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1引言德国数学家F·克莱因(F.Klein,1849—1925)曾将函数称为数学的“灵魂”~[1],并认为函数概念应该成为中学数学的“基石”~[2].20世纪60年代,我国高中数学课程已经开始体现F·克莱因的上述思想.然而,从历史上看,函数概念经历了漫长的演变过程.美国数学家和数学史家M·克莱因(M.Kline,1908-1992)在抨击新数运动时曾说:“从伽利略到狄利克雷,数学家一直绞尽脑汁去理解函数的概念,但现在却由定义域、值域
1 INTRODUCTION The German mathematician F. Klein (1849-1925) once referred to the function as the ”soul“ of mathematics [1] and thought that the concept of function should become the ”cornerstone“ of mathematics in middle school. In the 1960s, the high school mathematics curriculum in our country started to embody the above thought of F. Klein, however, the concept of function has undergone a long evolutionary process from the historical perspective.American mathematician and math historian M · In his attack on the new movement, M. Kline (1908-1992) said: ”From Galileo to Dirichlet, mathematicians have been racking their brains to understand the notion of function, but now they are defined by the domain, value area