具有高等数学背景的高考题摘要 一百年前，F.克莱因就提倡 “高观点下的初等数学”意识，强调要用近代数学的观点改造中学数学内容。这一观点深深地影响了近代的中学数学教育。当然，在中国高考则直接影响着中学数学教学。本文研究具有高等数学背景的高考题。首先，阅读了大量的参考文献，对已有相关研究进行梳理与分析。包括在“高观点”题的功能、编写和教学探究；从基本理念中和课程内容解读《课标》中的“高观点”；给出“高观点”题的界定与分类。接着，从量和质两个方面对 2019 年的全国数学高考题进行研究分析。研究发现：2019 年高考试卷中出现了更多的带有高等数学背景的高考题，重视学生在“高观点”下解答问题能力的考查。最后，提出了若干教学建议。教的方面：（1）教师要努力创设“高观点”题学习情景；（2）进行适当的知识迁移和拓展；（3）“高观点”题讲解时，要充分挖掘“高观点”的知识和背景，重视数学思想和方法教学。学的方面：（1）在日常学习中，要会积累高等数学背景知识；（2）在解题特别是在解答高考数学题时，要尽力“站得高”、“析得透”。关键词 高观点题 高等数学 中学数学 解题教学Research On College Entrance Examination Questions With Advanced Mathematics BackgroundAbstract A hundred years ago, F. Klein advocated the consciousness of "primary mathematics with a high viewpoint", emphasizing the need to use modern mathematics to transform the content of middle school mathematics. This point of view has profoundly influenced the mathematics education in modern high schools. Of course, the college entrance examination in China directly affects mathematics teaching in middle schools. This paper studies college entrance examination questions with advanced mathematics background.First, read a lot of references, and sort out and analyze the existing related research. Including the function, writing and teaching inquiry of the "high viewpoint" question; Interpret the "High Viewpoint" in the "Curriculum Standards" from the basic concepts and content of the course; Give the definition and cl...
