美国《线性代数及其应用》教材中的数学文化研究
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摘要
《线性代数及其应用》是美国线性代数课程改革后具有代表意义的主流教材。通过对该教材数学文化呈现方式、内容分布和运用方式的文本分析,发现其数学文化内容主要通过习题呈现,且总量相当丰富,而"数学与科学技术"内容在数学文化中所占比例大、运用水平高。就数学文化而言,美国《线性代数及其应用》教材对我国教材编写和课程改革都具有较高的参考和借鉴价值。
Linear Algebra and Its Applications is the mainstream textbook with representative meaning after the reform of American linear algebra curriculum.Through a text analysis of the presentation mode,content distribution and application methods,we concluded that mathematical culture in the textbook is mainly presented through exercises,and the total amount is quite rich,while "mathematics and science and technology" accounts for a large proportion and is applied in high level.The American textbook Linear Algebra and Its Applications may provide us with some new perspectives in the cultivation of mathematical culture in China.
Linear Algebra and Its Applications is the mainstream textbook with representative meaning after the reform of American linear algebra curriculum.Through a text analysis of the presentation mode,content distribution and application methods,we concluded that mathematical culture in the textbook is mainly presented through exercises,and the total amount is quite rich,while "mathematics and science and technology" accounts for a large proportion and is applied in high level.The American textbook Linear Algebra and Its Applications may provide us with some new perspectives in the cultivation of mathematical culture in China.
引文
[1]王建磐,汪晓勤,洪燕君.中、法、美高中数学教科书中的数学文化比较研究[J].教育发展研究,2015(20):28-32.
[2]KLINE M.The ancients versus the moderns:a new battle of the books[J].Mathematics Teacher,1958,51(6):418-427.
[3]KLINE M.Mathematics in western culture [M].New York:Oxford University Press,1953:Ⅵ.
[4]吴笑千,高剑明.工科专业“线性代数”课程的教学改革探讨[J].纺织服装教育,2015(4):327-330.
[5]王利东,刘婧.从应用实例出发的线性代数教学模式探讨[J].数学教育学报,2012(3):83-85.
[6]张志让.一本别具风格适应面宽的线性代数教程:《线性代数教程及其应用》一书简介[J].大学数学,1994(S2):13-15.
[7]项晶菁.HPM视角下向量组线性相关性概念的教学设计[J].数学教育学报,2015,24(4):57-60.
[8]朱琳,蒋启芬.国外线性代数的教学研究述评[J].数学教育学报,2018,27(1):79-83.
[9]CARLSON D,JOHNSON C R.The linear algebra curriculum study group recommendations for the first course in linear algebra[J].College Mathematics Journal,1993,24(1):41-46.
[10]LAY C D.Linear algebra and its applications[M].3th ed.New York:Pearson Education Inc,2003.
[11]汪晓勤.HPM:数学史与数学教育[M].北京:科学出版社,2017:1-39.
[12]陈晏蓉,汪晓勤.基于数学史的新知引入课例分析[J].上海课程教学研究,2018(1):38-44.
[13]李继闵.《九章算术》导读与译注[M].西安:陕西科学技术出版社,1998:624-682.
[14]刘汝佳,黄亮.算法艺术与信息学竞赛[M].北京:清华大学出版社,2004:Ⅱ.
[2]KLINE M.The ancients versus the moderns:a new battle of the books[J].Mathematics Teacher,1958,51(6):418-427.
[3]KLINE M.Mathematics in western culture [M].New York:Oxford University Press,1953:Ⅵ.
[4]吴笑千,高剑明.工科专业“线性代数”课程的教学改革探讨[J].纺织服装教育,2015(4):327-330.
[5]王利东,刘婧.从应用实例出发的线性代数教学模式探讨[J].数学教育学报,2012(3):83-85.
[6]张志让.一本别具风格适应面宽的线性代数教程:《线性代数教程及其应用》一书简介[J].大学数学,1994(S2):13-15.
[7]项晶菁.HPM视角下向量组线性相关性概念的教学设计[J].数学教育学报,2015,24(4):57-60.
[8]朱琳,蒋启芬.国外线性代数的教学研究述评[J].数学教育学报,2018,27(1):79-83.
[9]CARLSON D,JOHNSON C R.The linear algebra curriculum study group recommendations for the first course in linear algebra[J].College Mathematics Journal,1993,24(1):41-46.
[10]LAY C D.Linear algebra and its applications[M].3th ed.New York:Pearson Education Inc,2003.
[11]汪晓勤.HPM:数学史与数学教育[M].北京:科学出版社,2017:1-39.
[12]陈晏蓉,汪晓勤.基于数学史的新知引入课例分析[J].上海课程教学研究,2018(1):38-44.
[13]李继闵.《九章算术》导读与译注[M].西安:陕西科学技术出版社,1998:624-682.
[14]刘汝佳,黄亮.算法艺术与信息学竞赛[M].北京:清华大学出版社,2004:Ⅱ.