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引文資料
題名:
Developing Eleventh Graders’ Conjecturing and Justifying Power on Generalization of Binary Number Patterns
書刊名:
臺灣數學教育期刊
作者:
劉致演
/
秦爾聰
作者(外文):
Liu, Chih-yen
/
Chin, Erh-tsung
出版日期:
2016
卷期:
3:2
頁次:
頁31-53
主題關鍵詞:
臆測
;
一般化
;
數學探究
;
特殊化
;
Conjecturing
;
Generalizing
;
Mathematical inquiry
;
Specializing
原始連結:
連回原系統網址
相關次數:
被引用次數:期刊(0) 博士論文(0) 專書(0) 專書論文(0)
排除自我引用:0
共同引用:0
點閱:12
本研究針對五位十一年級學生參與為期四週的課外數學探究活動進行觀察,藉以了解學生如何在解決數字樣式問題的過程中發展臆測及辯證能力。研究架構以社會學習面向為基礎,主要考量學生的臆測及辯證能力發展於同儕間之互動、對話與論證等學習行為。另本研究以個案研究為主進行資料蒐集及分析,從而瞭解學生數學臆測及辯證學習行為發展過程。研究結果顯示,學生在臆測情境氛圍中能夠有機會揭露並發展內在的數學能力,此外,學生在數學臆測的過程中不僅能彈性運用特殊化及一般化策略,更能提出令人驚豔的說明為其數學想法進行辯證。根據研究發現「關係式理解」對於學生臆測及辯證能力之發展至為關鍵。
以文找文
This study is due to investigate five eleventh graders of how they developing conjecturing and justifying power in the context of binary number pattern-finding problems. The framework of the research is situated in the social perspective which considers that the development of students’ conjecturing and justifying power should be much relied on interactions, dialogues and argumentations within peers. Qualitative case study design and analysis strategy is adopted in the study for constructing a holistic viewpoint of students’ mathematical conjecturing and justifying behavior. Research results show that students’ inherent capabilities could be revealed when they are engaged in an atmosphere of conjecturing. Besides, students could not only apply specializing and generalizing strategies flexibly but also propose impressive justifications to make others convinced during the process of conjecturing. All of the findings seem to imply that relational understanding is crucial for students to develop their conjecturing and justifying power.
以文找文
期刊論文
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Zack, V.、Graves, B.(2001)。Making mathematical meaning through dialogue: “Once you think of it, the Z minus three seems pretty weird”。Educational Studies in Mathematics,46(1-3),229-271。
2.
Stylianides, A. J.(2007)。Proof and proving in school mathematics。Journal for Research in Mathematics Education,38(3),289-321。
3.
Schoenfeld, A. H.(1989)。Explorations of students' mathematical beliefs and behavior。Journal for Research in Mathematics Education,20(4),338-355。
4.
Elbers, E.(2003)。Classroom interaction as reflection: Learning and teaching mathematics in a community of inquiry。Educational Studies in Mathematics,54(1),77-99。
5.
Fennema, E.、Carpenter, T. P.、Franke, M. L.、Levi, L.、Jacobs, V. R.、Empson, S. B.(1996)。A longitudinal study of learning to use children's thinking in mathematics instruction。Journal for Research in Mathematics Education,27(4),403-434。
6.
Kieran, C.、Forman, E.、Sfard, A.(2001)。Guest editorial learning discourse: Sociocultural approaches to research in mathematics education。Educational Studies in Mathematics,46(1-3),1-12。
7.
Kwon, O. N.、Park, J. S.、Park, J. H.(2006)。Cultivating divergent thinking in mathematics through an open-ended approach。Asia Pacific Educational Review,7(1),51-61。
8.
Shimizu, Y.(1999)。Aspects of mathematics teacher education in Japan: Focusing on teachers’ roles。Journal of Mathematics Teacher Education,2(1),107-116。
9.
Wood, T.、Sellers, P.(1997)。Deepening the analysis: Longitudinal assessment of a problem-centered mathematics program。Journal for Research in Mathematics Education,28(2),163-186。
10.
Cañadas, M. C.、Deulofeu, J.、Figueiras, L.、Reid, D.、Yevdokimov, O.(2007)。The conjecturing process: Perspectives in theory and implications in practice。Journal of Teaching and Learning,5(1),55-72。
11.
Coe, R.、Ruthven, K.(1994)。Proof practices and constructs of advanced mathematics students。British Educational Research Journal,20(1),41-53。
12.
Francisco, J. M.(2013)。Learning in collaborative settings: Students building on each other's ideas to promote their mathematical understanding。Educational Studies in Mathematics,82(3),417-438。
13.
Stillman, G.(2000)。Impact of prior knowledge of task context on approaches to applications tasks。Journal of Mathematical Behavior,19(3),333-361。
會議論文
1.
Blanton, M.、Kaput, J.(2002)。Developing elementary teachers' algebra “eyes and ears" Understanding characteristics of professional development that promote generative and self-sustaining change in teacher practice。Annual Meeting of the American Educational Research Association。New Orleans, LA。
2.
Kilpatrick, J.(1987)。What constructivism might be in mathematics education。the Eleventh Conference of the International Group for the Psychology of Mathematics Education。Montreal:PME。3-27。
3.
Lin, F. L.(20061200)。Designing mathematics conjecturing activities to foster thinking and constructing actively。The meeting of the APEC-TSUKUBA International Conference。Tokyo。
圖書
1.
National Research Council(1989)。Everybody Counts: A Report to the Nation on the Future of Mathematics Education。Washington, DC:National Academy Press。
2.
Skemp, R. R.(1987)。The Psychology of Learning Mathematics。Hillsdale, New Jersey:Lawrence Erlbaum Associates。
3.
Mason, J.、Johnston-Wilder, S.(2004)。Fundamental Constructs in Mathematics Education。Routledge Falmer。
4.
Martin, M. O.、Mullis, I. V. S.、Foy, P.、Stanco, G. M.(2012)。TIMSS 2011 international results in science。Chestnut Hill, MA:TIMSS & PIRLS International Study Center, Boston College。
5.
American Association for the Advancement of Science(1990)。Project 2061: Science for all Americans。New York, NY:Oxford University Press。
6.
Lakatos, Imre(1976)。Proofs and Refutations: The Logic of Mathematical Discovery。Cambridge。
7.
Popper, Karl R.(1972)。Objective knowledge: An evolutionary approach。Oxford University Press。
8.
American Association for the Advancement of Science(1993)。Benchmarks for scientific literacy: Project 2061。New York, NY:Oxford University Press。
9.
Baroody, A. J.、Coslick, R. T.(1993)。Problem solving, reasoning, and communication, K-8: Help children think mathematically。New York, NY:Macmillan Publishing Company。
10.
Mason, J.、Burton, L.、Stacey, K.(2010)。Thinking mathematically。Pearson Education Limited。
11.
National Council of Teachers of Mathematics(2000)。Principles and Standards for School Mathematics。National Council of Teachers of Mathematics。
12.
Patton, Michael Quinn(1987)。How to use qualitative methods in evaluation。Sage Publications。
13.
Fischbein, E.(1987)。Intuition in science and mathematics: An educational approach。Dordrecht:D. Reidel。
14.
Davis, P. J.、Hersh, R.、Marchisotto, E. A.(1995)。The Mathematical Experience。Birkhäuser。
15.
Vygotsky, L. S.(1978)。Mind and society: The development of higher psychological processes。Cambridge, MA:Harvard University Press。
16.
Ausubel, D. P.(1968)。Educational psychology: A cognitive view。New York:Holt, Rinehart & Winston。
17.
Polya, G.(1954)。Mathematics and plausible reasoning, Volume II: Patterns of plausible inference。Princeton, NJ:Princeton University Press。
18.
National Council of Teachers of Mathematics(1989)。Curriculum and evaluation standards for school mathematics。Reston, VA:National Council of Teachers of Mathematics。
19.
Yin, Robert Kuo-Zuir(2009)。Case Study Research: Design and Methods。Sage Publications。
20.
Strauss, Anselm L.、Corbin, Juliet M.(1990)。Basics of qualitative research: Grounded theory procedure and techniques。Sage。
圖書論文
1.
Ernest, P.(1995)。The one and the many。Constructivism in education。Hillsdale, N. J.:Lawrence Erlbaum Associates, Inc.。
2.
Lakatos, I.(1978)。A renaissance of empiricism in the recent philosophy of mathematics?。Mathematics, science and epistemology。New York, NY:Press Syndicate of the University of Cambridge。
3.
Adler, J.、Lerman, S.(2003)。Getting the description right and making it count: Ethical practice in mathematics education research。Second international handbook of mathematics education。Dordrecht:Kluwer。
4.
Cobb, P.(2000)。The importance of a situated view of learning to the design of research and instruction。Multiple perspectives on mathematics teaching and learning。Westport, CT:Ablex。
5.
Dörfler, W.(1991)。Forms and means of generalization in mathematics。Mathematical knowledge: Its growth through teaching。Dordrecht:Kluwer。
6.
Mason, J.(2002)。Generalisation and algebra: Exploiting children's powers。Aspects of teaching secondary mathematics: Perspectives on practice。London:Routledge Falmer。
7.
Wertsch, J. V.、del Rίo, P.、Alvarez, A.(1995)。Socioculural Studies: History, Action, and Mediation。Sociocultural Studies of Mind。Cambridge University Press。
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