the derivative at a point of the function is the slope of the tangent of the curve at that point.2.The implementation of HPM lesson examples can stimulate students' learning motivation and increase students' interest in the history of mathematics.The practice of the HPM case really allows students to understand Pascal's method of seeking the limit,the history of the derivative concept,Newton and Leibniz's contributions to the derivative,and their interest in the concept of derivative has increased.3.Participate in the HPM lesson.The design can enrich the mathematics knowledge of teachers.Practice has proved that HPM can enrich the mathematics knowledge needed by teachers to complete the teaching of the concept of derivatives and the geometric meaning of derivatives,and promote the professional development of teachers to a certain extent.