Permutation,Combination And Binomial Theorem From The Perspective Of HPM In Lesson Study

Permutation,Combination and Binomial theorem is an independent branch of high school mathematics.It is widely used in daily life and production.The content is unique and abstract.The method of problem solving is flexible.It‘s one of the important basic knowledge of high school mathematics.Permutation and combination is helpful to train students in the list,guess,inductive and systematic thinking ability.Binomial theorem is an important tool of learning calculus,probability theory and other courses.However,students tend to despise this chapter.First,there is little connection between this part and other content.Secondly,the score of the college entrance examination isn‘t much.So,students maybe think that permutation,combination and binomial theorem are a series of formulas.As a result,students may be tired with mathematics learning.The instructional design from the perspective of HPM shows the necessity of learning mathematics formula,experiencing the proof of formula,feeling the charm of mathematical culture.The article developes three HPM design: 16.2 Permutation,16.4 Combination,16.5 Binomial Theorem.Teaching design is from the perspective of HPM.Questionnaire and interviewing is adopted in this survey.First,I refer to the textbooks for Algebra in the west,in order to classify the definition and proof of relevant content.With the historical materials,I select the appropriate materials,and discuss with my tutor.Then,I have a class.According to the actual record of the class,the students’ interviews and questionnaires,finally I will improve my teaching design and reflect.The article is aimed at solving the following two questions: 1)What‘s the view of students on HPM? 2)Can HPM help students to overcome the obstacles that may occur in the traditional class?Through sorting and analyzing the data,we get the following conclusions:(1)Students are accepted and like class with HPM.The history of mathematics enables the students to understand the practical significance behind the mathematical formula,to experience the development of mathematics knowledge,to understand the human side of mathematics,and to experience the pluralism of mathematical culture.(2)The history of mathematics,in some extent,helps students solve the cognitive obstacles.The effect is related to the theme of class and not all of mathematic subject fit for integrating the history of mathematics.To sum up,teaching Permutation,Combination and Binomial Theorem from the perspective of mathematics is meaningful.It can promote the students’ mathematics attainment and the professional growth of teachers.