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1、数学专业英语论文翻译班级：信计C123姓名：卜宏宇学号:126533NotsuccessfulbreakthroughFrankly,inmypersonalproblem-solvingexperience,"notsuccessfill11andevenfailures,theyaremuchmorethansuccessofexciting.However,MnotsuccessfulHisnotonlytotheauthorleftanegativeresult,thesmoothfaceoccasionallyIalwayslookforthem
2、tocontinuetothe"problemsolvingstupid'1，Idonotknowthepersonalexperiencetosaywhetherthelaughingstockofthereadersalittlehelp,butIcanconfirmthatthisismyalreadymeagerwealthofthemainassetsofproblemsolving,andmyviews(includingArticles1998problemsolvinganalysisofserialandMIntroductiontoma
3、thematicalproblemsolvinglearning11book)hascausedsomeconcernandsympathycounterparts,needtoapologizeforthat,sometimes,ontheproblemsolvingandproblem-solvinganalysisofalargenumberofreadershavewrittenIcannotreplytoeveryone,today'stopicislargelyadeliberatecover.Next,Iwanttobethreecaseso
4、fproblemsolvingtodemonstratehowthefailuretosuccess,howtocontroltheshallowsuccess・1.Case1-toobtainusefulinformationfromthefailureExample1Ifa,b,carerealandunequal,andx/(a-b)=y/(b・c)=z/(c-a),seekingx+y+z・Solution:getthegeometrictheoremsx/(a-b)=y/(b-c)=z/(c-a)①=(X+y+z)/[(a-b)+(b-c)+(c
5、-a)].②However,②thedenominatoriszero-based(a-b)+(b-c)+(c-a)=0,③Ourproblem-solvingeffortsfailed.Comment:Thisisacaseoffailedproblemsolving,[3]referredtointhesolutionafterthedirectionofsomedeal,actuallyused③style.Therefore,thefailureoftheprocesswasexactlythesubjectofanimpliedcondition
6、,whichisapositivegain,asweremovetheunsuccessfill②style,tolookatthe(3)typeand①styleatthesametime,①stylemakeusseethecoincidenceoftwolines:xX+yY+z=0,④(A-b)X+(b-c)Y+(c-a)=0.⑤And③stylehasenabledustoseethroughthepoint⑤linex=l,Y=1.forfurtherinference,linear®alsothroughpoint(1.1),thenx+y+
7、z=0.Comparedwith[3],itisaninnovativesolution,itsbirthdependsontwothings:1,toobtainausefulproblem-solvinginformationfromfailurethatis③style.2,typeon①，③styleisto"fbcusshift”fromtheperspectiveofanalyticgeometrytoseethem.Withthisstep,theremainingworkatbestcanbecompletedwithin30seconds
8、・2.Case2-tohavenotyetsucceededdoe
