连贯性视阈下“代数思维”课程设置的比较研究——以“中”“美”“英”“澳”“新”“南非”六国课程内容为例
|
摘要
代数思维作为代数课程的基础内容,作为链接"算术"与"代数"课程的桥梁,历来受到国内外数学教育家们的关注.选择澳大利亚、中国、英国、新加坡、美国、南非作为代表国家,基于课程连贯性视阈,围绕"代数思维"课程的内容分布、知识主题选择、设置始末年级、连续性以及逻辑结构等方面进行"小学—初中—高中"国际比较研究,从而审视中国代数思维内容设置的基本特征,以期在全面深化课程改革的大背景下对中国"代数思维"内容的分布情况、内容的选择与组织有一定的启示作用.
The "Algebraic Thinking" was the basic content of Algebra Curriculum,which was the bridge connected "arithmetic" and "Algebra".Many mathematical educators at home and abroad always were focus on this problem.This study chose behalf of the state such as Australia,China,United Kingdom,Singapore,United States and South Africa.From the coherence visual threshold,the international comparative study revolves "Algebraic Thinking" content,for content distribution,topic selecting,setting time,continuous,and logical structure,which studies from primary school,junior high school to senior middle school.And it got some basic characteristics about curriculum settings of "Algebraic Thinking" in our country.The study took some inspiration for the distributed situation,the choice and organization of content for our country curriculum.
The "Algebraic Thinking" was the basic content of Algebra Curriculum,which was the bridge connected "arithmetic" and "Algebra".Many mathematical educators at home and abroad always were focus on this problem.This study chose behalf of the state such as Australia,China,United Kingdom,Singapore,United States and South Africa.From the coherence visual threshold,the international comparative study revolves "Algebraic Thinking" content,for content distribution,topic selecting,setting time,continuous,and logical structure,which studies from primary school,junior high school to senior middle school.And it got some basic characteristics about curriculum settings of "Algebraic Thinking" in our country.The study took some inspiration for the distributed situation,the choice and organization of content for our country curriculum.
引文
[1]程荣.同义词大词典[M].上海:上海辞书出版社,2010:198.
[2]林崇德.中国中学教学百科全书·教育卷[M].沈阳:沈阳出版社,1990:160.
[3]占小红,张新宇,范轶.教材“连贯性”评价工具设计及应用[J].全球教育展望,2010,39(9):51-56.
[4]和学新,马苏静.我国基础教育课程教材开发与管理的问题检视与改进[J].教育理论与实践,2013,33(28):47-51.
[5]马健生,苑大勇.《从先学前班到8年级的课程焦点:追求连贯性》报告述评[J].比较教育研究,2007,29(5):48-52.
[6]Common Core State Standards Initiative.Common core state standards for mathematics[EB/OL].(2016-08-02)[2017-03-29].http://www.corestandards.org/Math.
[7]严虹.六国基础教育阶段数学课程内容的衔接性研究[J].数学教育学报,2016,25(4):63-68.
[8]康玥媛,曹一鸣.中、澳、芬数学课程标准中内容分布的比较研究[J].教育学报,2012,8(1):62-66.
[9]严虹,吴立宝,康玥媛.中美初中数学课程的比较研究[J].比较教育研究,2015,37(2):96-101.
[10]严虹.中、新、韩、日四国高中数学课程目标的比较研究[J].外国中小学教育,2015(1):60-64.
[11]曹一鸣,贾思雨.高中平面解析几何课程设置的国际比较--基于12个国家高中数学课程标准的研究[J].外国中小学教育,2015(10):58-65.
[12]宋丹丹,曹一鸣.高中课程标准中函数内容的国际比较研究[J].数学通报,2014,53(12):1-7,16.
[13]曹一鸣,王万松.高中概率统计内容设置的国际比较--基于15个国家数学课程标准的研究[J].数学教育学报,2016,25(1):1-4.
[14]曹一鸣,严虹.高中数学课程内容及其分布的国际比较--基于12个国家数学课程标准的研究[J].数学通报,2015,54(7):9-14.
[15]曹一鸣,代钦,王光明.十三国数学课程标准评介(高中卷)[M].北京:北京师范大学出版社,2013:1-6.
[16]曹一鸣.十三国数学课程标准评介(小学、初中卷)[M].北京:北京师范大学出版社,2012:1-5.
[17]史宁中,孔凡哲.十二个国家普通高中数学课程标准国际比较研究[M].长沙:湖南教育出版社,2013:1-6.
[18]徐乃楠,孔凡哲,史宁中.俄罗斯高中数学教育标准、示范性大纲和教科书的最新变化特征及启示[J].全球教育展望,2015,44(1):100-109.
[19]吕世虎,史宁中,陈婷.《标准》与《大纲》中几何部分内容难度的比较研究[J].课程·教材·教法,2006,26(8):38-43.
[20]徐文彬.试论算术中的代数思维:准变量表达式[J].学科教育,2003(11):6-10,24.
[21]KRIEGLER S.Just what is algebraic thinking submitted for algebraic concept in the middle school[J].A Special Edition of Mathematics:Teaching in the Middle School,1994(5):1-10.
[22]刘久成,刘久胜.代数思维及其教学[J].课程·教材·教法,2015,35(12):76-81.
[23]RADFORD,LUIS.The progressive development of early embodied algebraic thinking[J].Mathematics Education Research Journal,2014,26(2):257-277.
[24]RADFORD,LUIS.On the development of early algebraic thinking[J].PNA,2012,6(4):117-133.
[25]WARREN,ELIZABETH.Early childhood teachers'professional learning in early algebraic thinking:a model that supports new knowledge and pedagogy[J].Mathematics Teacher Education and Development,2008(10):30-45.
[26]WILLIAM S.Survey of mathematics and science opportunities(curriculum analysis technical report series No.5 general topic trace mapping:data collection and processing)[M].East Lansing:Michigan State University,1995:10-12.
[27]SCHMIDT W H,WANG H C,McKNIGHT C C.Curricular coherence:an examination of US mathematics and science content standards from an international perspective[J].Curriculum Studies,2005,37(5):525-559.
[28]SCHMIDT W H,PRAWAT R S.Curriculum coherence and national control of education:issue or non-issue[J].Journal of Curriculum Studies,2006,38(6):641-658.
[29]ACARA.The Australian curriculum:mathematics f-12 version 7.2[EB/OL].(2016-08-03)[2017-03-19].http://www.australiancurriculum.edu.au/Curriculum/Overview.
[30]ACARA.The Australian curriculum:mathematics senior secondary version 7.2[EB/OL].(2016-08-03)[2017-03-19].http://www.australiancurriculum.edu.au/SeniorSecondary/Overview.
[31]康玥媛.澳大利亚全国统一数学课程标准评析[J].数学教育学报,2011,20(5):81-85.
[32]董连春,Max Stephens.澳大利亚全国统一高中数学课程标准评述[J].数学教育学报,2013,22(4):16-20.
[33]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,2012:16-41.
[34]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,2003:12-65.
[35]Department of Education.National curriculum in England:mathematics programmes of study[EB/OL].(2016-03-09)[2017-08-03].https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmesof-study.
[36]徐文彬,杨玉东.英国国家数学课程标准的确立与变革及其启示[J].数学教育学报,2002,11(3):48-51.
[37]Singapore Examinations and Assessment Board.Mathematics syllabus[EB/OL].(2016-11-03)[2017-03-19].https://www.seab.gov.sg/pages/nationalExaminations/PSLE/general_information.asp.
[38]宁连华,崔黎,金海月.新加坡高中数学课程标准评介[J].数学教育学报,2013,22(4):1-5.
[39]张守波.新加坡高中数学教学大纲的特色与启示[J].数学教育学报,2013,22(6):58-61.
[40]Common Core State Standards Initiative.Common core state standards for mathematics[EB/OL].(2017-03-29)[2017-08-03].http://www.corestandards.org/Math.
[41]曹一鸣,王立东,Paul Cobb.美国统一州核心课程标准高中数学部分述评[J].数学教育学报,2010,19(5):8-11.
[42]廖运章.美国《州共同核心数学标准》的内容与特色[J].数学教育学报,2012,21(4):68-72.
[43]CAPS.Curriculum and assessment policy statement foundation phase mathematics[EB/OL].(2016-11-03)[2017-03-19].http://www.education.gov.za/Curriculum/NCSGradesR12/CAPS/tabid/420/Default.aspx.
[44]李娜,曹一鸣,Lyn Webb.南非国家高中数学课程与评价标准评介[J].数学教育学报,2013,22(4):6-10.
[2]林崇德.中国中学教学百科全书·教育卷[M].沈阳:沈阳出版社,1990:160.
[3]占小红,张新宇,范轶.教材“连贯性”评价工具设计及应用[J].全球教育展望,2010,39(9):51-56.
[4]和学新,马苏静.我国基础教育课程教材开发与管理的问题检视与改进[J].教育理论与实践,2013,33(28):47-51.
[5]马健生,苑大勇.《从先学前班到8年级的课程焦点:追求连贯性》报告述评[J].比较教育研究,2007,29(5):48-52.
[6]Common Core State Standards Initiative.Common core state standards for mathematics[EB/OL].(2016-08-02)[2017-03-29].http://www.corestandards.org/Math.
[7]严虹.六国基础教育阶段数学课程内容的衔接性研究[J].数学教育学报,2016,25(4):63-68.
[8]康玥媛,曹一鸣.中、澳、芬数学课程标准中内容分布的比较研究[J].教育学报,2012,8(1):62-66.
[9]严虹,吴立宝,康玥媛.中美初中数学课程的比较研究[J].比较教育研究,2015,37(2):96-101.
[10]严虹.中、新、韩、日四国高中数学课程目标的比较研究[J].外国中小学教育,2015(1):60-64.
[11]曹一鸣,贾思雨.高中平面解析几何课程设置的国际比较--基于12个国家高中数学课程标准的研究[J].外国中小学教育,2015(10):58-65.
[12]宋丹丹,曹一鸣.高中课程标准中函数内容的国际比较研究[J].数学通报,2014,53(12):1-7,16.
[13]曹一鸣,王万松.高中概率统计内容设置的国际比较--基于15个国家数学课程标准的研究[J].数学教育学报,2016,25(1):1-4.
[14]曹一鸣,严虹.高中数学课程内容及其分布的国际比较--基于12个国家数学课程标准的研究[J].数学通报,2015,54(7):9-14.
[15]曹一鸣,代钦,王光明.十三国数学课程标准评介(高中卷)[M].北京:北京师范大学出版社,2013:1-6.
[16]曹一鸣.十三国数学课程标准评介(小学、初中卷)[M].北京:北京师范大学出版社,2012:1-5.
[17]史宁中,孔凡哲.十二个国家普通高中数学课程标准国际比较研究[M].长沙:湖南教育出版社,2013:1-6.
[18]徐乃楠,孔凡哲,史宁中.俄罗斯高中数学教育标准、示范性大纲和教科书的最新变化特征及启示[J].全球教育展望,2015,44(1):100-109.
[19]吕世虎,史宁中,陈婷.《标准》与《大纲》中几何部分内容难度的比较研究[J].课程·教材·教法,2006,26(8):38-43.
[20]徐文彬.试论算术中的代数思维:准变量表达式[J].学科教育,2003(11):6-10,24.
[21]KRIEGLER S.Just what is algebraic thinking submitted for algebraic concept in the middle school[J].A Special Edition of Mathematics:Teaching in the Middle School,1994(5):1-10.
[22]刘久成,刘久胜.代数思维及其教学[J].课程·教材·教法,2015,35(12):76-81.
[23]RADFORD,LUIS.The progressive development of early embodied algebraic thinking[J].Mathematics Education Research Journal,2014,26(2):257-277.
[24]RADFORD,LUIS.On the development of early algebraic thinking[J].PNA,2012,6(4):117-133.
[25]WARREN,ELIZABETH.Early childhood teachers'professional learning in early algebraic thinking:a model that supports new knowledge and pedagogy[J].Mathematics Teacher Education and Development,2008(10):30-45.
[26]WILLIAM S.Survey of mathematics and science opportunities(curriculum analysis technical report series No.5 general topic trace mapping:data collection and processing)[M].East Lansing:Michigan State University,1995:10-12.
[27]SCHMIDT W H,WANG H C,McKNIGHT C C.Curricular coherence:an examination of US mathematics and science content standards from an international perspective[J].Curriculum Studies,2005,37(5):525-559.
[28]SCHMIDT W H,PRAWAT R S.Curriculum coherence and national control of education:issue or non-issue[J].Journal of Curriculum Studies,2006,38(6):641-658.
[29]ACARA.The Australian curriculum:mathematics f-12 version 7.2[EB/OL].(2016-08-03)[2017-03-19].http://www.australiancurriculum.edu.au/Curriculum/Overview.
[30]ACARA.The Australian curriculum:mathematics senior secondary version 7.2[EB/OL].(2016-08-03)[2017-03-19].http://www.australiancurriculum.edu.au/SeniorSecondary/Overview.
[31]康玥媛.澳大利亚全国统一数学课程标准评析[J].数学教育学报,2011,20(5):81-85.
[32]董连春,Max Stephens.澳大利亚全国统一高中数学课程标准评述[J].数学教育学报,2013,22(4):16-20.
[33]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,2012:16-41.
[34]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,2003:12-65.
[35]Department of Education.National curriculum in England:mathematics programmes of study[EB/OL].(2016-03-09)[2017-08-03].https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmesof-study.
[36]徐文彬,杨玉东.英国国家数学课程标准的确立与变革及其启示[J].数学教育学报,2002,11(3):48-51.
[37]Singapore Examinations and Assessment Board.Mathematics syllabus[EB/OL].(2016-11-03)[2017-03-19].https://www.seab.gov.sg/pages/nationalExaminations/PSLE/general_information.asp.
[38]宁连华,崔黎,金海月.新加坡高中数学课程标准评介[J].数学教育学报,2013,22(4):1-5.
[39]张守波.新加坡高中数学教学大纲的特色与启示[J].数学教育学报,2013,22(6):58-61.
[40]Common Core State Standards Initiative.Common core state standards for mathematics[EB/OL].(2017-03-29)[2017-08-03].http://www.corestandards.org/Math.
[41]曹一鸣,王立东,Paul Cobb.美国统一州核心课程标准高中数学部分述评[J].数学教育学报,2010,19(5):8-11.
[42]廖运章.美国《州共同核心数学标准》的内容与特色[J].数学教育学报,2012,21(4):68-72.
[43]CAPS.Curriculum and assessment policy statement foundation phase mathematics[EB/OL].(2016-11-03)[2017-03-19].http://www.education.gov.za/Curriculum/NCSGradesR12/CAPS/tabid/420/Default.aspx.
[44]李娜,曹一鸣,Lyn Webb.南非国家高中数学课程与评价标准评介[J].数学教育学报,2013,22(4):6-10.