高中生對反證法的理解.pdf

1、華東師范大學碩士學位論文高中生對反證法的理解姓名：孫宇申請學位級別：碩士專業(yè)：教育（數學）指導教師：汪曉勤20061101ABSTRACTThepmofbycontradictionisoneofthemostimponalltmethodsofproVingpropositionsinmamematicsBeingusedproperly，itcaIlreducethecomplexitytOsimplicity，di艏cultyto

2、easiness，impossibilitytopossibility，thusplayingadistinctiVerolewhichthedirectproofcaIlnotplayBecausethelogicalthinkinginVolVedisstrongaIldmeprecisionofmathematicallallguageishigh，tlIeproofbycontradjctjonalsoplaysanimport

3、antroleinthetra抽ingofstudents’abilitiesofrigorouslogicalthinkingandreadingcomprehensionandeStablishing0foonectconc印tionsofmathematicsM0reover，thismethOdiswidelyusedincOllegemathematjcsHOweVer，theproofbyc0Ⅱtradictionisdif

4、ficultbothtoteachandtole鋤Howtoe骶ctiVelyiInprovetheteachingofthjsmethodisanimportanttaskfacingmiddles出00lmathematicsteacherST11isp印erreportsanempjricalstudyonseniormiddleschoolstudeⅡts’understandingabouttheproofbycontradi

5、ction1kou曲atestc咖ductcdto268seniormiddleschoolstudentsfIomshanghaiandzhejiangandinterviewswithsomeofthesubjectsfromShanghaiwhoseaIlswersa他typical，thefollowingresults盯erevealed：(1)nestudents’abilitytonegatestatemeDtSisofl

6、owleVels，whichdirectlyaffecttheirunderstandiIlgandapplicationoftheproofbycontradiction；(2)Thescopeunderstoodbythestudentswithinwhichtllepr00fbycontradictionisapplicableisnarrow，andthelo昏calbasisandthetypesofcontradiction

7、sarebeyondtheirhlowledge(3)Thestudems’awarenessto印plytheproofbycontradictionisweak，andtheiroperationleVelislow(4)Withthegrade，students’abilitytonegatestatcmentsiIlcreases，butthedifferenceisnotevident(5)Thereexistsdiffefe