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;0Studentsareobservedtochangethecurvefromhyperbolatoparabolaandthentoellipse
Fromthisconjecture:
Thetrajectoryofthepointatwhichthedistancebetweenthepointtothepointandthedistancetothelineisconstantiszero
(three)reasoning,demonstrating,andrevealingtheprinciples
1,teachersguidestudentstoexploretheaboveconclusionsofthemathematicalproof
Aftertheformulationoftheequation,combinedwiththestandardequationofconiccurve,thetypeofthecurverepresentedbytheequationcanbeexplained.Thus,theunifieddefinitionofconiccurveisobtained:
Thetrajectoryofthepointatwhichthedistancebetweenthepointtothepointandthedistancetothelineisconstantiszero
2,afurtherunderstandingofthedefinition:
Theteacherguidesthestudentstothinkmoredeeplyabouttheseconddefinitionofellipseandhyperbola:
(1)thefirstdefinitionandtheseconddefinitionofellipseandhyperbolarecognizetheformationofcurvesfromdifferentangles;
(2)thedefinitionofconic