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題名:表徵與國小學生代數思考之初探性研究
書刊名:教育研究集刊
作者:陳嘉皇 引用關係梁淑坤 引用關係
作者(外文):Chen, Chia-huangLeung, Shuk-kwan
出版日期:2014
卷期:60:2
頁次:頁1-40
主題關鍵詞:一般化代數思考表徵GeneralizationAlgebraic thinkingRepresentations
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(3) 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:3
  • 共同引用共同引用:12
  • 點閱點閱:49
本研究旨在透過不同表徵問題,檢驗理解學生一般化表現情形,依據表現顯示之難易度,解析學生一般化適用之表徵類型,並探索表徵可提供何種相關啟示來協助學生一般化。研究樣本為國小五、六年級學生,共423人,利用測驗調查及訪談方式蒐集資料,資料分析採量化與質性併陳方式進行。研究發現包括:一、六年級學生一般化的表現較五年級學生佳,且有顯著差異存在;二、學生在各問題的反應呈現以表格表徵的問題表現最佳,其次是文字與圖形表徵,再者為圖像表徵問題的表現,而數字表徵則最感困難;三、表格、圖形與文字表徵的問題可適用於學生一般化歷程發想、問題的理解、變數的辨識、結構關係的連結和發展;四、圖像與數字表徵問題可激發學生對變數關係的發展加以推理與臆測,形成規則進行解題。
This study provided various representation problems with which to evaluate students’ performance in generalization. The types of representation appropriate for generalization were determined according to the difficulty and characteristics of the representation problems. A total of 423 fifth and sixth grade students underwent generalization tests and interviews, the results of which were subjected to both quantitative and qualitative analysis. The results showed that sixth grade students significantly outperformed fifth grade students in generalization problems. In addition, students performed most favorably in table representation problems, followed by text, graphs, and pictorial representations. The students felt that numeric representation was the most difficult. We found that representation problems adopting tables, graphs, and text are suitable for thinking in the process of generalization problems, variable recognition, and the connection and development of structural relationships. Pictorial and numeric representations were shown to stimulate students to speculate about variable relationships and form rules with which to solve problems. We believe that the results of this study provide a valuable reference for researchers in terms of algebraic thinking and instructional development.
期刊論文
1.陳嘉皇(20070700)。學童「圖卡覆蓋」代數推理歷程之研究--以三個個案為例。國民教育研究學報,19,79-107。new window  延伸查詢new window
2.陳嘉皇(20060900)。國小五年級學童代數推理策略應用之研究:以「圖卡覆蓋」解題情境歸納算式關係為例。屏東教育大學學報,25,381-412。new window  延伸查詢new window
3.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。new window  延伸查詢new window
4.Earnest, D.、Balti, A. A.(2008)。Instructional strategies for teaching algebra in elementary school。Teaching Children Mathematics,14(9),518-522。  new window
5.Nathan, M. J.、Kim, S.(2007)。Pattern generalization with graphs and words: A cross-sectional and longitudinal analysis of middle school students' representational fluency。Mathematical Thinking and Learning,9(3),193-219。  new window
6.Steffe, L. P.(1992)。Schemes of action and operation involving composite units。Learning and Individual Differences,4(3),259-309。  new window
7.Friel, S. N.、Curcio, F. R.、Bright, G. W.(2001)。Making sense of graphs: Critical factors influencing comprehension and instructional implications。Journal for Research in Mathematics Education,32(2),124-158。  new window
8.Rivera, F. D.(2010)。Visual templates in pattern generalization activity。Educational Studies in Mathematics,73(3),297-328。  new window
9.Goldin, G. A.(1998)。Representational systems, learning, and problem solving in mathematics。The Journal of Mathematical Behavior,17(2),137-165。  new window
10.Koedinger, K. R.、Nathan, M. J.(2004)。The real story behind story problems: Effects of representations on quantitative reasoning。Journal of the Learning Science,13(2),129-164。  new window
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。  new window
2.Kaput, J.(1998)。Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the k-12 curriculum。Washington, DC:National Research Council, National Academy Press。25-26。  new window
圖書
1.教育部(2003)。國民中學九年一貫課程綱要--數學學習領域。臺北市:教育部。  延伸查詢new window
2.Kilpatrick, J.、Swafford, J.、Findell, B.(2001)。Adding it up: Helping children learn mathematics。Washington, DC:National Academy Press。  new window
3.National Council of Teachers of Mathematics(2000)。Principles and standards for school mathematics。Reston, Virginia:National Council of Teachers of Mathematics。  new window
圖書論文
1.Goldin, G. A.、Kaput, J. J.(1996)。A joint perspective on the idea of representation in learning and doing mathematics。Theories of mathematical learning。Mahwah, New Jersey:Erlbaum。  new window
2.Dreyfus, T.(1991)。Advanced mathematical thinking processes。Advanced mathematical thinking。Dordrecht:Kluwer。  new window
3.Goldin, G. A.(2003)。Representation in school mathematics: A unifying research perspective。A research companion to principle and standards for school mathematics。Reston, VA:The National Council of Teachers of Mathematics。  new window
4.Kieran, C.(1996)。The changing face of school algebra。Eighth international conference on mathematical education: Selected lectures。Seville, Spain:S.A.E.M. Thales。  new window
 
 
 
 
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