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題名：數學建模--社會文化與集體論證的觀點
書刊名：科學教育學刊
作者：黃志賢 引用關係
作者(外文)：Huang, Chih-hsien
出版日期：2014
卷期：22:3
頁次：頁237-258
主題關鍵詞：社會文化；集體論證；微積分；論述；數學建模能力；Sociocultural；Collective argumentation；Calculus；Discourse；Mathematical modeling competency
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  • 被引用次數被引用次數:期刊(1) 博士論文(0) 專書(0) 專書論文(0)
  • 排除自我引用排除自我引用:1
  • 共同引用共同引用:15
  • 點閱點閱:108
本研究基於社會文化與集體論證的觀點，設計嵌入微積分課程的數學建模活動培養學生的數學建模能力，在此教學介入下，逐漸發展大一微積分學生的數學建模能力。研究對象為54位科技大學微積分學生，研究方法採用數學建模教學實驗、課堂觀察及晤談。教學實驗將建模教學活動融入正規的微積分課程，以避免習慣接受傳統教學的學生的阻力，研究結果發現多數學生最缺乏的是「給定模型的變數和參數」、「圖形表徵與代數表徵的轉換」及「缺乏詮釋和效化的能力」。但經由數學建模教學，學生確實可以透過獨立作業及集體論證，逐漸發展其數學建模能力。學生的數學建模能力從「只瞭解給定的情境，但無法結構化和簡化情境或不能發現有關的數學想法」的層次，逐漸發展到「能經驗數學建模過程和效化與給定情境有關的數學解答」層次。本研究證實將教學與學習脈絡聚焦在社會文化取向與集體論證觀點，確實能幫助學生強化舊知識、發展新知識及培養數學建模能力。
In this paper, I outline a sociocultural perspective of modelling in mathematics education and discuss implications for analysis of students' activities at the micro level. I explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. The research reported in this paper is situated within an ongoing study where first year calculus students are using the practices of Collective Argumentation to bring about change in their classrooms. This paper reports on one aspect of the study that sought to explore whether students who use Collective Argumentation on a regular basis in their classrooms view mathematics as providing a forum where personal understandings can be expressed, re-considered, shared and coauthored when they go about mathematical modelling in a novel context-a reducing transportation costs problem. The results of the exploration are discussed and situated within the context of the findings of the on-going study. Through mathematical modeling instruction, students can gradually develop their mathematical modelling competency by working on their own and through discussion with their peers.
期刊論文
1.Blum, W.、Niss, M.(1991)。Applied mathematical problem solving, modeling, applications, and links to other subjects-state, trends and issues in mathematics instruction。Educational Studies in Mathematics，22(1)，37-68。  new window
2.Englishe, L. D.、Fox, J. L.、Watters, J. J.(2005)。Problem posing and solving with mathematical modeling。Teaching Children Mathematics，12(3)，156-163。  new window
3.Doerr, H. M.、English, L. D.(2003)。A Modeling perspective on students’ mathematical reasoning about data。Journal of Research in Mathematics Education，34(2)，110-136。  new window
4.Barbosa, J. C.(2006)。Mathematical modelling in classroom: A socio-critical and discursive perspective。Zentralblatt für Didaktik der Mathematik，38(3)，293-301。  new window
5.Blomhøj, M.、Jensen, T. H.(2003)。Developing mathematical modelling competence: Conceptual clarification and educational planning。Teaching Mathematics and Its Applications，22(3)，123-139。  new window
6.Blum, W.、Borromeo Ferri, R.(2009)。Mathematical modelling: Can it be taught and learnt。Journal of Mathematical Modelling and Application，1(1)，45-58。  new window
7.Boaler, J.(2001)。Mathematical modelling and new theories of learning。Teaching Mathematics and Its Applications，20(3)，121-128。  new window
8.Burkhardt, H.(2006)。Modelling in mathematics classrooms: Reflections on past developments and the future。Zentralblatt für Didaktik der Mathematik，38(2)，178-195。  new window
9.Freudenthal, H.(1968)。Why to teach mathematics so as to be useful?。Educational Studies in Mathematics，1(1/2)，3-8。  new window
10.Gravemeijer, K.、Doorman, M.(1999)。Context problems in realistic mathematics education: A calculus course as an example。Educational Studies in Mathematics，39(1)，111-129。  new window
11.Kaiser, G.、Schwarz, B.(2006)。Mathematical modelling as bridge between school and university。Zentralblatt für Didaktik der Mathematik,，38(2)，196-208。  new window
12.Kaiser, G.、Sriraman, B.(2006)。A global survey of international perspectives on modelling in mathematics education。Zentralblatt für Didaktik der Mathematik，38(3)，302-310。  new window
13.Kaiser, G.、Blomhøj, M.、Sriraman, B.(2006)。Towards a didactical theory for mathematical modeling。Zentralblatt für Didaktik der Mathematik，38(2)，82-85。  new window
14.Lerman, S.(2001)。Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics。Educational Studies in Mathematics，46(1-3)，87-113。  new window
15.Lesh, R.、English, L. D.(2005)。Trends in the evolution of models and modeling perspectives on mathematical learning and problem solving。Zentralblatt für Didaktik der Mathematik，37(6)，487-489。  new window
16.Lesh, R. A.、Lehrer, R.(2003)。Models and modeling perspectives on the development of students and teachers。Mathematical Thinking and Learning: An International Journal，5(2/3)，109-130。  new window
17.Maaß, K.(2006)。What are modelling competencies?。Zentralblatt für Didaktik der Mathematik，38(2)，113-142。  new window
18.Sfard, A.、Kieran, C.(2001)。Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions。Mind, Culture, and Activity，8(1)，42-76。  new window
19.Yoon, C.、Dreyfus, T.、Thomas, M. O. J.(2010)。How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity。Mathematics Educational Research Journal，22(2)，141-157。  new window
20.楊凱琳、林福來、蕭志如(20120800)。數學建模評量規準之研究。科學教育學刊，20(4)，319-342。new window  延伸查詢new window
21.楊凱琳、林福來(20061000)。探討高中數學教學融入建模活動的支撐策略及促進參與教師反思的潛在機制。科學教育學刊，14(5)，517-543。new window  延伸查詢new window
22.Ferri, R. B.(2006)。Theoretical and empirical differentiations of phases in the modelling process。Zentralblatt fur Didaktik der Mathematik，38(2)，86-95。  new window
會議論文
1.Doorman, M.、Gravemeijer, K.(2008)。Learning mathematics through applications by emergent modeling: The case of slope and velocity。The second international symposium on mathematics and its connections to the arts and sciences (MACAS2)。Odense, Danmark：University of Southern Denmark Press。37-56。  new window
2.Romberg, T. A.(2001)。Mathematics goals and achievement in the United States。Utrecht, The Netherlands：PME。180-185。  new window
3.Niss, M.(2003)。Mathematical competencies and the learning of mathematics: The Danish KOM project。The 3rd Mediterranean Conference on Mathematical Education。Athens：The Hellenic Mathematical Society。115-124。  new window
圖書
1.Chronaki, A.、Christiansen, I. M.(2005)。Challenging perspectives on mathematics classroom communication。Greenwich, UK：Information Age。  new window
2.Perkins, D. N.(1992)。Smart schools: Better thinking and learning for every child。New York：The Free Press。  new window
3.Wertsch, J. V.(1993)。Voices of the mind。Cambridge, UK：Harvard University Press。  new window
4.Wertsch, J. V.(2002)。Voices of collective remembering。New York, US：Cambridge University Press。  new window
5.Cohen, L.、Manion, L.、Morrison, K.(2000)。Research Methods in Education。London：New York：Routledge Falmer：Routledge Falmer。  new window
6.Freudenthal, H.(1991)。Revisiting mathematics education: China Lectures。Dordrecht, the Netherlands：Kluwer Academic Publishers。  new window
7.National Council of Teachers of Mathematics(2000)。Principles and standards for school mathematics。Reston, Virginia：National Council of Teachers of Mathematics。  new window
8.Wertsch, James V.(1998)。Mind as Action。Oxford University Press。  new window
9.Strauss, Anselm、Corbin, Juliet(1998)。Basics of Qualitative Research: Techniques and Procedures for Developing Grounder Theory。Sage。  new window
10.Ritchhart, R.(2002)。Intellectual Character: What It Is, Why It Matters, How to Get It。San Francisco, CA：Jossey-Bass。  new window
其他
1.CCSSO and NGA Center(2010)。Common core state standards for mathematics，Washington, DC：CCSSO and the NGA Center。，http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf， 2012/10/21。  new window
圖書論文
1.Steffe, L. P.、Thompson, P. W.(2000)。Teaching experiment methodology: Underlying principles and essential elements。Handbook of research design in mathematics and science education。Lawrence Erlbaum Associates。  new window
2.Antonius, S.、Haines, C.、Jensen, H. T.、Niss, M.、Burkhardt, H.(2007)。Classroom activities and the teacher。Modelling and applications in mathematics education: The 14th ICMI Study。New York：Springer。  new window
3.Blomh(2007)。Learning the integral concept through mathematical modelling。CERME 5-Proceedings of the fifth congress of the european society for research in mathematics education。Larnaca, Cyprus：University of Cyprus。  new window
4.Blum, W.、Leiß, D.(2006)。How do students and teachers deal with mathematical modeling problems? The example "Sugarloaf " and the DISUM project。Mathematical modelling (ICTMA12): Education, engineering and economics。Chichester, UK：Horwood。  new window
5.Brown, R. A. J.、Renshaw, P. D.(2000)。Collective argumentation: A sociocultural approach to reframing classroom teaching and learning。Social interaction in learning and instruction: The meaning of discourse for the construction of knowledge。Pergamon Press。  new window
6.Christiansen, I. M.(2001)。The effect of task organization on classroom modelling activities。Modelling and mathematics education: ICTMA9–applications in science and technology。Chichester, UK：Horwood。  new window
7.English, C.(1999)。Modelling for the new millennium。Rethinking the mathematics curriculum。London：Falmer Press。  new window
8.Kaiser, G.(2005)。Mathematical modelling in school -- Examples and experiences。Mathematikunterricht im spannungsfeld von evolution und evaluation。Hildesheim, Deutschland：Franzbecker。  new window
9.Kaiser, G.(2007)。Modelling and modelling competencies in school。Mathematical modelling: Education, engineering and economics ICTMA 12。Chichester, UK：Horwood。  new window
10.Lesh, R.、Doerr, H. M.(2000)。Symbolizing, communicating, and mathematizing: Key components of models and modeling。Symbolizing and communicating in mathematics classroom: Perspectives on discourse, tools, and instructional design。Mahwah, NJ：Lawrence Erlbaum Association。  new window
11.Lesh, R.、Doerr, H. M.(2003)。Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving。Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching。Mahwah, NJ：Lawrence Erlbaum Association。  new window
12.Lesh, R.、Hoover, M.、Hole, B.、Kelly, A.、Post, T.(2000)。Principles for developing thoughtrevealing activities for students and teachers。Handbook of research design in mathematics and science education。Mahwah, NJ：Lawrence Erlbaum Association。  new window
13.Lester, F. K.、Kehle, P. E.(2003)。From problem solving to modeling: The evolution of thinking about research on complex mathematical activity。Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching。Mahwah, NJ：Lawrence Erlbaum Association。  new window
14.Schoenfeld, A. H.(2002)。A highly interactive discourse structure。Social constructivist teaching: Affordances and constraints。New York：Elsevier。  new window
15.Schorr, R. Y.、Lesh, R.(2003)。A modeling approach for providing teacher development。Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching。Mahwah, NJ：Lawrence Erlbaum Association。  new window
16.Kehle, P. E.、Lester, F. K.(2003)。A semiotic look at modeling behavior。Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching。Mahwah, NJ：Lawrence Erlbaum Association。  new window
 
 
 
 
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