反证法在中学数学中的运用

The application of proofs by contradiction in middle school mathematicsAbstract As a common proof method in mathematics,proofs by contradiction has been widelyapplied in dealing with practical matters,not least in middle school mathematics.Mostly,studentsare baffled in search of direct answers to questions,but if they think the way round,that is,useproofs by contradiction,which appears frequently in middle school courses,more often than not,answers manifests themselves quite easily.However,for one thing,teachers can only partiallyintroduce the method with certain key points due to variety and complexity of such questions;foranother thing,despite similar questions having been researched at home and abroad,studentsfind it difficult to master the method systematically because little has been done to study theapplication of proofs by contradiction in middle school mathematics.This thesis,consideringmiddle school students'thinking pattems and teaching materials,systematically summarizes theapplication of proofs by contradiction in middle school mathematics through some specificquestions.The thesis is divided into three parts.The first part turns on the definition of proofs bycontradiction,its theoretical basis and steps of working out questions.The second part exemplifiesthe various types of questions proofs of contradiction have addressed through specific questionsand then classifies the questions accordingly.The last part,on the basis of what have beendiscussed above,summarizes the matters needing attention while applying it into teaching,so thatthe expertise in proofs of contradiction becomes more systematic.This will contribute to bothteaching and learning.Key words:Proofs by Contradiction Middle school mathematics Application