教学转换理论视角下高中数学新编教材中数学建模的知识形态Mathematical Modeling Knowledge in the New Edition of High School Mathematics Textbook from the Theory of Didactic Transposition
黄健,徐斌艳,王思凯
摘要(Abstract):
数学建模在各个领域内发挥着重要作用,教育界也对其日益重视。随着高中新课标与新教材的出版,数学建模教学也正紧锣密鼓地开展实践。然而,数学建模知识在不同背景下的表现形态与关注重点等却不尽一致。本研究在教学转换理论的视角下,选取三个关于数学建模的知识样本,比较分析数学建模的学术知识、待授知识、教学知识在概念界定、过程描述、教学目标与教学侧重四个维度上的差异。由此,本研究厘清了数学建模概念进入教学环境的演变路径与关键特征,以帮助教师更好地使用新编数学教材进行数学建模教学,也为数学建模素养的培养与研究提供理论参考。
关键词(KeyWords): 数学建模;教学转换理论;高中新编教材;学术知识;教学知识
基金项目(Foundation): 上海市高校“立德树人”人文社科重点研究基地课题“数学课程中跨学科综合实践的设计与实施”(项目编号:15500-412224-21A45/004)的研究成果
作者(Author): 黄健,徐斌艳,王思凯
参考文献(References):
- [1] 科技部办公厅,教育部办公厅,中科院办公厅,自然科学基金委办公室.关于加强数学科学研究工作方案[EB/OL].http://www.cas.cn/zcjd/201909/t20190918_4715042.shtml,2019-07-12/2021-03-01.
- [2][19] Kaiser,G.The Teaching and Learning of Mathematical Modelling[A].Cai,J.(ed.).Compendium for Research in Mathematics Education[C].The National Council of Teachers of Mathematics,2017:267-291.
- [3] Cai,J.,Cirillo,M.,Pelesko,J.,et al.Mathematical Modeling in School Education:Mathematical,Cognitive,Curricular,Instructional and Teacher Educational Perspectives[A].Liljedahl,P.,et al.(eds.).Proceedings of the Joint Meeting of PME38 and PME-NA36[C].Vancouver:PME,2014:145-172.
- [4] 中华人民共和国教育部.普通高中数学课程标准(2017年版2020年修订版)[S].北京:人民教育出版社,2020:1-180.
- [5] Herbel-Eisenmann,B.A.From Intended Curriculum to Written Curriculum:Examining the Voice of a Mathematics Textbook[J].Journal for Research in Mathematics Education,2007(4):344-369.
- [6] Brown,M.& Edelson,D.Teaching as Design:Can We Better Understand the Ways in Which Teachers Use Materials So We Can Better Design Materials to Support Their Changes in Practice[R].Evanston,IL:The Center for Learning Technologies in Urban Schools,2003.
- [7] 徐斌艳.教材内涵及其研究的国际视野[J].全球教育展望,2019(3):119-127.
- [8] Love,E.& Pimm,D.“This Is So”:A Text on Texts[A].Bishop,A.J.,et al (eds.).International Handbook of Mathematics Education[C].Dordrecht:Springer,1996:371-409.
- [9] Chevallard,Y.& Bosch,M.Didactic Transposition in Mathematics Education[A].Lerman,S.(ed.).Encyclopedia of Mathematics Education[C].Dordrecht:Springer,2020:214-218.
- [10] 张奠宙.教育数学是具有教育形态的数学[J].数学教育学报,2005(3):1-4.
- [11] Mullis,I.V.S.& Martin,M.O.(eds.).TIMSS 2019 Assessment Frameworks[EB/OL].https://timssandpirls.bc.edu/timss2019/frameworks,2019-12-25/2021-03-01.
- [12][31] Winsl?w,C.Anthropological Theory of Didactic Phenomena:Some Examples and Principles of Its Use in the Study of Mathematics Education[A].Bosch,M.,et al (eds.).Un Panorama de TAD,CRM Docume[C].Barcelona:Centre de Recerca Matemàtica,2011:117-138.
- [13] 史宁中,王尚志.普通高中数学课程标准(2017年版)解读[M].北京:高等教育出版社,2018:1-308.
- [14] Kuckartz,U.Qualitative Text Analysis:A Guide to Methods,Practice and Using Software[M].London:SAGE,2014:62-118.
- [15] Niss,M.Models and Modeling in Mathematics Education[J].EMS Newsletter,2012 (12):49-52.
- [16] Saeki,A.& Matsuzaki,A.Dual Modelling Cycle Framework for Responding to the Diversities of Modellers[A].Stillman,G.A.,et al.Teaching Mathematical Modelling:Connecting to Research and Practice[C].Dordrecht:Springer,2013:89-99.
- [17] Frejd,P.& Bergsten,C.Mathematical Modelling as a Professional Task[J].Educational Studies in Mathematics,2016(1):11-35.
- [18] Blum,W.& Niss,M.Applied Mathematical Problem Solving,Modelling,Applications,and Links to Other Subjects—State,Trends and Issues in Mathematics Instruction[J].Educational Studies in Mathematics,1991(1):37-68.
- [20] Garfield,J.& Franklin,C.Assessment of Learning,for Learning,and as Learning in Statistics Education[A].Batanero,C.,et al (eds.).Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education[C].Dordrecht:Springer,2011:133-145.
- [21] Frejd,P.Modes of Modelling Assessment—A Literature Review[J].Educational Studies in Mathematics,2013(3):413-438.
- [22][23] 黄健,鲁小莉,王鸯雨,徐斌艳.20世纪以来中国数学课程标准中数学建模内涵的发展[J].数学教育学报,2019(3):18-23.
- [24][26] 人民教育出版社.普通高中教科书·数学必修第一册(A版)[M].北京:人民教育出版社,2019:60,162.
- [25][27] 上海教育出版社.普通高中教科书·数学必修第四册[M].上海:上海教育出版社,2020:2,1.
- [28] 章建跃,张艳娇,金克勤.数学建模活动的课程理解、教材设计与教学实施(续)[J].中学数学教学参考,2020(16):13-16.
- [29] Blomh?j,Morten.Towards Integration of Modelling in Secondary Mathematics Teaching[A].Stillman,G.A.& Brown,J.P.(eds.).Lines of Inquiry in Mathematical Modelling Research in Education[C].Dordrecht:Springer,2019:37-51.
- [30] Czocher,J.A.Precision,Priority,and Proxies in Mathematical Modelling[A].Stillman,G.A.& Brown,J.P.(eds.).Lines of Inquiry in Mathematical Modelling Research in Education[C].Dordrecht:Springer,2019:105-123.
- [32] Wolfsberg,A.‘Literature’ on Mathematical Modelling from a Teacher Perspective:A Textbook's Portrayal[A].CERME 9-Ninth Congress of the European Society for Research in Mathematics Education[C].Prague:Na'a Vondrová,2015:951-957.