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引文資料
題名:
姿勢、言辭表徵與代數思考之研究
書刊名:
教育學報
作者:
陳嘉皇
/
梁淑坤
作者(外文):
Chen, Chia-huang
/
Leung, S. Shuk-kwan
出版日期:
2015
卷期:
43:1
頁次:
頁103-127
主題關鍵詞:
一般化
;
代數思考
;
姿勢
;
圖形樣式
;
Generalization
;
Algebraic thinking
;
Gesture
;
Graphic pattern
原始連結:
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相關次數:
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:
1
共同引用:
6
點閱:8
本研究旨在探索學生在圖形樣式作業之一般化的表現,理解他們:如何利用姿勢與言辭對一般化各階段物件辨識出共通性;如何對樣式物件進行結構關係的連結;如何對一般化不同算式的等價進行認知;對代數的演變持何種觀點。本研究採用個案研究法進行探究,樣本來自台灣南部某公立小學兩名六年級學生;利用攝影、訪談與寫作方式蒐集資料,並採質性方法予以分析。研究發現,學生於:(1)發想階段運用視覺化圖形要素、比對分析物件變化的數量與配合項次數字形成規則,配合圖像的、直證的與比喻的姿勢知覺物件產出的共通性特質。(2)連結階段大多運用直證的和比喻的姿勢與語意做連結,配合數字、符號算式等對問題結構進行關係的連結。(3)以比喻的姿勢配合運算結果的驗證、算式結構的比對、物件關係的比對等策略,以作認知不同算式等價的基礎。(4)對一般化路徑中代數概念的演變,以指示樣式物件的數量、圖形項次的數字序號、與圖形結構關係的未知數等觀點持續發展。作者並針對學生一般化歷程代數概念發展與符號指示間的關係、多元表徵應用等議題提出建議,以作精進學生代數思考的教學參考。
以文找文
This study investigated how students generalize graphic patterns, aiming to understand how they utilize words and gestures at each phase of generalization, how they identify links between problems and recognize the equivalence of generalized equations, and how their understanding of algebra evolves. We conducted a case study of two sixth-grade students from a public elementary school in southern Taiwan, using video recordings, interviews and writing to collect data, which was then analyzed qualitatively. The study found that: (a) In the concept phase, students form rules by using visual graphics to compare changes in objects and item numbers, in accordance with the common elements of iconic, deictic and metaphoric gestures and perceptions. (b) In the linking phase, most students use deictic and metaphoric gestures and semantics, along with numbers and equations, to identify relationships in the problem structure. (c) Students employ strategies such as verifying metaphoric and computational outcomes, and comparing equation structure and object relationships, to comprehend the equivalence of different equations. (d) Students continue to develop their understanding of algebraic concepts based on item numbers, numbering of symbols, and the unknowns of relationship diagrams. Recommendations on diverse permeation and the relationship between development of algebraic concepts and symbol indication were provided. They can serve as references in advancing algebraic thinking.
以文找文
期刊論文
1.
Alibali, M. W.、Kita, S.、Young, A. J.(2000)。Gesture and the process of speech production: We think, therefore we gesture。Language & Cognitive Processes,15(6),593-613。
2.
陳嘉皇(20130300)。國小六年級學生運用一般化基模進行圖形規律問題解題之研究。教育科學研究期刊,58(1),59-90。
延伸查詢
3.
Carraher, D. W.、Schliemann, A. D.、Brizuela, B. M.、Earnest, D.(2006)。Arithmetic and algebra in early mathematics education。Journal for Research in Mathematics Education,37(2),87-115。
4.
Swafford, J. O.、Langrall, C. W.(2000)。Grade 6 students' pre-instructional use of equations to describe and represent problem situations。Journal for Research in Mathematics Education,31(1),89-112。
5.
Reynolds, F. J.、Reeve, R. A.(2002)。Gesture in collaborative mathematics problem-solving。Journal of Mathematical Behavior,20(4),447-460。
6.
Alibali, M. W.、DiRusso, A. A.(1999)。The function of gesture in learning to count: More than keeping track。Cognitive Development,14(1),37-56。
7.
Cai, J.、Knuth, E. J.(2005)。Introduction: The development of students' algebraic thinking in earlier grades from curricular, instructional, and learning perspective。Zentralblatt für Didaktik der Mathematik [International Journal on Mathematics Education,37(1),1-4。
8.
Cai, J.、Lester, F. A. Jr.(2005)。Solution representations and pedagogical representations in Chinese and U.S. classrooms。Journal of Mathematical Behavior,24(3/4),221-237。
9.
Dörfler, W.(2008)。En route from patterns to algebra: Comments and reflections。ZDM,40(1),143-160。
10.
Goldin, G. A.(1998)。Representational systems, learning, and problem solving in mathematics。Journal of Mathematical Behavior,17(2),137-165。
11.
Goldin-Meadow, S.、Singer, M. A.(2003)。From children's hands to adults' ears: Gesture's role in the learning process。Developmental Psychology,39(3),509-520。
12.
Parrill, F.、Sweetser, E.(2004)。What we mean by meaning: Conceptual integration in gesture analysis and transcription。Gesture,4(2),197-219。
13.
Radford, L.(2010)。The eye as a theoretician: Seeing structures in generalizing activities。For the Learning of Mathematics,30(2),2-7。
14.
Rivera, F. D.(2010)。Visual templates in pattern generalization activity。Educational Studies in Mathematics,73(3),297-328。
15.
Duval, R.(2006)。A cognitive analysis of problems of comprehension in a learning of mathematics。Educational Studies in Mathematics,61(1/2),103-131。
會議論文
1.
Blanton, M.、Kaput, J.(200204)。Developing elementary teachers' algebra "eyes and ears": Understanding characteristics of professional development that promote generative and self-sustaining change in teacher practice。The annual meeting of the American Educational Research Association。New Orleans, LA。
2.
Kieran, C.(199607)。The changing face of school algebra。8th International Congress on Mathematical Education。Sevilla, Spain。
3.
Radford, L.(2006)。Algebraic thinking and the generalization of patterns: A semiotic perspective。28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education。Mérida, Mexico:Universidad Pedagógica Nacional。2-21。
圖書
1.
Driscoll, Mark(1999)。Fostering algebraic thinking: A guide for teachers, grades 6-10。Portsmouth, New Hampshire:Heinemann。
2.
Goldin-Meadow, Susan(2003)。Hearing gesture: How our hands help us think。Cambridge, MA:Belknap Press of Harvard University Press。
3.
McNeill, David(2005)。Gesture and thought。Chicago, IL:University of Chicago Press。
4.
Kilpatrick, J.、Swafford, J.、Findell, B.(2001)。Adding it up: Helping children learn mathematics。Washington, DC:National Academy Press。
5.
Fauconnier, Gilles、Turner, Mark(2002)。The way we think: Conceptual blending and the mind's hidden complexities。New York, NY:Basic Books。
6.
教育部(2008)。國民中小學九年一貫課程綱要數學學習領域。台北:教育部。
延伸查詢
7.
National Council of Teachers of Mathematics(2000)。Principles and standards for school mathematics。Reston, Virginia:National Council of Teachers of Mathematics。
8.
Carpenter, T. P.、Franke, M. L.、Levi, L. W.(2003)。Thinking mathematically: Integrating arithmetic and algebra in elementary school。Portsmouth, NH:Heinemann。
圖書論文
1.
Presmeg, N. C.(1997)。Reasoning with metaphors and metonymies in mathematics learning。Mathematical reasoning: Analogies, metaphors, and images。Mahwah, NJ:Lawrence Erlbaum。
2.
Mason, J.(1996)。Expressing generality and roots of algebra。Approaches to algebra: perspectives for research and teaching。Dordrecht:Kluwer Academic Publishers。
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