4M-克莱因的HPM思想-以-微积分-为例

214Vol.21,No.420128JOURNALOFMATHEMATICSEDUCATIONAug.,20122012–03–10DIA110251zc090221976—MHPM12112002412310018MHPM4MHPMG4009A1004–9894201204–0024–04MMorrisKline20[1]90019671977JohnWiley&SonsDover1998[2]MHPM1[2]150[2][3]M.Scheffer[4]2[2]1744MHPM252.1xy00yx[2]2.21700[2]1615[5][2]2.3[2]sinx3M[346][7][8][3]M[2]HPM3.1[2]M32)3(xxy32632'xxxyy353xx2495'xxy3.2111111)1(11nn[2]111111S10)11()11()11(S21)11()11(1S3SS11111(121S317~184§2621[2][2]25123456789101112131415161718192021222324254.124813223914151623510111218191615[5][5]1637[9]1636[5][9][10]4.2[4]1821[10]4.3[2]1000k=234[11]16Jyesthadeva15MadhavaNilakanthak[11]17k1[9]4.4[11]4MHPM27M5MHPM4HPMMMM[1][J]1980312889–894[2]KlineM.Calculus:AnIntuitiveandPhysicalApproach[M].NewYork:DoverPublications,Inc,1998.[3]KlineM.LogicVersusPedagogy[J].AmericanMathematicalMonthly,1970,77(3):264–282.[4]AlexandersonGL,KlineM.AnInterviewwithMorrisKline:Part1[J].TheTwo-yearCollegeMathematicsJournal,1979,10(3):172–178.[5]2[M]2004[6]KlineM.AProposalfortheHighSchoolMathematicsCurriculum[J].MathematicsTeacher,1966,59(4):322–330.[7][M]2003[8][M]2006[9][M]2003[10][M]2010[11]KatzVJ.UsingtheHistoryofCalculustoTeachCalculus[J].ScienceandEducation,1993,2(3):243–249.MorrisKline’sHPMThought:ExemplifiedbyHisCalculusGAOXue-fen1,2,WANGXiao-qin1(1.DepartmentofMathematics,EastChinaNormalUniversity,Shanghai200241,China;2.DepartmentofMathematics,ZhejiangSci-techUniversity,ZhejiangHangzhou310018,China)Abstract:MorrisKlineisanoutstandingmathematicianandmathematicseducationalist.TheHPMthoughtinhisCalculuscanbesummarizedas:approachingtheoriginandthenatureofmathematicsbyanintuitiveandphysicalapproach;introducingsubjectsbyquestionsorproblemstorevealthehistoricalmotivationsformathematicsdevelopment;improvinganalysisabilitythroughdifficultiesencounteredandmistakesmadebymathematicians;organizingthesubjectsbasedonthecognitivelevelofstudentsandthehistoricalsequenceofcalculus.Keywords:MorrisKline;HPM;historyofmathematics;[]