数学建模的教育研究:主要方法与研究案例
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摘要
本文向工作在数学建模教与学的一线教师和对数学建模教与学的研究有兴趣的教学工作者和研究者介绍在数学建模教与学的过程中实施教育研究的方法.为了系统地介绍这些教育研究的方法,借鉴国际数学与科学趋势研究的课程模型,将数学建模课程进行分类——预期课程、实施课程和达到课程,一方面介绍关于这些课程的常用研究方法;另一方面选择几个关于这些课程的研究案例,细述其研究设计和研究方法的具体实施过程.
This paper aims to introduce methods to conduct educational research for the teaching and learning of mathematical modelling.It could be particularly useful for frontline teachers who are now working on the teaching and learning of mathematical modelling,as well as educators who are interested in the relevant themes.In order to have a systematical introduction to the methods,the curriculum model proposed by the Trends of the International Mathematics and Science Study was used in this paper,which categorises the curriculum into three levels,i.e.,intended,implemented,and attained curricula,followed by several frequently-used methods in curriculum research.Afterwards,three wellpublished empirical studies,corresponding to the three levels of curriculum,were carefully selected for the elaboration of usage of those methods,including their research design,detailed implementation and the research findings.This paper ends with conclusions,clarifications and further advices for the practitioners.
This paper aims to introduce methods to conduct educational research for the teaching and learning of mathematical modelling.It could be particularly useful for frontline teachers who are now working on the teaching and learning of mathematical modelling,as well as educators who are interested in the relevant themes.In order to have a systematical introduction to the methods,the curriculum model proposed by the Trends of the International Mathematics and Science Study was used in this paper,which categorises the curriculum into three levels,i.e.,intended,implemented,and attained curricula,followed by several frequently-used methods in curriculum research.Afterwards,three wellpublished empirical studies,corresponding to the three levels of curriculum,were carefully selected for the elaboration of usage of those methods,including their research design,detailed implementation and the research findings.This paper ends with conclusions,clarifications and further advices for the practitioners.
引文
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[2]史宁中.高中数学课程标准修订中的关键问题[J].数学教育学报,2018,27(1):8-10.
[3]Saxena R,Shrivastava K,Bhardwaj R.Teaching mathematical modeling in mathematics education[J].Journal of Education and Practice,2016,7(11):34-44.
[4]Mullis I V S.TIMSS 2019assessment framework:Introduction[M].TIMSS&PIRLS International Study Center,Lynch School of Education,Boston College,2017.
[5]Cavanagh S.Content analysis:Concepts,methods and applications[J].Nurse Researcher,1997,4(3):5-16.
[6]Rosengren K E.Advances in content analysis[M].Beverly Hills,CA:Sage,1981:9-19.
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[8]Tesch R.Qualitative research:Analysis types and software tools[M].Bristol,PA:Falmer,1990.
[9]Hsieh H F,Shannon S E.Three approaches to qualitative content analysis[J].Qualitative Health Research,2005,15(9):1277-1288.
[10]Kondracki N L,Wellman N S.Content analysis:Review of methods and their applications in nutrition education[J].Journal of Nutrition Education and Behavior,2002(34):224-230.
[11]Patton M Q.Qualitative research and evaluation methods[M].Thousand Oaks,CA:Sage,2002.
[12]Morse J M,Field P A.Qualitative research methods for health professionals[M].2nd ed.Thousand Oaks,CA:Sage,1995.
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[15]Holsti O R.Content analysis for the social sciences and humanities[M].Reading,MA:Addison-Wesley,1969.
[16]Babbie E.The practice of social research[M].New York:Macmillan,1992.
[17]Morrison K R B.Planning and accomplishing school-centred evaluation[M].Norfolk:Peter Francis Publishers,1993.
[18]Patton M Q.Qualitative evaluation and research methods[M].2nd ed.London:Sage Publications,1990.
[19]Cohen L,Manion L,Morrison K.Research methods in education[M].5ed.London and New York:Taylor&Francis Group,2005.
[20]Kvale S.Interviews[M].London:Sage Publications,1996.
[21]Tuckman B W.Conducting educational research[M].New York:Harcourt Brace Jovanovich,1972.
[22]Wilson N,McLean S.Questionnaire design:A practical introduction[M].Newtown Abbey,Co.Antrim:University of Ulster Press,1994.
[23]Nisbet J,Watt J.Case study[M]//Bell J,Bush T,Fox A,et al.Conducting Small-scale Investigations in Educational Management.London:Harper&Row,1984:79-92.
[24]Hitchcock G,Hughes D.Research and the teacher[M].2nd ed.London:Routledge,1995.
[25]Yin R K.Case study research:Design and methods[M].Beverly Hills:Sage Publication,1984.
[26]Adelman C,Kemmis S,Jenkins D.Rethinking case study:Notes from the second cambridge conference[M]//Simons H.Towards a Science of the Singular.Centre for Applied Research in Education,University of East Anglia,1980:45-61.
[27]Corey S M.Action research to improve school practice[M].New York:Teachers College,Columbia University,1953.
[28]Zuber-Skerritt O.New directions in action research[M].London:Falmer,1996:243-255.
[29]Kemmis S,McTaggart R.The action research planner[M].2nd ed.Geelong,Victoria:Deakin University Press,1988.
[30]Hult M,Lennung S.Towards a definition of action-research:A note and bibliography[J].Journal of Management Studies,1980:17(2):241-50.
[31]Gage N.Handbook of research on teaching[M].Chicago:Rand McNally,1963:171-246.
[32]Germain-Williams T L.Mathematical modelling in algebra textbooks at the onset of the common core state standards[D].Columbia:Columbia University,2014.
[33]Supriadi S D,Sumarmo U,Rakhmat C.Developing mathematical modeling ability students elementary school teacher education through ethnomathematics-based contextual learning[J].International Journal of Education and Research,2014,2(8):439-452.
[34]Mehraein S,Gatabi A R.Gender and mathematical modeling competency:Primary students′performance and their attitude[J].Social and Behavioral Sciences,2014(128):198-203.
[2]史宁中.高中数学课程标准修订中的关键问题[J].数学教育学报,2018,27(1):8-10.
[3]Saxena R,Shrivastava K,Bhardwaj R.Teaching mathematical modeling in mathematics education[J].Journal of Education and Practice,2016,7(11):34-44.
[4]Mullis I V S.TIMSS 2019assessment framework:Introduction[M].TIMSS&PIRLS International Study Center,Lynch School of Education,Boston College,2017.
[5]Cavanagh S.Content analysis:Concepts,methods and applications[J].Nurse Researcher,1997,4(3):5-16.
[6]Rosengren K E.Advances in content analysis[M].Beverly Hills,CA:Sage,1981:9-19.
[7]Weber R P.Basic content analysis[M].Beverly Hills,CA:Sage,1990.
[8]Tesch R.Qualitative research:Analysis types and software tools[M].Bristol,PA:Falmer,1990.
[9]Hsieh H F,Shannon S E.Three approaches to qualitative content analysis[J].Qualitative Health Research,2005,15(9):1277-1288.
[10]Kondracki N L,Wellman N S.Content analysis:Review of methods and their applications in nutrition education[J].Journal of Nutrition Education and Behavior,2002(34):224-230.
[11]Patton M Q.Qualitative research and evaluation methods[M].Thousand Oaks,CA:Sage,2002.
[12]Morse J M,Field P A.Qualitative research methods for health professionals[M].2nd ed.Thousand Oaks,CA:Sage,1995.
[13]Hickey G,Kipping C.Issues in research.A multi-stage approach to the coding of data from open-ended questions[J].Nurse Researcher,1996(4):81-91.
[14]Potter W J,Levine-Donnerstein D.Rethinking validity and reliability in content analysis[J].Journal of Applied Communication Research,1999,27(3):258-284.
[15]Holsti O R.Content analysis for the social sciences and humanities[M].Reading,MA:Addison-Wesley,1969.
[16]Babbie E.The practice of social research[M].New York:Macmillan,1992.
[17]Morrison K R B.Planning and accomplishing school-centred evaluation[M].Norfolk:Peter Francis Publishers,1993.
[18]Patton M Q.Qualitative evaluation and research methods[M].2nd ed.London:Sage Publications,1990.
[19]Cohen L,Manion L,Morrison K.Research methods in education[M].5ed.London and New York:Taylor&Francis Group,2005.
[20]Kvale S.Interviews[M].London:Sage Publications,1996.
[21]Tuckman B W.Conducting educational research[M].New York:Harcourt Brace Jovanovich,1972.
[22]Wilson N,McLean S.Questionnaire design:A practical introduction[M].Newtown Abbey,Co.Antrim:University of Ulster Press,1994.
[23]Nisbet J,Watt J.Case study[M]//Bell J,Bush T,Fox A,et al.Conducting Small-scale Investigations in Educational Management.London:Harper&Row,1984:79-92.
[24]Hitchcock G,Hughes D.Research and the teacher[M].2nd ed.London:Routledge,1995.
[25]Yin R K.Case study research:Design and methods[M].Beverly Hills:Sage Publication,1984.
[26]Adelman C,Kemmis S,Jenkins D.Rethinking case study:Notes from the second cambridge conference[M]//Simons H.Towards a Science of the Singular.Centre for Applied Research in Education,University of East Anglia,1980:45-61.
[27]Corey S M.Action research to improve school practice[M].New York:Teachers College,Columbia University,1953.
[28]Zuber-Skerritt O.New directions in action research[M].London:Falmer,1996:243-255.
[29]Kemmis S,McTaggart R.The action research planner[M].2nd ed.Geelong,Victoria:Deakin University Press,1988.
[30]Hult M,Lennung S.Towards a definition of action-research:A note and bibliography[J].Journal of Management Studies,1980:17(2):241-50.
[31]Gage N.Handbook of research on teaching[M].Chicago:Rand McNally,1963:171-246.
[32]Germain-Williams T L.Mathematical modelling in algebra textbooks at the onset of the common core state standards[D].Columbia:Columbia University,2014.
[33]Supriadi S D,Sumarmo U,Rakhmat C.Developing mathematical modeling ability students elementary school teacher education through ethnomathematics-based contextual learning[J].International Journal of Education and Research,2014,2(8):439-452.
[34]Mehraein S,Gatabi A R.Gender and mathematical modeling competency:Primary students′performance and their attitude[J].Social and Behavioral Sciences,2014(128):198-203.