Present Situation And Improvement Ways Of The Teaching Of Proof By Contradiction In Junior Middle School Mathematics

The proof by contradiction is an important proof method in mathematics,which has certain application in junior middle school mathematics teaching.The application process of reduction to absurdity can be divided into three parts.The first is to take the conclusion of the negative problem as the starting point.The second is to explore the contradictions through strict logical reasoning.The third is to start from the conditions to get the correct conclusion from the conclusion.The reduction to absurdity plays an important role in junior high school mathematics teaching.In the process of reasoning,it can not only cultivate students’ logical thinking ability,but also improve the rigor of students’ thinking,and effectively improve students’ reasoning ability and problem-solving ability.If we can link the teaching of reduction to absurdity with the reality of life,let students from life problems to mathematical problems,and then from mathematical problems to life problems,cultivate students’ awareness of looking at life problems with mathematical theoretical knowledge,so as to promote better learning and life.Using reduction to absurdity to prove mathematical problems is a difficult point in students’ learning.Teachers need to strengthen the analysis of reduction to absurdity in teaching,and infiltrate the idea of reduction to absurdity into students as early as possible and repeatedly,so as to improve students’ problem-solving efficiency and logical thinking ability.This paper adopts the methods of literature research,questionnaire survey and interview to study the current situation of reduction to absurdity in junior middle school mathematics teaching.Firstly,it studies by collecting and sorting out relevant literature.Secondly,it understands junior middle school students’ mastery of reduction to absurdity through questionnaire survey and test questions.Thirdly,it understands the current situation of junior middle school mathematics teachers’ teaching of reduction to absurdity through questionnaire survey and interview,and combines teachers’ “teaching”and students’ “learning”to study the related problems of reduction to absurdity.The study found that students’ mastery of reduction to absurdity is low,mainly from two reasons : First,teachers do not pay enough attention to the teaching of reduction to absurdity;second,students’ logical thinking ability is weak,and it is not easy to understand the related concepts and theoretical basis of reduction to absurdity.In order to improve teachers’ attention to the teaching of reduction to absurdity,improve students’ ability to use reduction to absurdity to solve problems,and cultivate students’ reverse logical thinking,this paper comprehensively analyzes the important role of reduction to absurdity in junior high school mathematics teaching.In view of the current situation of reduction to absurdity in junior middle school mathematics teaching,this paper points out the problems that should be paid attention to in the application of reduction to absurdity,and gives the relevant improvement ways.Based on this,this paper studies the teaching status and improvement methods of reduction to absurdity in junior high school mathematics,mainly in the following aspects :(1)Explain the Related Theory of the proof by contradiction;(2)Comprehensive analysis of the significance of reduction to absurdity in junior middle school mathematics teaching;(3)By means of questionnaire survey and interview,this paper analyzes and studies the junior high school students’ mastery of the counter-evidence method and the current situation of teachers’ counter-evidence teaching;(4)Analyze the problems existing in the teaching of reduction to absurdity in junior middle school mathematics,and point out the problems that need attention in the application of reduction to absurdity;(5)Based on the above research,the case analysis and improvement methods of reduction to absurdity teaching in junior high school mathematics are given.