Based On The General High School Mathematics Curriculum Standard (2017 Edition) Calculus Content Exploration And Teaching Research

In 2013,the Ministry of Education launched the revision of the curriculum of senior high schools.This revision summarizes the valuable experience of the curriculum reform of senior high schools in China since the 21 st century,fully draws lessons from the excellent results of international curriculum reform,and constructs the curriculum system of senior high schools with Chinese characteristics.In order to better meet the requirements of the current curriculum standards and the development of educational reform,the author believes that it is necessary to make a comparative analysis between them and the 2011 edition,so as to profoundly implement the requirements.Therefore,the research direction of this paper is based on the research of calculus content and teaching under the general high school mathematics curriculum standard(2017 edition).The full text is divided into sevent parts:In the first part,the necessity and feasibility of introducing calculus into senior high school mathematics are discussed in detail under the background of general senior high school mathematics curriculum standard(2017 edition),and the significance of studying senior high school calculus teaching is given.That is,there are few achievements in this part in theory,which can provide some help for teachers in practice,and also provide experience for the next educational reform.In the second part,it summarizes the previous knowledge of calculus and the content settings of calculus in various countries.It is found that after more than 20 years of exploration,the theoretical basis of calculus teaching in senior high school has been relatively mature,but its educational value for senior high school students is still in the process of exploration.Although teachers generally approve of the introduction of calculus in senior high school,how to introduce calculus and how to teach calculus are worth discussing,and the guiding significance of existing research results has certain limitations.The third part is the theoretical analysis of calculus teaching design in Senior High School under the concept of the curriculum standard of the 2017 edition.Firstly,it expounds its new requirements for calculus teaching,that is,the local government should focus on the overall promotion of the implementation of high school mathematics programs in the region,highlighting the key points;schools should improve rules and regulations,increase investment in education,and properly develop school-based courses;teachers should constantly improve themselves and establish the concept of "lifelong learning".Then it makes a detailed comparison and analysis with the old curriculum standard,and makes clear the differences.Finally,it introduces the theoretical basis of calculus teaching design.The fourth part investigates and analyses the teaching situation of calculus in Senior High School Mathematics Textbook under the concept of curriculum standard of 2017.The main methods of investigation are questionnaire survey and interview.After careful analysis,four conclusions are drawn: the arrangement of teaching materials is irrational;teachers and students have some deviations in grasping the key and difficult points;teachers should pay attention to infiltrating knowledge of mathematical history,mathematical culture and other disciplines in the process of teaching;pay attention to the use of modern educational technology;evaluation should also be diversified.The fifth part,combined with the relevant theoretical knowledge,puts forward the corresponding strategies for the problems in the questionnaire.That is,the rational use of textbooks;careful study of curriculum standards,grasp the key and difficult points;clarify the relationship between elementary mathematics and calculus;infiltrate knowledge of other disciplines,pay attention to the use of modern educational technology.In the sixth part,two teaching cases are listed.The geometric meaning of derivative is selected from the 2-2 Mathematics Elective Course of Senior High School of People's Education Press.The line whose secant tends to be positioned at a certain point is defined as the tangent of the curve by approximation method,which reflects the essence of the tangent.Teachers can use mathematical software such as Geometric Sketchpad to make dynamic maps to enrich the classroom.The average rate of change of functions is selected from the content of the first lesson of the first section of Chapter 1 of General Senior Mathematics Experimental Textbook 2-2(B Edition),published by People's Education Publishing House.The concept of derivative is one of the core concepts of calculus,and the average rate of change is the basis of derivative.The main teaching purpose of this lesson is to construct the concept of average change rate spontaneously under the guidance of teachers from the specific situation of life,so as to further understand the mathematical thinking methods such as "direct substitution" and "approximation".The seventh part,on the basis of the whole paper,summarizes the main achievements of the research in this paper,points out the shortcomings,and puts forward the plan and hope for the future to become a teacher.