20世纪以来中国初中数学课程标准中推理论证能力的变化及启示
|
摘要
针对中国1923年至今,初中阶段的数学课程纲领性文件进行内容分析,发现其中关于数学推理论证的能力目标出现了4次"高峰";并结合史料分析,解释了合情推理和论证推理在百余年教育思潮变化中呈现的"钟摆"现象;进而指出,在建立具有中国特色的数学课程体系的过程中,需要谋求合情推理与论证推理之间的平衡.
Employing the content analysis method, this study reviewed mathematical reasoning-and-proving competency in the mathematics curricular programmatic documents at junior high school levels in China since 1923. The results showed that there are four "peaks" in the ability of mathematical reasoning-and-proving competency. Based on the analysis of historical documents, this paper explained the "pendulum phenomenon" of plausible reasoning and proving in the changes of educational trend of thought over the past hundred years. Then pointed out that to establish the mathematics curriculum system with Chinese characteristics, the balance between plausible reasoning and proving was needed.
Employing the content analysis method, this study reviewed mathematical reasoning-and-proving competency in the mathematics curricular programmatic documents at junior high school levels in China since 1923. The results showed that there are four "peaks" in the ability of mathematical reasoning-and-proving competency. Based on the analysis of historical documents, this paper explained the "pendulum phenomenon" of plausible reasoning and proving in the changes of educational trend of thought over the past hundred years. Then pointed out that to establish the mathematics curriculum system with Chinese characteristics, the balance between plausible reasoning and proving was needed.
引文
[1] BRODIE K. Teaching mathematical reasoning in secondary school classrooms[M]. Springer US, 2010:7.
[2] KILPATRICK J, MARTIN W G, SCHIFTER D. A research companion to principles and standards for school mathematics[M]. Reston, VA:National Council of Teachers of Mathematics, 2003:27-44.
[3] Common Core State Standards Initiative. Common core state standards for mathematics[J]. Common Core State Standards Initiative, 2010, 4(4):148.
[4] HATTIE J, FISHER D, FREY N. Visible learning for mathematics:What works best to optimize student learning[M].California:SAGE Publications, 2016:242-243.
[5] BRODIE K. Teaching mathematical reasoning in secondary school classrooms[M]. Springer US, 2010:6.
[6] LITHNER J. Mathematical reasoning in task solving[J]. Educational Studies in Mathematics, 2000, 41(2):165-190.
[7] LITHNER J. A research framework for creative and imitative reasoning[J]. Educational Studies in Mathematics, 2008,67(3):255-276.
[8] BALL DL, BASS H. Making mathematics reasonable in school[M]//KILPATRICK J, MARTIN WG, SCHIFTER DE.A research companion to principles and standards for school mathematics. Reston, VA:National Council of Teachers of Mathematics, 2003:27–44.
[9]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,2011:6.
[10]中华人民共和国教育部.普通高中数学课程标准[M].北京:人民教育出版社,2017:6.
[11]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.
[12]程靖,孙婷,鲍建生.我国八年级学生数学推理论证能力的调查研究[J].课程·教材·教法,2016,36(4):17-22.
[13]王桂荣.算学是什么?为什么要学算学?怎样学算学?[J].江苏学生,1932,3(1):49-60.
[14]彭基相.论理学之目的及定义[J].中法大学月刊,1931,1(2):59-63.
[15]王振瑄.新学制高级中学教科书论理学[M].上海:商务印书馆,1928:2.
[16]胡明复.新学制初级中学课程纲要草案:算学课程纲要[J].教育杂志,1923,15(5):7.
[17]教育部.修正初级中学数学课程标准[J].浙江教育,1941,4(1):55-60.
[18]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,2001:3-685.
[19]方晓东,李玉非,毕诚,等.中华人民共和国教育史纲[M].海口:海南出版社,2002:71.
[20]吕世虎.中国中学数学课程史论[M].北京:人民教育出版社,2013:100.
[21]章建跃.中学数学课程教材改革的钟摆——以平面几何为例[J].数学教学,2014,1(7):6-12.
[22]吕世虎,叶蓓蓓.1949—2011中国中学数学课程目标发展演变的特征分析[J].数学教育学报,2012,21(5):5-9.
[23]新青年数学教师工作室.当代中国数学教育名言解读[M].上海:上海教育出版社,2015:90-92.
[24]吕世虎.中学数学课程发展六十年[J].中国教育科学,2014(4):79-107.
[25]柯雅梅,刘良华.我国数学教育研究的三次争议[J].教育学术月刊,2017(10):38-44.
[26]陈重穆,宋乃庆.淡化形式,注重实质——兼论《九年义务教育全日制初级中学数学教学大纲》[J].数学教育学报,1993,2(2):4-9.
[27]郑毓信.再谈“淡化形式,注重实质”——《淡化形式,注重实质》读后[J].数学通报,1994,33(8):6-7.
[28]蔡闯,周迅,姜伯驹.新课标让数学课失去了什么[N].光明日报(教育周刊),2005-03-16(3).
[29]何小亚.回应《姜伯驹:新课标让数学课失去了什么》[J].广东教育,2006(11):55-57.
[30]綦春霞.数学认识论的历史及其发展趋势[J].数学教育学报,2002,11(1):28-31.
[31]高文杰,李晓娜.拉卡托斯拟经验主义数学观与启示[J].数学教育学报,2003,12(3):31-32.
[2] KILPATRICK J, MARTIN W G, SCHIFTER D. A research companion to principles and standards for school mathematics[M]. Reston, VA:National Council of Teachers of Mathematics, 2003:27-44.
[3] Common Core State Standards Initiative. Common core state standards for mathematics[J]. Common Core State Standards Initiative, 2010, 4(4):148.
[4] HATTIE J, FISHER D, FREY N. Visible learning for mathematics:What works best to optimize student learning[M].California:SAGE Publications, 2016:242-243.
[5] BRODIE K. Teaching mathematical reasoning in secondary school classrooms[M]. Springer US, 2010:6.
[6] LITHNER J. Mathematical reasoning in task solving[J]. Educational Studies in Mathematics, 2000, 41(2):165-190.
[7] LITHNER J. A research framework for creative and imitative reasoning[J]. Educational Studies in Mathematics, 2008,67(3):255-276.
[8] BALL DL, BASS H. Making mathematics reasonable in school[M]//KILPATRICK J, MARTIN WG, SCHIFTER DE.A research companion to principles and standards for school mathematics. Reston, VA:National Council of Teachers of Mathematics, 2003:27–44.
[9]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,2011:6.
[10]中华人民共和国教育部.普通高中数学课程标准[M].北京:人民教育出版社,2017:6.
[11]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.
[12]程靖,孙婷,鲍建生.我国八年级学生数学推理论证能力的调查研究[J].课程·教材·教法,2016,36(4):17-22.
[13]王桂荣.算学是什么?为什么要学算学?怎样学算学?[J].江苏学生,1932,3(1):49-60.
[14]彭基相.论理学之目的及定义[J].中法大学月刊,1931,1(2):59-63.
[15]王振瑄.新学制高级中学教科书论理学[M].上海:商务印书馆,1928:2.
[16]胡明复.新学制初级中学课程纲要草案:算学课程纲要[J].教育杂志,1923,15(5):7.
[17]教育部.修正初级中学数学课程标准[J].浙江教育,1941,4(1):55-60.
[18]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,2001:3-685.
[19]方晓东,李玉非,毕诚,等.中华人民共和国教育史纲[M].海口:海南出版社,2002:71.
[20]吕世虎.中国中学数学课程史论[M].北京:人民教育出版社,2013:100.
[21]章建跃.中学数学课程教材改革的钟摆——以平面几何为例[J].数学教学,2014,1(7):6-12.
[22]吕世虎,叶蓓蓓.1949—2011中国中学数学课程目标发展演变的特征分析[J].数学教育学报,2012,21(5):5-9.
[23]新青年数学教师工作室.当代中国数学教育名言解读[M].上海:上海教育出版社,2015:90-92.
[24]吕世虎.中学数学课程发展六十年[J].中国教育科学,2014(4):79-107.
[25]柯雅梅,刘良华.我国数学教育研究的三次争议[J].教育学术月刊,2017(10):38-44.
[26]陈重穆,宋乃庆.淡化形式,注重实质——兼论《九年义务教育全日制初级中学数学教学大纲》[J].数学教育学报,1993,2(2):4-9.
[27]郑毓信.再谈“淡化形式,注重实质”——《淡化形式,注重实质》读后[J].数学通报,1994,33(8):6-7.
[28]蔡闯,周迅,姜伯驹.新课标让数学课失去了什么[N].光明日报(教育周刊),2005-03-16(3).
[29]何小亚.回应《姜伯驹:新课标让数学课失去了什么》[J].广东教育,2006(11):55-57.
[30]綦春霞.数学认识论的历史及其发展趋势[J].数学教育学报,2002,11(1):28-31.
[31]高文杰,李晓娜.拉卡托斯拟经验主义数学观与启示[J].数学教育学报,2003,12(3):31-32.