研究生: |
張巧倪 Chang, Chiao-Ni |
---|---|
論文名稱: |
一元二次多項式配方法之數位學習環境設計與實作 |
指導教授: |
左台益
Tso, Tai-Yih |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2013 |
畢業學年度: | 101 |
語文別: | 中文 |
論文頁數: | 137 |
中文關鍵詞: | 配方法 、數位學習 、過程性技能 、結構性概念 |
英文關鍵詞: | completing the square, digital learning, process, structural |
論文種類: | 學術論文 |
相關次數: | 點閱:160 下載:24 |
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本研究目的在設計與實作配方法的數位學習環境,並探討使用不同數位學習環境下,學生自學效果之影響。實驗之操弄變項有兩個維度,分別為操作方式(觸控VS滑鼠)和教學指引(口說指引VS文字指引)。透過上述操弄變項分為四個實驗組,以檢驗不同數位學習環境下的學習效果。共81位八年級生參與此研究。本研究結果為量化分析和實作成品,其量化分析結果如下:
一、初學配方法或低程度的學生使用觸控操作,較有助於學習配方法之過程性技能,幫助學生強化心智表徵與外在表徵的鏈結。
二、已學過配方法或高程度的學生使用滑鼠操作,較有助於學習配方法之過程性技能和結構性概念。這些學生不需特別使用觸控操作建立過程性技能,相對的,學生使用滑鼠操作可更進一步的建立結構性概念。
三、低程度學生使用口說指引教學,較有助於學習配方法之過程性技能,降低學生無關的認知負荷,並產生有效的認知負荷。
四、高程度學生使用文字指引教學,較有助於學習配方法之過程性技能和結構性概念。這些學生除了有配方法之過程性技能,還可透過文句之前後脈絡,進一步建立結構性概念。
由上述結果可以得知,本研究設計之數位學習環境皆能幫助學生學習配方法。然而,如何讓低程度學生有結構性概念,而不只停留在過程性技能,還需要加入有效的教學策略,才能促使學生運用表徵做更深層的思考和互動,方能在配方法的數位學習環境中整合過程性技能與結構性概念。
一、中文文獻
左台益, 呂鳳琳, 曾世綺, 吳慧敏, 陳明璋 & 譚寧君(2011)。以分段方式降低任務複雜度對專家與生手閱讀幾何證明的影響。國立臺灣師範大學教育心理與輔導學系教育心理學報,43,291-314。
左台益 & 蔡志仁(2001)。高中生建構橢圓多重表徵之認知特性。科學教育學刊,9(3),281-297。
李盈賢(2006)。高雄市國二學生一元二次方程式迷思概念之研究(未出版之碩士論文)。高雄師範大學。
陳志全(2005)。國二學生「用配方法解一元二次方程式」單元錯誤類型分析之研究(未出版之碩士論文)。國立高雄師範大學。
二、英文文獻
Ainsworth, S. (2006). Deft: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183-198.
Babb, A. P. P. (2012). Incorporating the ipad2 in the mathematics classroom: Extending the mind into the collective. iJEP, 2(2), 23-29.
Bruner, J. (1966). Towards a theory of instruction. Belknap Press of Harvard University Press.
Dunham, P. H. & Dick, T. P. (1994). Research on graphing calculators. The Mathematics Teacher, 87(6), 40-445.
Graven, M. (2011). Mathematical learning opportunities for young learners with touch screen technology. Learning and Teaching Mathematics, 9(January), 43-45.
Gray, E. & Tall, D. (1991). Duality, ambiguity & flexibility in successful mathematical thinking. PME 15, 2, 72-79.
Gray, E. & Tall, D. (1992a). Success and failure in mathematics: Procept and procedure - a primary perspective. Workshop on Mathematics Education and Computers, 209-215.
Gray, E. & Tall, D. (1992b). Success and failure in mathematics: Procept and procedure - secondary mathematics. Workshop on Mathematics Education and Computers, 216-221.
Gray, E. & Tall, D. (1993). Success and failure in mathematics: The flexible meaning of symbols as process and concept. Mathematics Teaching, 142, 6-10.
Gray, E. & Tall, D. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 115-141.
Groves, S. (1994). Calculators: A learning environment to promote number sense.
Karadag, Z. & McDougall, D. (2009). Visual explorative approaches to learning mathematics. Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 5, 1630-1636.
Kilgore, K. E. & Capraro, M. M. (2010). A technology approach to teaching factorization. Journal of Mathematics Education, 3(2), 115-125.
Lesh, R., Post, T. & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. Hillsdale, NJ: Lawrence Erlbaum.
Mason, J. (1992). Doing and construing mathematics in screen-space. Paper presented at the the Fifteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). pp. Pages. University of Western Sydney: Hawkaid Conference Centre.
Mayer, R. E. (2009). Multimedia learning. Cambridge University Press.
Moyer, P. S. & Bolyard, J. J. (2002). Exploring representation in the middle grades: Investigations in geometry with virtual manipulatives. The Australian Mathematics Teacher, 58(1), 19-25.
Moyer, P. S., Bolyard, J. J. & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372-377.
NCTM (2000a). Illuminations. from http://illuminations.nctm.org/ActivitySearch.aspx.
NCTM (2000b). Principles and standards for school mathematics. Reston, VA: Author.
Oosterum, M. A. M. B.-v. (1990). Understanding of variables and their uses acquired by students in traditional and computer-intensive algebra. University of Maryland at College Park.
Paas, F. G. W. C. & Merriënboer, J. J. G. V. (1993). The efficiency of instructional conditions: An approach to combine mental effort and performance measures. The Journal of the Human Factors and Ergonomics Society, 35(4), 737-743.
Reed, J. (1998). Web resources design. from http://staff.argyll.epsb.ca/jreed/.
Rojano, T. (1996). Developing algebraic aspects of problem solving within a spreadsheet environment. (Ed.) Approaches to algebra, pp. 137-145. Kluwer Academic Publishers.
Segal, A. (2011 ). Do gestural interfaces promote thinking? Embodied interaction: Congruent gestures and direct-touch promote performance in math Columbia University. from http://hdl.handle.net/10022/AC:P:10390
Sfard, A.(1991)。On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin。Educational Studies in Mathematics,22(1),1-36。
Suh, J. & Moyer-Packenham, P. (2007). Developing students' representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155-173.
Sweller, J., van-Merrienboer, J. J. G. & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251-296.
Tall, D. (2004). The three worlds of mathematics. For the Learning of Mathematics, 23(3), 29-33.
Tall, D. (2007). Embodiment symbolism and formalism in undergraduate mathematics education. Paper presented at the Plenary at 10th Conference of the Special Interest Group of the Mathematical Association of America on Reasearch in Undergraduate Mathematics Education. pp. Pages. California, USA: San Diego.
Tall, D., Graya, E., Alia, M. B., Crowleya, L., DeMaroisa, P., McGowena, M. ,..., Yusofa, Y. (2001). Symbols and the bifurcation between procedural and conceptual thinking. Canadian Journal of Science, Mathematics and Technology Education, 1(1), 81-104.
Tall, D. & Mejia-Ramos, J. P. (2006). The long-term cognitive development of different types of reasoning and proof. Paper presented at the the Conference on Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. pp. Pages. Germany: Essen.
Thomas, M. O. J. & Hong, Y. Y. (2011). Representations as conceptual tools: Process and structural perspectives. Proceedings of The 25th Conference of the International Group for the Psychology of Mathematics Education, 257-264.
Tyng, K. S., Zaman, H. B. & Ahmad, A. (2011). Visual application in multi-touch tabletop for mathematics learning: A preliminary study. Proceedings of the Second international conference on Visual informatics: sustaining research and innovations - Volume Part I, 319-328.
Utah_State_University (1999). National library of virtual manipulatives. from http://nlvm.usu.edu/en/nav/vlibrary.html.
Yang, H., Liu, L., Xu, W. & Chandler, S. (2011). Ipod touch tutorial for 6th grade math. Society for Information Technology & Teacher Education International Conference 2011, 2281-2286.