20世纪以来中国中学数学课程中数学表征能力的发展趋势与启示——以几何为例
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摘要
依据20世纪以来中国各年代的中学数学课程标准(大纲),采用文本分析法,从表达交流、操作转换和建模应用3个水平构建数学表征能力的水平分析框架.分别对初、高中数学课程标准中的平面几何、立体几何教学内容进行分析,进而探讨20世纪以来,数学表征能力在中国不同时期中学数学课程标准中的发展趋势以及获得的启示.结果表明,在数学表征能力方面,中国中学几何课程标准对操作转换的要求逐步上升,对表达交流的要求相对稳定,而对建模应用水平关注较少,课改后期开始才得到一定重视.
According to the Chinese mathematics syllabi of middle school in different eras since the 20th century, the paper used text analysis method to construct an analytical framework of mathematical representational competency based on related research, which contained three levels, i.e.(1) expression and communication,(2) operation and transformation, and (3) modelling and application. Based on the framework, we then analyzed the content of plane geometry and solid geometry in Chinese mathematics syllabi for middle school respectively, and further discussed the developmental trend of the competency in Chinese middle school mathematics syllabi since the 20th century and the enlightenment. The results showed that Chinese middle school mathematics syllabi gradually paid more attention to operation and transformation, whereas the request for expression and communication remained relatively stable. Compared with them, the syllabi showed less attention to the modelling and application, though the situation was slightly better than before.
According to the Chinese mathematics syllabi of middle school in different eras since the 20th century, the paper used text analysis method to construct an analytical framework of mathematical representational competency based on related research, which contained three levels, i.e.(1) expression and communication,(2) operation and transformation, and (3) modelling and application. Based on the framework, we then analyzed the content of plane geometry and solid geometry in Chinese mathematics syllabi for middle school respectively, and further discussed the developmental trend of the competency in Chinese middle school mathematics syllabi since the 20th century and the enlightenment. The results showed that Chinese middle school mathematics syllabi gradually paid more attention to operation and transformation, whereas the request for expression and communication remained relatively stable. Compared with them, the syllabi showed less attention to the modelling and application, though the situation was slightly better than before.
引文
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[3]孙雪梅,赵永香,朱维宗,等.云南民族地区六年级彝族学生数学问题解决表征水平的调查研究[J].数学教育学报,2016,25(3):85-92.
[4]张晋宇,姜慧慧,谢海燕.数学表征与变换能力的评价指标体系研究综述[J].全球教育展望,2016,45(11):13-21.
[5]夏征农,陈至立.辞海[M].6版彩图本.上海:上海辞书出版社,2009:161.
[6] LERMAN S. Encyclopedia of mathematics education[M]. Dordrecht:Springer Netherlands, 2014:409.
[7]全美数学教师理事会.美国学校数学教育的原则和标准[M].蔡金法,译.北京:人民教育出版社,2004:65.
[8] OECD. PISA for development assessment and analytical framework:Reading, mathematics and science[M]. Paris:OECD Publishing, 2018:56.
[9]徐斌艳.数学学科核心能力研究[J].全球教育展望,2013,42(6):67-74.
[10] NISS M. Mathematical competencies and the learning of mathematics:The Danish KOM project[C]. 3rd Mediterranean conference on mathematical education, 2003:115-124.
[11]课程教材研究所.20世纪中国中小学课程标准·教学大纲汇编(数学卷)[M].北京:人民教育出版社,1999:228,264,428,400,434,456,461,578.
[12]中国教育年鉴编辑部.中国教育年鉴(1988)[M].北京:人民教育出版社,1989:334.
[13]孔凡哲,刘晓玫,孙晓天.《义务教育阶段国家数学课程标准》“空间与图形”的特点[J].数学教育学报,2001,10(3):58-61.
[14]史宁中,马云鹏,刘晓玫.义务教育数学课程标准修订过程与主要内容[J].课程·教材·教法,2012,32(3):50-56.
[15]吕世虎.中国当代中学数学课程发展的历程与启示[D].长春:东北师范大学,2009:5.
[16]陈重穆,曾崇燊,宋乃庆.从素质教育看21世纪的高中数学课程[J].课程·教材·教法,1995,15(9):40-42.
[17]《国家高中数学课程标准》制订组.《高中数学课程标准》的框架设想[J].数学教育学报,2002,11(2):1-7.
[18]夏明德,顾泠沅.面向实际不断修订[J].数学通报,1982,21(7):1-3.