職前和在職數(shù)學(xué)教師對無理數(shù)概念的理解.pdf

1、華東師范大學(xué)碩士學(xué)位論文職前和在職數(shù)學(xué)教師對無理數(shù)概念的理解姓名：馮璟申請學(xué)位級別：碩士專業(yè)：課程與教學(xué)論數(shù)學(xué)指導(dǎo)教師：陳月蘭20100401ABSTRACTInthispapertheauthortakesasurveyonpreserviceandinservicemathematicsteachers’understandingofirrationalnumbersbyusingquestionnaireandinterviewT

2、hisinvestigationfocusesonthefollowingsixaspectssuchasconceptdefinitionandconceptimageofirrationalnumbers，therelationshipbetweenirrationalnumbersandrealnumbersystemandbetweenirrationalnumbersandrealnumberaxis，incommensura

3、bilityandthecomparisonofrationalandirrationalnumbersFromthesurveytheauthorobtainsthefollowingresults：aAlthoughthere’reseveraltypesofdefinitionforirrationalnumbers，thesubjectsarelimitedtotheinfinitenon—repetitiondecimalty

4、pewhichconstrainstheirunderstandingandcausesthemlessthanidealperformanceontheproofofirrationalnumbersbIntheirconceptimage，radicaltypeofdefinitiontakesfirstplace，thenthe萬一andetype，andthelogarithmic，triangularandcontinuedf

5、ractiontypearerelativelyweakTheirone—sideunderstandingofirrationalnumberscausescognitiveobstacleinthegraphicrepresentationcTheirperformanceintheidentificationofvariousnumbersacrosssetsislessthanidealdTheirknowledgeoftheb

6、ijectionbetweenrealnumberandtherealnumberlinestaysonlyinthememorylevel，whichcausesthemtomakewrongjudgmentsonwhetheranumberCanberepresentedonthenumberlineeTheirintuitiveknowledgeof“anytwosegmentsarecommensurable’’causesco

7、gnitiveobstacleintheunderstandingofirrationalnumbers￡Inthecomparisonofrationalandirrationalnumbers，theirintuitiveknowledgetosomeextenthelpsthemmaketherightjudgment，buttheweaknessinformalknowledgeleadsthemtomakemistakesSo