A Study On Elementary Number Theory In The Mathematical Olympiad Of Middle School

Elementary number theory has simple and easy-to-understand concept propositions and flexible and clever problem-solving methods,which can cultivate students' logical reasoning and mathematical computing ability.Some of its simple knowledge points are interspersed in the mathematics curriculum at the compulsory education stage,and the elementary number theory is explicitly mentioned in the high school mathematics curriculum standards.This shows that the elementary number theory is recognized for the cultivation of human beings and is worthy of research.How to solve the problems of elementary number theory,and how to teach it so that students can understand it well and achieve the goal of cultivating students' mathematical thinking ability ?These are the problems this paper wants to study.Since elementary number theory appears more frequently in the Mathematical Olympiad,this paper starts with the elementary number theory problem in the middle school Mathematical Olympiad in various countries,analyzes and studies it from three aspects of problem solving,compiling and teaching,aiming to study how to solve and compile elementary number theory,and how it should be taught.This paper firstly analyzes the problem solving of elementary number theory with the combination of mathematical methodology.Through the real problems inmiddle school Mathematical Olympiad in various countries in recent years,specific ideas are given for the use of general mathematical methods to analyze the problem of elementary number theory,and use special mathematical methods to solve it.Secondly,it provides some methods for teachers to compile elementary number theory problems,supplies some self-compiled problems,which give some help for the teaching of middle school mathematics teachers in elementary number theory.Finally,combining with personal practice experience,this paper puts forward the teaching experience of elementary number theory from the three aspects of definition,proposition and problem solving.It gives a teaching design for first two parts by referring to mathematics education psychology.Beside,it also carries out teaching practice for problem solving,and analyzes the effect of practice by combining with students' homework situation.The innovation of this paper is to put forward some self-made elementary number theory problems referring to domestic and foreign competition questions,and to focus on the teaching of elementary number theory based on personal practical experience.This paper uses literature analysis,case analysis and practice summary to reach the following conclusions: mathematical methodology can be used to solve the problem of elementary number theory;the compilation of elementary number theory should pay attention to innovation;the teaching of elementarynumber theory should take notice of guiding students to explore independently,pay attention to impart mathematical thoughts and methods.