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題名：以 van Hiele 理論探討圖形樣式思考層次之研究
書刊名：教育研究集刊
作者：馬秀蘭
作者(外文)：Ma, Hsiu-lan
出版日期：2008
卷期：54:1
頁次：頁49-85
主題關鍵詞：van Hiele；思考層次；圖形樣式；Thinking levels；Pictorial patterns
原始連結：連回原系統網址new window
相關次數：
  • 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:14
  • 點閱點閱:45
本文旨在將van Hiele思考層次應用到數學的圖形樣式解題上。研究者修正了Fuys、Geddes與Tischler（1988）針對van Hiele幾何層次所提出的部分行為描述，建立國小高年級學童解決圖形樣式題之思考層次行為，並依21個有關學生實際解決圖形樣式題表現之原案，嘗試擴展van Hiele理論之應用範疇至van Hiele圖形樣式思考層次。研究發現，高年級生對圖形樣式規律的思考層次行為符合van Hiele之理論，學生圖形樣式之思考仍可分派至某一個層次；其中因思考深度不同，層次二及三再細分為二A、二B及三A、三B。學童之樣式思考層次亦具有次序性、內因性與外因性，以及語言性之特性。學生若能用幾何圖形結構之間的關係來辨認樣式，則有助於圖形樣式思考層次的提升及代數知識的建造。此探索性研究之結果將提供給未來有嚴謹設計之後續研究者進行大樣本之檢測。
The purpose of this paper is to discuss the application of van Hiele’s thinking lev-els to problem-solving of pictorial patterns. The researcher modified some of the van Hiele level descriptors described by Fuys, Geddes, & Tischler (1988) and established the van Hiele level descriptors regarding 21 upper graders solving pictorial-pattern problems. The conclusions drawn from this study are as follows. (1) The students’ thinking on pictorial patterns fitted in with van Hiele’s theorem and could be classified into certain levels. (2) According to the different thinking degrees of the students, level 2 and 3 were divided into 2A, 2B and 3A, 3B, respectively. (3) Four properties were shown in the thinking levels: sequential, intrinsic and/or extrinsic, and linguistic. (4) If students could use the relations between the structures of figures to identify patterns, they were able to advance their thinking levels of pictorial patterns and to construct algebraic knowledge. It is hoped that the results of this explorary research will contribute to a more rigid study design with a larger sample in the future.
期刊論文
1.馬秀蘭(20040300)。數學乘除問題情境發展之研究--以BBS為管理。科學教育學刊，12(1)，53-81。new window  延伸查詢new window
2.左台益、梁勇能(20011000)。國二學生空間能力與van Hiele幾何思考層次相關性研究。師大學報．科學教育類，46(1/2)，1-20。  延伸查詢new window
3.Mistretta, R. M.(2000)。Enhancing Geometric Reasoning。Adolescence，35(138)，365-379。  new window
4.謝貞秀、張英傑(20030900)。國小三四年級平面圖形概念之探究。國立臺北師範學院學報. 數理科技教育類，16(2)，97-133。new window  延伸查詢new window
5.Clements, D. H.、Swaminathan, S.、Hannibal, M. A. Z.、Sarama, J.、Swaminthan, S.(1999)。Young children's concepts of shape。Journal for Research in Mathematics Education，20(2)，192-212。  new window
6.Mayberry, J. W.(1983)。The Van Hiele Levels of Geometric Thought in Undergraduate Preservice Teachers。Journal for Research in Mathematics Education，14(1)，58-69。  new window
7.吳德邦、馬秀蘭、藍同利(2006)。探究國小視覺型與觸覺型兒童在繪製三角形活動之概念分析。臺中教育大學學報：數理科技類，20(2)，99-138。new window  延伸查詢new window
8.De Block-Docq, C.(1994)。Forms of Mathematical Thought of Twelve-year-old Students at Tiling Problems。Educational Studies in Mathematics，27(2)，165-189。  new window
9.盧銘法(1999)。國小學童四邊形幾何概念之分析。中師數理學報，3(1)，5-1。  延伸查詢new window
10.Herbert, K.、Brown, R. H.(1997)。Patterns as Tools for Algebraic Reasoning。Teaching Children Mathematics，3(6)，340-344。  new window
11.Naylor, M.(2002)。Who Am I?。Teaching PreK-8，32(4)，40-41。  new window
12.Malloy, C. E.(1999)。Perimeter and Area through the Van Hiele Model。Mathematics Teaching in the Middle School，5(2)，87-90。  new window
13.Jamime, A.、Gutierrez, A.(1995)。Connecting Research to Teaching: Guidelines for Teaching Plane Isometries in Secondary School。Mathematics Teacher，88(7)，591-597。  new window
會議論文
1.Ma, H. L.(2005)。Bulletin Board Systems--Another Supporting Channel for Helping Students Work on Mathematics。International Conference on Education, Redesigning Pedagogy: Research, Policy, Practice，(會議日期: 2005/05/30-06/01)。Singapore：National Institute of Education, Nanyang Technological University。  new window
2.吳德邦、李懿芳、馬秀蘭(2006)。立體幾何思考層次測驗編製歷程之研究584-608。  延伸查詢new window
3.吳德邦(1999)。臺灣中部地區國小學童Van Hiele幾何思考層次之研究－筆試部分。0。35-66。  延伸查詢new window
4.Wu, D. B.、Ma, H. L.(2006)。The Distributions of Van Hiele Levels of Geometric Thinking among 1st through 6th Graders。Prague (Praha), Czech。416-429。  new window
5.Wu, D. B.、Ma, H. L.、Hsieh, K. J.、Li, Y. F.(2007)。A Study of the Concept of Solid Geometry of Elementary Students from the 4th Grades to the 6th Grades in the General Region of Taiwan。Seoul, South Korea。295-295。  new window
6.Ma, H. L.(2007)。The Potential of Patterning Activities to Generalization。Seoul, South Korea。225-232。  new window
7.劉好(1993)。國小數學科新課程中幾何教材的設計。嘉義市。69-79。  延伸查詢new window
8.Ma, H. L.、Wu, D. B.(2006)。The Role of Pattern in the Algebraic Concept Learning via Internet。Chiang Mai, Thailand。143-150。  new window
研究報告
1.Usiskin, Zalman(1982)。Van Hiele Levels and Achievement in Secondary School Geometry。University of Chicago, Department of Education。  new window
2.洪萬生(2003)。青少年的立體幾何概念發展研究。臺北市。  延伸查詢new window
3.吳德邦(2004)。使用Van Hiele五階段學習模式開發九年一貫課程第一階段圖形與空間教材教法之詮釋性研究。臺中市。  延伸查詢new window
學位論文
1.Golinskaia, L.(1997)。Van Hiele theory in Russian and United states geometry curricula(博士論文)。Columbia University，Columbia。  new window
2.Land, J. E.(1991)。Appropriateness of the Van Hiele Model for Describing Students' Cognitive Processes on Algebra Tasks as Typified by College Students' Learning of Functions，0。  new window
3.Lee, W. I.(1999)。The Relationship between Students' Proof-writing Ability and Van Hiele Levels of Geometric Thought in a College Geometry Course (College Students)，Colorado。  new window
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。  new window
2.Penrose, Roger(1989)。The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics。Oxford University Press。  new window
3.Fuys, D.、Geddes, D.、Tischler, R.(1988)。The Van Hiele Model of Thinking in Geometry among Adolescents。Reston, VA：The National Council of Teachers of Mathematics, Inc.。  new window
4.林軍治(1992)。兒童幾何思考之van Hiele水準分析研究--VHL、城鄉、年級、性別、認知型式與幾何概念理解及錯誤概念之關係。書恒出版社。  延伸查詢new window
5.Miles, Matthew B.、Huberman, A. Michael、Newman, G.(1994)。Qualitative data analysis: an expanded sourcebook。Sage Publications。  new window
6.van Hiele, Pierre M.(1986)。Structure and Insight: A Theory of Mathematics Education。Academic Press。  new window
7.Lincoln, Yvonna S.、Guba, Egon G.(1989)。Fourth generation evaluation。Sage Publications。  new window
8.葉重新(2001)。教育研究法。台北：心理。  延伸查詢new window
9.Shorrocks-Taylor, D.、Threlfall, J.、Hargreaves, M.、Frobisher, L.(1999)。Children's Strategies with Linear and Quadratic Sequences。Pattern in the Teaching and Learning of Mathematics。London, UK。  new window
10.Biggs, E.、Shaw, K.(1985)。Maths Alive!。Maths Alive!。London, UK。  new window
11.Orten, A.、Orten, J.(1999)。Pattern and the Approach to Algebra。Pattern in the Teaching and Learning of Mathematics。London, UK。  new window
12.English, L. D.、Warren, E. A.(1999)。Introducing the Variable through Pattern Exploration。Algebraic Thinking, Grades K-12。Reston, VA。  new window
13.Assessment of Performance Unit。Mathematical Development: A Review of Monitoring in Mathematics 1978 to 1982。Mathematical Development: A Review of Monitoring in Mathematics 1978 to 1982。Slough, UK。  new window
14.Mason, J.、Graham, A.、Pimm, D.、Gowar, N.(1985)。Routes to/Roots of Algebra。Routes to/Roots of Algebra。Milton Keynes, UK。  new window
15.Zimmermann, W.、Cunningham, S.(1991)。What Is Mathematical Visualization?。Visualization in Teaching and Learning Mathematics。Washington, DC。  new window
圖書論文
1.Crowley, M. L.(1987)。The van Hiele model of the development of geometric thought。Learning and teaching geometry, k-12, 1987 Yearbook of the National Council of Teachers of Mathematics。NCTM。  new window
2.Orten, J.、Orten, A.、Roper, T.(1999)。Pictorial and Practical Contexts and the Perception of Pattern。Pattern in the Teaching and Learning of Mathematics。London：Cassell。  new window
 
 
 
 
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