高中微积分课程国际比较研究——基于十个国家和地区的十四个课标研究

International Comparisons on Calculus of Mathematics Curriculum in Senior High School——Involving 14 Mathematics Standard in 10 Countries or Regions

考察10个国家、地区的14个最新课标中的微积分内容，并做比较细致的定量和定性分析．定量分析包括广度、深度、难度、内容分布、聚类分析；定性分析包括分析核心概念、命题的引入和处理方式．得出的部分结论如下，每个国家、地区选基础水平或理科作为代表，绝对难度从大到小排名：法国（理科）、澳大利亚（基础）、英国AQA、韩国、中国香港（应用）、俄罗斯（基础）、新加坡、中国台湾（理科）、中国（理科）、加拿大；分别按课标、知识点聚类分析，得出了微积分内容设置比较相似的课标分类和知识点受重视程度相似的一些分类．通过比较研究，对中国高中微积分课程发展与教学改革提供一些思考和建议．

Through quantitative and qualitative analysis methods, we investigate the intemational comparisons of calculus for Senior high school, which involves 14 mathematics standard in 10 countries or regions. The quantitative analysis methods include analysis of the breadth, depth, difficulty, cognitive level distribution, module knowledge distribution, and the cluster analysis on curriculum standard and knowledge points. The qualitative analysis methods contain the analysis of how core concepts and propositions are introduced and arranged. Based on the local basic level or science requirements, the difficulty ranks from the most to the least as follows： France （science）, Australia （basic）, England AQA, South Korea, Hong Kong （application）, Russian （basic）, Singapore, Taiwan （Science）, China （Science）, Canada （Japan only has breadth analysis）. Clustering analysis is applied on contents to obtain the calculus standard with similar setting and applied to knowledge points to obtain the knowledge points with similar levels of importance. Through comparison, we give some constructive suggestions for curriculum development and teaching reform for calculus for our senior high school.