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1、中北大学理学院英语论文专业:信息与计算科学班级:07070242学号:0707024231姓名:朱胜明2010年5月13日NotsuccessfulbreakthroughFrankly,inmypersonalproblem-solvingexperience,"notsuccessful"andevenfailures,theyaremuchmorethansuccessofexciting.However,"notsuccessful"isnotonlytotheauthorleftanegativeresult,thesmoothfaceoccasionallyIalways
2、lookforthemtocontinuetothe"problemsolvingstupid",Idonotknowthepersonalexperiencetosaywhetherthelaughingstockofthereadersalittlehelp,butIcanconfirmthatthisismyalreadymeagerwealthofthemainassetsofproblemsolving,andmyviews(includingArticles1998problemsolvinganalysisofserialand"Introductiontomathem
3、aticalproblemsolvinglearning"book)hascausedsomeconcernandsympathycounterparts,needtoapologizeforthat,sometimes,ontheproblemsolvingandproblem-solvinganalysisofalargenumberofreadershavewrittenIcannotreplytoeveryone,today'stopicislargelyadeliberatecover.Next,Iwanttobethreecasesofproblemsolvingtode
4、monstratehowthefailuretosuccess,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-a)].②However,②thedenominatorisze
5、ro-based(a-b)+(b-c)+(c-a)=0,③Ourproblem-solvingeffortsfailed.Comment:Thisisacaseoffailedproblemsolving,[3]referredtointhesolutionafterthedirectionofsomedeal,actuallyused③style.Therefore,thefailureoftheprocesswasexactlythesubjectofanimpliedcondition,whichisapositivegain,asweremovetheunsuccessful
6、②style,tolookatthe③typeand①styleatthesametime,①stylemakeusseethecoincidenceoftwolines:xX+yY+z=0,④(A-b)X+(b-c)Y+(c-a)=0.⑤And③stylehasenabledustoseethroughthepoint⑤lineX=1,Y=1.forfurtherinference,linear④alsothroughpoint(1.1),thenx+y+z=0.Comparedwith[3],itisaninnovativesolution,itsbirthdependsont
7、wothings:1,toobtainausefulproblem-solvinginformationfromfailurethatis③style.2,typeon①,③styleisto"focusshift"fromtheperspectiveofanalyticgeometrytoseethem.Withthisstep,theremainingworkatbestcanbecompletedwithin30seconds.2.Case2-toh