20世纪以来中国数学课程标准中算术与代数表征功能的变化及启示

Arithmetic and Algebra Representation Function in Mathematics Curriculum Standards in China since the 20th Century: Its Change and Enlightenment

根据《20世纪中国中小学课程标准·教学大纲汇编(数学卷)》和21世纪以来的课程标准中算术与代数的内容,围绕数学表征的表达交流、操作转换、建模应用3种功能,采用历史研究方法,编码分析1902—2017年中国中小学数学课程文件(标准)中算术与代数表征的变化趋势.研究结果表明:数学表征的功能会随着课程标准的变化而变化,并且3种表征功能的侧重点和相互关联性在不同学段也有不同的特点.表达交流功能在小学阶段依赖于建模应用,而初高中阶段依赖于操作转换;操作转换功能在3个学段均处于主导地位;建模应用功能在小学、初中阶段并没有受到重视,而在高中阶段新课程改革后逐步受到重视.

On the basis of arithmetic and algebra in Complication of Curriculum Standards and Syllabus for Chinese Primary and Secondary Schools in the 20th Century(Mathematics Volume)and the curriculum standards since the 21st century,the variation trend of the arithmetic and algebraic representation in Chinese primary and secondary school mathematics curriculum standards from 1902 to 2017 was investigated using the historical research method and coding-analysis by focusing on three functions of mathematical representation(i.e.,expression communication,operational transformation and modelling application.Results showed that,the function of mathematical representation changes as the curriculum standard changes.Moreover,the emphasis and correlation among three representation functions also had different features in different stages.Particularly,the function of expression communication was depended on the modelling application in the primary school stage,but the operational transformation in the middle and high school stage.The function of operational transformation was dominant in three stages.The function of the modelling application was not taken seriously in the primary school and junior high school.However,more attention had been paid to the high school stage since the new curriculum was reformed.