Research On High School Mathematics Problem Solving Based On RMI Principle ——Take Function As An Example

Problem solving is one of the tasks of mathematics teaching in senior high school.It has been deeply concerned by the educational circles.Problem solving is not only to solve a certain problem or a certain kind of problem,but also to infiltrate mathematical thinking and methods,use mathematical methodology to guide problem solving and improve students' mathematical literacy.As the focus of high school mathematics teaching,function covers many knowledge points,and is often combined with geometry,equations,inequalities and other knowledge for examination.The question type is more complex and difficult to solve,which has always been a difficult problem in problem-solving teaching.As an important mathematical method,RMI principle(relational mapping inversion method)can split and transform complex function problems,and make the problems become familiar and simple.Therefore,this paper studies the application of RMI principle in senior high school function problems from the perspective of mathematical thinking methods,which can not only provide a certain reference value for front-line teachers' problem-solving teaching,but also help to cultivate students' mathematical thinking ability and improve students' problem-solving ability.Firstly,the relationship between functions and knowledge of each chapter under RMI principle is analyzed.By understanding the mathematical method of RMI principle and mining function knowledge,this paper analyzes the mapping relationship between functions,between functions and geometric figures,between functions and equations,between functions and inequalities,and between function models and practical problems under RMI principle,and draws the mapping inversion block diagram between functions and various knowledge.This paper reveals five mapping ways of function problems,which helps students form a complete structure of function knowledge.Secondly,it explores the application of RMI principle in five typical examples of functions in senior high school.RMI principle is widely used in senior high school function problems,and the mapping methods of different types of questions are different.This paper studies the application of RMI principle in five typical problems: exponential function and logarithmic function,trigonometric function,function and equation,function and inequality,and function modeling,analyzes how to use RMI principle to realize the mapping and inversion of function problems,and explores the mapping method of RMI principle in each kind of problems.These highlight the guiding significance of RMI principle in function problem solving,and enable teachers to realize the value of using this ideological method to guide function problem solving.Finally,based on the research of RMI principle,this paper puts forward seven suggestions on the teaching of function problem-solving,and applies them to the teaching design of two exercise courses: zero point of function and function modeling of practical problems,which verifies the operability of the above seven suggestions in the teaching of function problem-solving in senior high school.At the same time,it provides a certain reference for teachers to use RMI principle in the teaching design of exercise class.