20世纪以来中国数学课程标准中数学建模内涵的发展
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摘要
采用主题质性文本分析法,综合梳理中国1902—2018年小学、初中、高中的数学课程纲领性文本(教学大纲、课程标准)中数学建模的内涵.研究发现:长期以来,中国数学大纲中没有"数学建模"的提法,1996年的高中大纲中首次出现"数学模型"一词;大纲(课标)对"数学建模"过程的描述从不完备的"四阶段循环模型"逐步发展成"七阶段循环模型";21世纪以来,高中课标对"数学建模"的重视程度与具体要求显著高于义务教育阶段,但缺乏情感态度的描述.基于这些发现,文章最后提出了关于数学建模教与学实践的启示.
Employing the thematic qualitative text analysis, this study reviews mathematical modelling in the mathematics curricular syllabi/standards at primary, middle and high school levels in China from 1902 to 2018. The results indicated that 1) the notion of mathematical modelling had not been found in the Chinese mathematics syllabi until 1996 in the high school syllabus; 2) the description of the modelling process in the curricular syllabi/standards had been changed from a "four-stage modelling cycle" to "seven-stage modelling cycle"; and 3) since the 21 st century, high school curricular standards paid more attention to mathematical modelling than those for the compulsory education stage, but lacked requirements in affective aspects. Based on these, this paper ended with implications for the teaching and learning of mathematical modelling.
Employing the thematic qualitative text analysis, this study reviews mathematical modelling in the mathematics curricular syllabi/standards at primary, middle and high school levels in China from 1902 to 2018. The results indicated that 1) the notion of mathematical modelling had not been found in the Chinese mathematics syllabi until 1996 in the high school syllabus; 2) the description of the modelling process in the curricular syllabi/standards had been changed from a "four-stage modelling cycle" to "seven-stage modelling cycle"; and 3) since the 21 st century, high school curricular standards paid more attention to mathematical modelling than those for the compulsory education stage, but lacked requirements in affective aspects. Based on these, this paper ended with implications for the teaching and learning of mathematical modelling.
引文
[1] BLUM W. Modelling and application in mathematics education:The 14th ICMI study[J]. New ICMI Study, 2007(10):xi.
[2] NISS M. Models and modelling in mathematics education[J]. European Mathematical Society Newsletter, 2012(86):49–52.
[3] LESH R, FENNEWALD T. Introduction to part I modelling:What is it? Why do it?[M]//LESH R, GALBRAITH P L,HAINES C R, et al. Modelling Students’ Mathematical Modelling Competencies, 2010:5–10.
[4] The Consortium for Mathematics and Its Applications. Mathematical modelling handbook[EB/OL].(2018–03–11)[2018–08–07]. http://www.comap.com.
[5] GREER B. Modelling reality in mathematics classrooms:the case of word problems[J]. Learning&Instruction, 1997,7(4):293–307.
[6] INITIATIVE C C S S. Common core state standards for mathematics[J]. Common Core State Standards Initiative,2010, 4(4):148.
[7] MAA?K. What are modelling competencies[J]. ZDM, 2006, 38(2):113–142.
[8] BLUM W, NISS M. Applied mathematical problem solving, modelling, applications, and links to other subjects:state,trends and issues in mathematics instruction, in educational studies in mathematics[J]. Educational Studies in Mathematics, 1991, 22(1):37–68.
[9] KAISER G, BRAND S. Modelling competencies:past development and further perspectives[M]//Mathematical modelling in education research and practice, 2015:129–149.
[10] KAISER G. The teaching and learning of mathematical modelling[C]//CAI J. Compendium for research in mathematics education. United States:The National Council of Teachers of Mathematics, 2017:267–291.
[11] The National Governors Association(NGA)and the Council of Chief State School Officers(CCSSO). Common core state standards for mathematics[J]. Common Core State Standards Initiative, 2010, 4(4):148.
[12]王林全.美国高中数学建模标准——分析、评价与思考[J].数学教学,2011(10):4–6.
[13]朱娅梅.义务教育阶段学生数学建模能力评价研究[D].上海:华东师范大学,2014:14.
[14]?RLEB?CK J B. Mathematical modelling in the Swedish curriculum documents governing the upper secondary mathematics education between the years 1965—2000[R]. Link?ping:Link?pingsuniversitet, Matematiskainstituti tionen, 2009.
[15]王尚志.数学建模在中国各学段的发展历程及展望[J].数学教育学报,2017,26(6):8.
[16]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,2001:1–685.
[17]中华人民共和国教育部.全日制义务教育数学课程标准(实验稿)[M].北京:北京师范大学出版社,2001:1–102.
[18]中华人民共和国教育部.普通高中数学课程标准(实验)[M].北京:人民教育出版社,2003:1–122.
[19]中华人民共和国教育部.义务教育数学课程标准(2011年版)[M].北京:北京师范大学出版社,2012:1–132.
[20]中华人民共和国教育部.普通高中数学课程标准(2017年版)[M].北京:人民教育出版社,2018:1–180.
[21] KUCKARTZ U. Qualitative text analysis:A guide to methods, practice and using software[M]. London:SAGE, 2014:62–118.
[22] POOL I D S. Trends in content analysis[M]. Urbana:University of Illinois Press, 1959:189–233.
[23]蔡金法,徐斌艳.也论数学核心素养及其构建[J].全球教育展望,2016,45(11):3–12.
[24] KAISER G. Modelling and modelling competencies in school[J]. Mathematical Modelling, 2007, 3(3):110–119.
[25] KAISER G, SRIRAMAN B. A global survey of international perspectives on modelling in mathematics education[J].ZDM, 2006, 38(3):302–310.
[26]吕世虎,鲍建生,缴志清.21世纪高中数学课程改革的“成就”“问题”与“挑战”[J].数学教育学报,2018,27(1):14–17.
[27]牛伟强,张倜,熊斌.中国中小学数学建模研究的回顾与反思——基于1989—2016年核心期刊文献的统计分析[J].数学教育学报,2017,26(5):66–70.
[28]徐斌艳.关于德国数学教育标准中的数学能力模型[J].课程·教材·教法,2007,27(9):84–87.
[2] NISS M. Models and modelling in mathematics education[J]. European Mathematical Society Newsletter, 2012(86):49–52.
[3] LESH R, FENNEWALD T. Introduction to part I modelling:What is it? Why do it?[M]//LESH R, GALBRAITH P L,HAINES C R, et al. Modelling Students’ Mathematical Modelling Competencies, 2010:5–10.
[4] The Consortium for Mathematics and Its Applications. Mathematical modelling handbook[EB/OL].(2018–03–11)[2018–08–07]. http://www.comap.com.
[5] GREER B. Modelling reality in mathematics classrooms:the case of word problems[J]. Learning&Instruction, 1997,7(4):293–307.
[6] INITIATIVE C C S S. Common core state standards for mathematics[J]. Common Core State Standards Initiative,2010, 4(4):148.
[7] MAA?K. What are modelling competencies[J]. ZDM, 2006, 38(2):113–142.
[8] BLUM W, NISS M. Applied mathematical problem solving, modelling, applications, and links to other subjects:state,trends and issues in mathematics instruction, in educational studies in mathematics[J]. Educational Studies in Mathematics, 1991, 22(1):37–68.
[9] KAISER G, BRAND S. Modelling competencies:past development and further perspectives[M]//Mathematical modelling in education research and practice, 2015:129–149.
[10] KAISER G. The teaching and learning of mathematical modelling[C]//CAI J. Compendium for research in mathematics education. United States:The National Council of Teachers of Mathematics, 2017:267–291.
[11] The National Governors Association(NGA)and the Council of Chief State School Officers(CCSSO). Common core state standards for mathematics[J]. Common Core State Standards Initiative, 2010, 4(4):148.
[12]王林全.美国高中数学建模标准——分析、评价与思考[J].数学教学,2011(10):4–6.
[13]朱娅梅.义务教育阶段学生数学建模能力评价研究[D].上海:华东师范大学,2014:14.
[14]?RLEB?CK J B. Mathematical modelling in the Swedish curriculum documents governing the upper secondary mathematics education between the years 1965—2000[R]. Link?ping:Link?pingsuniversitet, Matematiskainstituti tionen, 2009.
[15]王尚志.数学建模在中国各学段的发展历程及展望[J].数学教育学报,2017,26(6):8.
[16]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,2001:1–685.
[17]中华人民共和国教育部.全日制义务教育数学课程标准(实验稿)[M].北京:北京师范大学出版社,2001:1–102.
[18]中华人民共和国教育部.普通高中数学课程标准(实验)[M].北京:人民教育出版社,2003:1–122.
[19]中华人民共和国教育部.义务教育数学课程标准(2011年版)[M].北京:北京师范大学出版社,2012:1–132.
[20]中华人民共和国教育部.普通高中数学课程标准(2017年版)[M].北京:人民教育出版社,2018:1–180.
[21] KUCKARTZ U. Qualitative text analysis:A guide to methods, practice and using software[M]. London:SAGE, 2014:62–118.
[22] POOL I D S. Trends in content analysis[M]. Urbana:University of Illinois Press, 1959:189–233.
[23]蔡金法,徐斌艳.也论数学核心素养及其构建[J].全球教育展望,2016,45(11):3–12.
[24] KAISER G. Modelling and modelling competencies in school[J]. Mathematical Modelling, 2007, 3(3):110–119.
[25] KAISER G, SRIRAMAN B. A global survey of international perspectives on modelling in mathematics education[J].ZDM, 2006, 38(3):302–310.
[26]吕世虎,鲍建生,缴志清.21世纪高中数学课程改革的“成就”“问题”与“挑战”[J].数学教育学报,2018,27(1):14–17.
[27]牛伟强,张倜,熊斌.中国中小学数学建模研究的回顾与反思——基于1989—2016年核心期刊文献的统计分析[J].数学教育学报,2017,26(5):66–70.
[28]徐斌艳.关于德国数学教育标准中的数学能力模型[J].课程·教材·教法,2007,27(9):84–87.
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