从获得知识到拥有智慧From knowledge to wisdom.docx

从获得知识到拥有智慧From knowledge to wisdom.docx

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从获得知识到拥有智慧Fromknowledgetowisdom

从获得知识到拥有智慧（Fromknowledgetowisdom）

Fromknowledgetowisdom

Explorationandpracticeofinquirylearning

ZhaoXin,theSecondAffiliatedMiddleSchoolofBeijingNormalUniversity

Keywords:

mathematicseducation;learningstyle;informationtechnology;inquirylearning

First,thequestionraised

（1）thebasicpurposeofmathematicseducation;

Aftermanystudentsgotowork,notdirectlyusedmanymiddleschoolmathematicsknowledgeandthepeople,areoftenabletousemathematicalknowledgeinmiddleschoolandevenfewerpeople.SowethinkofthefamousmathematicianMr.HuaLuogeng'swords:

"whatisthenumber?

Fromthespecificdefinition,itsformulaandtheorem,therestisthenumber."Theplainlanguagecontainsaprofoundphilosophy.Weputthissentencetomigratetothesecondaryschoolmathematicsteaching,cansay:

"whatismathematics?

Fromthespecificdefinition,itsformulaandtheorem,therestisthemiddleschoolmathematics."Basedontheidea,teachersshouldcreatealearningenvironmentforstudentstoexploreMath:

whentheyenteredtheworldofmathematics,canseethegraphicbeauty,symmetricalbeauty,ofbeauty,ofbeauty,...Andforthesebeautyandadmiration;whentheyareoutofthemathematicalworld,therewillbeamethodofexploringscience,thecouragetoconquerthedifficulties,firmandindomitablequalityoflife--whichmayaccompanythem,shouldbethefundamentalpurposeofmathematicsteaching.

Infact,thenewcurriculumreformadvocatestheconstructionoflearning,studentsareconstructorsofknowledge.Learningisreorganizedandreexperiencetheprocessofunderstanding.Toachievethepurposeofmathematicsteaching,weneedintheprocessofteaching,letthestudentsundertheguidanceofteachers,independentinquiry,foundtocompletethelearningofnewknowledgetheprocessofteaching.Thiswillnotonlyenablestudentstomastertheknowledgemorefirmly,morethoroughunderstanding,moreimportantly,inthelearningprocessofstudentsthinkingabilitytrainingandimprove.Studentslearnthroughtheprocessnotonlytoacquireknowledge,butmoreimportantly,havethewisdomoflong-termdevelopment

（two）students'learningstyle;

Improvingstudents'mathematicslearningmethodisareformgoaladvocatedbythenewcurriculumstandard.Thenewcurriculumstandardclearlypointsoutthateffectivemathematicslearningactivitiescannotrelysolelyonimitationandmemory.Hands-onpractice,independentexplorationandcooperationandcommunicationareimportantwaysforstudentstolearnmathematics.Obviously,thiswayoflearningisbeneficialforstudentstoexperiencetheformationofmathematicalknowledge,helptorestorethetruefeaturesofmathematicalknowledge,andalsohelptoachievethebasicgoalofmathematicseducation.Therefore,teachersshouldmakegreateffortstopromotethechangeofstudents'learningstyle,andthechangeofstudents'learningstyledependsonthechangeofteachingmethodsandtherichnessofteachingmethods.

（three）thecontinuousdevelopmentofinformationtechnology;

Withtherapiddevelopmentofsociety,variousmeansofinformationtechnologyareconstantlyenriched.Therationalapplicationoftheseinformationtechnologiescaneffectivelypromoteclassroomteachingandprovideabroaderspaceforstudentstoexploreindependently.

Thegraphiccalculatorisdevelopedafterthescientificcalculator,ithasverystrongdrawingfunction,exceptconventionalmapping,butalsodynamicdemonstration,graphicalexploration;symboliccomputationsymbolicalgebrasystemcanalgebra,calculus;dataprocessingsystem,toexplorethedataofregressionanalysis;transmissionbetweengraphiccalculatorandthegraphiccalculatorandcomputercancarrydata,imageandprogram,easytocommunicate,modifyfileandoutput.Thesefeaturesmakethegraphiccalculatorbecomestudentsinclassandoutsideofselflearninginquiry.

Basedontheaboveseveralaspectsofthinking,Ibelieveintheconceptofthenewcurriculum,thechangeoflearningstyleistheinevitabletrendoftheinquirylearningtomakestudentslearnhowtofindtheproblem,fromthepointofviewofmathematicstosolveproblemsinthelearningprocess,theconstructionofcompletesenseoftheirowncognition,developexplorationandinnovationconsciousness.Theabundanceofinformationtechnologyenablesstudentstohavemoreextensivespaceforselfexploration,

Therefore,Ihavecarriedonthebeneficialexplorationtotheteachingcontent,theteachingobjectandtheteachingpatternofinquirylearningsupportedbytheinformationtechnology,andhasformedsomeconclusionswhichhavethepopularizationvalue

Two,concretepractice

（1）theroleofinquirylearningindifferentclassroomteachingcontents

1,theroleofinquirylearninginconceptualTeaching

Thetraditionalconceptofteachingmainlyteachersteachmainlypassiveacceptanceofstudents,studentshavenospacetothink,nodoubt,eachconceptasinputtothecomputerinordertotransfertothestudentsasstiff.Someteachersusedtoquicklyexplaintheconceptafteralotofpracticeatalllevelstocopewiththeexamination,whichisobviouslycontrarytothegoalofmathematicseducation.Thestudentsdonotgettheexerciseofthinkingintheprocessoflearningconcepts,andunderstandingoftheconceptisscanty,oftenthepast,studentsdeveloptheconceptoflearningisnotconsideredhabits,becomeawareoftheseriousgapbetweenthemachines,conceptandproblemsolving,andproblemsolvingonthebackquestionstheformofmemory,onlyknowingbutnotthewhy,

Therefore,theconceptofteaching,studentsshouldbeinthecurrentlevelofknowledgeontheformationprocess,letstudentsexperiencemathematicsconcept,throughthestudents'selfexploration,theformationofanewconcept.Thegraphiccalculatormakestudentsindependentinquiryaspossible,canbecarriedoutonconcreteanalysisofthephenomenonandtoabstractmathematicalconceptsbygraphiccalculatorstudentstheprocessofteaching,theconceptofstudentsintotheprocessofactiveconstructionofknowledge.Soinordertomaximizetheconceptofteachingtoimprovethelevelofstudents'thinking,toenablestudentstounderstandtheconceptcorrectlyandthoroughly.

Typicalcase:

theunifieddefinitionofconiccurves

[teachingprocess]

（a）createsituationsandaskquestions

Thedefinitionofanalogyquestions:

whatistheparabolicgeometrymeaningofellipseandhyperbolainline?

Ellipticandhyperbolic,studentscallprogramforagiveninputa,bvalues,andthenenterfreelyintherangeofxvalue,calculatorwillautomaticallycalculatetheyvalueandtheratiooflinetopointtofocusanddistance.

Throughtheresearchanddemonstrationofcomputerstudentscangetonthepropertiesofellipse,hyperbola,ellipseandhyperbolaonpointtofocusandtothecentrifugalratecurvealignmentdistance.

Parabola,ellipse,hyperbolahasmanycommonareas,suchassatellitetoorbitataratedifferentrangewhenareellipse,hyperbolaandparabola;theycanbecut.Theconicalsurfacewhethertherearesimilaritiesinthewayoftrajectoryformation?

（two）observationexperimentandreasonableconjecture

Thepropertiesoftheaboveellipticandhyperbolicpointsandthedefinitionandtheconjectureoftheanalogicalparabola:

Theellipseandhyperbolacanberegardedasthelocusofthepointwhosedistanceisfixedtothefixedline

ThederivationofthestandardequationforParabolicEquationsremains:

ThetrajectoryofthedistancebetweenthefixedpointFandthefixedlineLisconstante（）

SetthedistancefromFtoP,establishtheCartesiancoordinatesystem,andmakeF（straightline）:

Thetrajectoryofanypoint（x,y）（projection）accordingtothegeometricconditionslistedalgebraicformula:

Simplifyandarrange,

Inthisway,weobtainthetrajectoryequationofthepointatwhichthedistancebetweenthefixedpointandthefixedlineistheconstante.Wefindthatitisnotthestandardequationoftheellipseandhyperbola.Whatcurvedoesthisequationrepresent?

Becausetheequationiscomplicated,it'sdifficultforstudentstorecognizeit.Wecanusegraphicalcalculatorstohelpusanalyze.We'llcalltheprograminthecalculatorbelow

AslongasthestudentstakeagroupofEandPgraphicscalculatorwillautomaticallydrawthecurve.Theequationthatyoucantryforagivenp,enteradifferentE;andthengivenae,enteradifferentP,seewhatdifferentresults.Studentsarefoundbyrunningtheprogram:

e>1thatise=1,isahyperbola;parabola;0

Studentsareobservedtochangethecurvefromhyperbolatoparabolaandthentoellipse

Fromthisconjecture:

Thetrajectoryofthepointatwhichthedistancebetweenthepointtothepointandthedistancetothelineisconstantiszero

（three）reasoning,demonstrating,andrevealingtheprinciples

1,teachersguidestudentstoexploretheaboveconclusionsofthemathematicalproof

Aftertheformulationoftheequation,combinedwiththestandardequationofconiccurve,thetypeofthecurverepresentedbytheequationcanbeexplained.Thus,theunifieddefinitionofconiccurveisobtained:

Thetrajectoryofthepointatwhichthedistancebetweenthepointtothepointandthedistancetothelineisconstantiszero

2,afurtherunderstandingofthedefinition:

Theteacherguidesthestudentstothinkmoredeeplyabouttheseconddefinitionofellipseandhyperbola:

（1）thefirstdefinitionandtheseconddefinitionofellipseandhyperbolarecognizetheformationofcurvesfromdifferentangles;

（2）thedefinitionofconic