Derivative Problem Solving And Teaching Research In Senior High School From High Viewpoints

With the advancement of Mathematics Curriculum Reform in General High School,the Mathematics Curriculum Standards for General High School(2017 Edition,Revised in 2020)suggested that the math teachers should understand the mathematics content of Higher Mathematics that is closely relevant to the high school curriculum.It also set higher requirements for the math teachers' understanding of the mathematics knowledge.Derivative,regarded as a vital bridge connecting Higher Mathematics and Elementary Mathematics,shared certain similarities in the parts of the derivative test design.For this reason,this study took the derivatives content in high school as its research topic and achieved following three aims from point of view of Higher Mathematics:(1)to reveal the higher mathematics background of some derivative tests in the college entrance examinations;(2)to explore the possible path to integrate the viewpoints and methods of higher mathematics into middle school mathematics;(3)to probe into the high school derivative teaching by investigating serval certain cases with the perspective of the Higher Mathematics.With the help of two questionnaire for high school teachers and students,this study investigates the problem solving and teaching of derivative content in high school from the point of view of Higher Mathematics,and drew the conclusions as follow:Through the review of the College Entrance Examination of different areas in the recent decades,four similarities of derivative test were found,namely,the proposition background based on the basic definitions and properties for Higher Mathematics proposition background,with the important theorem of Higher Mathematics and the formula for the proposition background,famous inequalities proposition for background,based on the important thought method for higher mathematics proposition background.Similarly,this study also concluded four kinds of mistakes in solving the derivative questions of college entrance examination from the point of Higher Mathematics: knowledge error,logic error,strategic error and psychological error.Five test-taking technique are then put forward: create lemma,L'H?pital rule,derivative definition,constructed function,and multivariate partial derivative.Concerning the teachers' teaching,through the analysis of the quantitative data collected from the questionnaires from the students and the teachers and the comparison with the previous studies,this study proposed three characteristics of high school derivative teaching from the point of Higher Mathematics: cohesion,selectivity and guidance.It was implied that the derivative teaching of the high school should follow four basic teaching principles: the principle of rigor,the principle of intuition,the principle of teaching students in accordance with their aptitude,and the principle of measuring their abilities.Then,five corresponding teaching strategies were put forward: developing sample exercises,expanding sublimation strategy,introducing four rules,diversifying knowledge presentation strategy,first practicing operation,then reasoning strategy,integrating information technology,intuitive explanation strategy,guiding direction,and autonomous learning strategy.