Flexibleuse
Theabilitytothinklogicallydoesnotmeanthatyoucansolvedifficultproblems.Onlyintermsoflogic,thereareproblemswithusingskills.Wheredoesitcomefrom?Practicemakesperfect.Fromstudyingmathematics,youknowthatifyousolvemoreproblems,youwillknowwhatkindofsituationmustoccurtosolvetheproblem.Itcanbecalledthephilosophyofmathematics.Ingeneral,thedifferencebetweenliberalartsstudentsandsciencestudentsliesinthis,notinthepresenceorabsenceoflogicalthinking.Atthesametime,inreality,whatpeoplethinkthatlogicalthinkingabilityisstrongisactuallystrongthinkingability,andthereisnoliberalarts.Moreover,ideasarenotobtainedlogically,butlogicallyexplained.
Adheretocommonsense
Infact,Ieasilygetpersonalconclusionsabouthumanrights.Thereasonisthatnomatterhowbig-nameexpertsare,thereisonlyonereasonIdon’tagreewith.Istickto"NoonewantstoOne’sownlegitimaterightshavebeenviolated,unlessitisalastresort.”Thiscommonsense.Becauseweadheretothiscommonsense,wemustanalyzethesovereigntyindetail.Forexample,thecountryhastherighttomaintainthemilitary.Thisrightwillrequirecitizenstoundertakedifferentobligationsunderdifferentcircumstances.Itseemsthathumanrightsareviolatedduringwar,butthisisakindofcontributionforeveryone’ssafetyneeds.Sovereigntymustbejustified.Thisshowstheimportanceofstickingtocommonsenseandlogicalconclusions.Itshouldbenotedthattheconclusionsobtainedbyinductioncannotbeadheredto,becauseinductionisalwaysapartoftheinduction,anditcannotbethewhole.Itviolatesthecommonsensethathowpartisnotequaltoall,suchasphilosophy.Chinesepeopleoftenusephilosophytoexplainproblems,alwaysfromonegeneraltoanother,soitisnotcleartosay,itseemsthattheycannotthinklogically,anditisridiculous.
Participateinthedebate
Thoughtsaregeneratedinthedebate,includingoneselfandoneself.Forexample,regardingwhethersovereigntyissuperiortohumanrightsortheopposite,Ibelievethatthesovereigntytoprotecthumanrightsisgreaterthanthatofhumanrights.Itcannotincludethesovereigntythatcausesthekingtoenjoythebabyfeast.Sovereigntymustbedefined,andtheformerisconditionallyestablished.Thereasonforthisrealizationisthatthereisadebateonthisissue,otherwiseIwouldnotthinkaboutit.
Toprotectthesovereigntyofhumanrights,thereisalogicalthinkingherethatexplainsthathumanrightsmustbeprotected.Therefore,wecan’tchangetheconcepttosaythatsovereigntyisgreaterthanhumanrights.Infact,thislogicshowsthathumanrightsarehigherthansovereignty.
Abilitytraining
First,focusonthecultivationoflogicalreasoningthinking.
Thetypesofreasoningaredividedaccordingtocertainstandards.Accordingtothedifferentnumberofreasoningpremises,itcanbedividedintodirectreasoningandindirectreasoning;accordingtothedirectionofreasoning,thatis,thedifferenceinthethinkingprocessfromgeneraltospecial,orfromspecialtogeneral,orfromspecialtospecial,traditionallogicdividesreasoningintoTherearethreecategoriesofdeductivereasoning,inductivereasoningandanalogicalreasoning.
Asfarasjuniormiddleschoolmathematicsisconcerned,syllogisticreasoningisanimportantdeductivereasoning.Itistheabbreviationofpropertyjudgmentsyllogismreasoning,whichisderivedfromtwopropertyjudgmentsthatcontainacommonterm..Thenamesofthethreequalitativejudgmentsinthesyllogismaremajorpremise,minorpremiseandconclusion.Thepremisethatcontainsthemajoritemisthemajorpremise,thepremisethatcontainstheminoritemistheminorpremise,andthejudgmentthatcontainsthemajorandminoritemsistheconclusion.Forexample,allplantsneedwater(majorpremise),andwheatisaplant(minorpremise),sowheatalsoneedswater(conclusion).Asawayofthinking,syllogismcontainsthreenaturejudgmentsusuallyarrangedintheorderofmajorpremises,minorpremises,andconclusions.However,whenexpressingsyllogismsinnaturallanguage,theorderofsentencesisflexible,andellipticalformsareoftenused(thereareformsofomittingmajorpremisesorminorpremisesorconclusions).Forexample,itisoftensaidinspokenlanguagethat"thisistheschool'sregulations",andtocompleteitis:allschoolregulationsshouldbeimplemented(majorpremise),thissentenceistheschool'sregulations(minorpremise),sothissentenceShouldbeimplemented(conclusion).
Asabasicreasoning,syllogismreasoningcanbestreflectthecharacteristicsoflogicalreasoning.Itisthemostbasicandextensivereasoningintheapplicationofgeometryinjuniorhighschool,anditiseasierforstudentstounderstandandmaster.Therefore,itshouldbeusedasthefocalpointandentrypointforthetrainingoflogicalreasoningabilityofjuniorhighschoolstudents.
Second,masterthebasicmethodsoflogicalreasoning.
Intheteachingpracticeofjuniorhighschoolmathematics,especiallyintheteachingofgeometricproofs,itisnotdifficultforteacherstoteach,anditisnotdifficultforstudentstounderstand,butstudentsoftendonotknowhowtodoit.Complicatedtopicsareevenmoredifficulttostart.Geometricproofhasbecomeadifficultpointinteachingandamajorobstacletotheimprovementofstudentperformance.Tobreakthroughthisdifficultyandobstacle,inadditiontomasteringthebasiclogicalthinkingoftheabove-mentionedsyllogismreasoning,wemustalsopayattentiontothecultivationofthebasicmethodsoflogicalreasoning-synthesisandanalysis.
Toprovethecorrectnessofaproposition,wefirststartfromtheknownconditions,throughaseriesofestablishedpropositions(suchasdefinitions,theorems,etc.),stepbystepforwarddeduction,andfinallydeductwhatwewanttoproveAsaresult,thiswayofthinkingiscalledacomprehensivemethod.Itcanbebrieflysummarizedas:"causeleadstoeffect",thatis,"causeleadstoresult".
Toprovethatapropositioniscorrect,inordertofindthecorrectmethodorwaytoproveit,wecanfirstassumethatitsconclusioniscorrect,andtheninvestigatethereasonsforitsestablishment,andthenstudythesereasonsseparatelyandlookatthemWhataretheconditionsfortheestablishmentof,andsograduallyreverseupwarduntiltheknownfactsarereached.Thiswayofthinkingiscalledanalyticalmethod.Itcanbebrieflysummarizedas:"holdtheeffectandcausethecause."Thatis,"holdtheresulttofindthecause."Forexample,provethattwolinesegmentsareequal.
Theideaofthecomprehensivemethod:knownconditions→triangularcongruenceorparallelogram→correspondingsidesoroppositesidesareequal(linesegmentsareequal).
Analysismethod:thecorrespondingsidesoroppositesidesareequal(linesegmentsareequal)→trianglecongruentorparallelogram→knownconditions.
Thecharacteristicoftheanalyticalmethodistostartfromtheconclusiontobeprovedandtoseektheconditionsforitsestablishmentstepbystep,untilitfindstheknownconditions.Thecharacteristicofthesynthesismethodistostartfromtheknownconditions,deducetheresultstepbystep,andfinallydeducetheresulttobeproved.Whenprovinggeometricproblems,theanalyticalmethodisworsethanthecomprehensivemethodinthinking,andtheanalyticalmethodisinferiortothecomprehensivemethodinexpression.Theanalyticalmethodisgoodforthinking,andthecomprehensivemethodissuitableforpresentation.Insolvingproblems,itisbesttousethemtogether.Foranewproblem,wegenerallyfirstusetheanalyticalmethodtofindasolution,andthenusethecomprehensivemethodtoformulateitinanorderlymanner.
Forsomemorecomplexgeometricproblems,wecanusethemethodofcombiningsynthesismethodandanalysismethodtofindawaytoprove,whichcanbecalledcomprehensiveanalysismethod;thatis,startingfromtheknownconditions,seeWhatresultscanbedrawn,thenstartfromtheconclusiontobeproved,seewhatconditionsitneedstobeestablished,andfinallyseewherethegapsare,soastofindthecorrectwaytoprovetheproblem.
3.Severalabilitiesthatshouldbepaidattentiontoincultivatingstudents’logicalreasoningability
Logicalthinkingusesconceptsasthinkingmaterialsandlanguageasthecarrier.Further,thereisawell-foundedthinking,whichischaracterizedbyabstraction,anditsbasicformsareconcepts,judgmentsandinferences.Therefore,theso-calledlogicalthinkingabilityistheabilitytothinkcorrectlyandreasonably.Toenablestudentstotrulyhavetheabilityoflogicalreasoningandimprovetheabilitytosolveproblems;educationandteachingshouldalsofocusonthecultivationofthefollowingabilities.
1.Theabilitytodeeplyunderstandandusebasicknowledgeflexibly.Logicalreasoningrequiresdeepknowledgeaccumulation,soastoprovideasufficientbasisforeachstepofreasoning.Anexampleinlifecanexplain:"Whyisitthatradishesthatarechoppedandcutarebettertocookandtastebetterthanradishesthatarecutneatlyandregularly?".Ajuniorhighschoolstudentdidn’tknowhowtoanswer,buthismotherexplaineditwell:“Becauseradishthatischoppedandcuthasalargersurfaceareathanradishesthatarecutneatlyandregularly,andcanabsorbmoreheat,andvariouscondimentscanbebetter.Whenthegroundenterstheradish,ofcourseitwillbebettercookedandtastebetter."Obviously,themother'sunderstandingandapplicationofdailylifeknowledgeismuchbetterthanthatofthechildren.Therefore,theabilitytounderstandandusebasicknowledgeflexiblyisthefoundationofstudents'logicalreasoningability.
2,imagination.Becauselogicalthinkinghasstrongflexibilityanddevelopment,theuseofimaginationcangreatlypromotetheimprovementoflogicalreasoningability.Thestrongertheknowledgebaseandthebroadertheknowledge,themoreabletouseone'simagination.Ofcourse,itdoesnotmeanthatthemoreknowledge,therichertheimagination.Youneedtodevelopthehabitofunderstandingthingsfrommultipleangles,andfullyunderstandthevariousconnectionsbetweentheinsideandoutsideofthings,andbetweensomethingandotherthings,inordertoexpandyourimagination.Thisisofgreatsignificancetotheimprovementoflogicalthinkingability.
3,languageability.Thequalityoflanguageabilitynotonlydirectlyaffectsthedevelopmentofimagination,butalsologicalreasoningreliesonrigorouslanguageexpressionandcorrectwrittenexpression.Therefore,itisimportanttopayattentiontothecultivationofstudents'language,especiallythecultivationofmathematicallanguageandgeometriclanguage,whichisanindispensablekeytotheformationofstudents'logicalreasoningability.
4.Theabilityofdrawingandrecognizingpictures.Thelogicalreasoningatthejuniorhighschoollevelismoredirectlyappliedtogeometry,andgeometryandgraphicsareinseparable;geometricgraphicscontainmanyhiddenknownconditionsandalargeamountofreasoningmaterialsandinformation.Whetheryouhaveadeepunderstandingofgraphics,itisdirectAffectwhethertheproblemcanbesolved.Therefore,students'abilityofdrawingandrecognizingpicturescanneverbeignoredintheteachingoflogicalreasoningabilitytraining.
Daretoquestion
Theexerciseoflogicalthinkingabilitycanimproveone'sunderstandingofdifferentaspectsofthingsandtheinnerrelationshipthroughtheprocessofconstantlyquestioningvariousthings,throughthewayofquestioningCometoputforwardmoredifferentperspectivesofthinkinganddiscrimination.Alargenumberofconnectionsbetweenthebrainandthingsaredevelopedtomakeitmoreeffectiveindevelopinglogicalthinking.