中學生對函數(shù)變換的理解.pdf

1、華東師范大學碩士學位論文中學生對函數(shù)變換的理解姓名：田新紅申請學位級別：碩士專業(yè)：教育（數(shù)學）指導教師：汪曉勤20051001ABSTRACTThefunctionconceptisoneofthecentraltopicsinschoolmathematicsanditappearsandreappearslikeathreadthroughouthighschoolmathematicsThetransformationoffunc

2、tionplaysallimportantroleinhi曲schoolmathematicstextbooksOneofthemostimportantproblemsontransformationsinwhichstudentsalwayshavedifficultiesis：Whatistherelationshipbetweenthetwographswhentheoneanalyticallyrepresentedfunct

3、ionistransformedintoanotheroneThisthesisfocusesonhigllschoolstudentsandmathematicsteachers’conceptionsoffunctiontranslationanddilationFindingsofthequestionnairesurveyandinterviewingrevealthatmostofthestudentsusethememori

4、zedrulestoexplainthehorizontMtranslationoffunction(“dotheopposite：plus—leftandminusright”)butdon’tunderstandwhytheserulesworkSimilarlytheyrelyonthememorizedrolestodothedilationproblemswithoutanydesiretOunderstandtheunder

5、lyingreasonsOtherexplanationsprovidedbythestudentsincludeconsideringthefunctionpointwise，operationoftheanalyticexpressions，graphplotting，attendingtotheaxesofsymmetryzeroorvertexof恤fimefioufindingtheperiodsubstitutionetcT

6、eachersprovidedavarietyofexplanationsofthesetwotypesoftransformations，includingcitingtherules，consideringthefunctionpoint—wiseandattendingtOthezeroofthefunction，ctcHowevernoneofthestrategiesusedbythestudentsorteachersale

7、helrlfulforthestudentstounderstandtransformationsoffunction，andtheyaleoftenmisleadingStudents’gtrorsinfunctiontranslationanddilafionincludeconfusionsofhorizontalandverticalshifts，rightandleftshifts，upanddownshifts，stretc

8、hingandshortening，andthedistanceofthehorizontalorverticalshiftThestudents’obstaclesintheirunderstandingofthefunctiontransformationsareanalyzedandsometeachingimplicationssuggestionsaregivenattheendofthepaperKeyWords：funct