Research On Constructive Thinking In Middle School Mathematics Competition

The International Mathematical Olympiad is the international league contest,so there are many educators and researchers who have conducted a systematic discussion on the methods of thinking in it.The method of constructive mathematics as one of the most important methods,has been widely used in the proposition and the solving processes.The existing researches about the "constructive thinking" are just methods for some specific topics,the lack of systematic researches on constructive thinking of problem solving is quite sharp.Construction method of exercises through the middle school mathematics contest in recent years are involved in the case analyses.The research involves the constructive thinking in the middle school mathematics competition,and explain how to classify the construction method in different mathematical disciplines.This paper is divided into six parts,and the fourth and the fifth chapter is the focus of this paper.Firstly,the dissertation outlines the background,history and current situation of the constructive thinking and the theoretical basis of constructive thinking.Secondly,this dissertation discusses the construction principle and strategy of problem solving combining with previous math competition subject.Then we puts forward the different construction method through the analysis of the literature and the title,including the conclusion construction of the life problem?negative-case constructs of negative propositions and the constructive construction of the transformation problem form.Finally we puts forward the method of construction in elementary number theory,Algebra,Geometric mathematical and Combinatorial mathematics through different instances of math competition.Discussed how to choose appropriate construction method according to the specific subject.The artical finally discusses the teaching and training advice of constructive thinking,including how to solve problem by the method of construction,the problem solving error of the construction method and cultivate suggestions of constructive thinking.It is hoped that the teaching ofcompetition mathematics and the cultivation of constructive thinking can be provided valuable reference.