簡易檢索 / 詳目顯示

研究生: 吳依芳
論文名稱: 建模教學活動對國二學生學習線型函數概念之影響
指導教授: 曹博盛
Tsao, Po-Son
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2003
畢業學年度: 91
語文別: 中文
論文頁數: 231
中文關鍵詞: 概念發展線型函數建模教學傳統教學數學學習態度
英文關鍵詞: modelling
論文種類: 學術論文
相關次數: 點閱:316下載:86
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 本研究主要目的是以「線型函數」單元為主題,探討「建模教學方式」與「傳統教學方式」兩種教學,對學生學習線型函數概念以及數學學習態度的影響。
    研究設計是採準實驗研究法。研究對象為台北市某國中兩個國二班級,分派一班為實驗班,進行建模教學活動,對照班則進行傳統教學課程。建模教學活動是以Lesh等人(2002)所建立的「模型發展序列」為架構設計而成;傳統教學是依照現行國民中學數學課本第三冊所呈現的內容順序進行。
    另外依據Sfard(1991)所提出的概念發展層次:「內化」、「壓縮」、「物化」,設計二元一次方程式測驗卷(前測)與線型函數測驗卷(後測及延後測),來安置學生在教學前、後與經過一段時間後(約莫一個月)的線型函數概念層次,以分析學生概念改變及保留情形。並於教學前、後實施數學學習態度問卷前、後測,以了解學生學習數學態度的改變情況。
    本研究主要發現如下:
    1.經過教學後,實驗班學生概念層次改變的人數較對照班學生多,且有達α=.05顯著水準。
    2.實驗班在前、後測中,物化層次人數增加的幅度比對照班大,建模教學方式對學生概念提升至物化層次較有幫助。
    3.經過一段時間後,實驗班概念層次退階的人數比對照班少,接受建模教學方式的學生概念保留的程度較接受傳統教學方式的學生高。
    4.實驗班學生在「學習數學的信心」部分分數進步的人數多於對照班,且有達α=.05顯著水準,實驗班的學生學習數學的信心比對照班增加較多。

    第壹章 緒論………………………………………………………………1 第一節 問題背景與動機…………………………………………………1 第二節 研究目的與研究問題……………………………………………6 第三節 理論架構…………………………………………………………7 第四節 名詞界定…………………………………………………………22 第貳章 文獻探討…………………………………………………………24 第一節 建模教學方式的理論基礎………………………………………24 第二節 建模教學方式與線型函數表徵概念學習………………………36 第三節 學習態度與動機…………………………………………………41 第四節 概念發展理論……………………………………………………45 第參章 研究方法…………………………………………………………50 第一節 研究設計…………………………………………………………50 第二節 研究對象…………………………………………………………53 第三節 研究資源與工具…………………………………………………55 第四節 研究步驟與過程…………………………………………………67 第五節 研究限制…………………………………………………………70 第肆章 分析與討論………………………………………………………71 第一節 建模教學方式對學生概念學習之影響…………………………71 第二節 建模教學方式對學生各表徵作答情況之影響………………108 第三節 建模教學方式對學生學習態度之影響………………………167 第伍章 結論與建議 ……………………………………………………183 第一節 結論……………………………………………………………183 第二節 檢討與建議……………………………………………………189 參考書目……………………………………………………………………197 中文部分……………………………………………………………………197 西文部份……………………………………………………………………199 附錄…………………………………………………………………………205 附錄一:建模教學活動教案………………………………………………205 附錄二:水荒相關報導……………………………………………………208 附錄三:活動二學習單……………………………………………………210 附錄四:活動四學習單……………………………………………………215 附錄五:二元一次方程式概念測驗卷……………………………………220 附錄六:線型函數概念測驗卷……………………………………………222 附錄七:線型函數概念延後測驗卷………………………………………224 附錄八:數學學習態度問卷前測…………………………………………226 附錄九:實驗班數學學習態度問卷後測…………………………………228 附錄十:回饋單……………………………………………………………231

    中文部分
    1.Gardner, H.(1996),超越教化的心靈(陳瓊森、汪益譯)。台北,遠流出版事業股份有限公司。(原文出版於1991)
    2.Skemp, R. R.(1995a),智性學習(許國輝譯)。香港,公開進修學院出版社。(原文出版於1989)
    3.Skemp, R. R.(1995b),數學學習心理學(陳澤民譯)。台北,九章出版社。(原文出版於1987)
    4.Vygosky, L. S.(1998),思維與語言(李維譯)。台北,桂冠出版社。(原為俄文,出版於1934,此為英文翻譯本)
    5.丁斌悅(民91),國二學生學習線型函數時的概念表徵發展研究。國立台灣師範大學數學研究所碩士論文。
    6.王明慧(民85),國一數學科活潑化教學模式對提升學習動機與班級學習氣氛之實驗研究。國立高雄師範大學數學研究所碩士論文。
    7.沈繼紅(民85),數學建模。哈爾濱工程大學,新華書店。
    8.吳明隆、蘇耕役(民84),國民小學學生控制信念、重要他人態度知覺與數學焦慮、數學態度及數學成就關係之研究。初等教育學刊,4,頁181-210。
    9.吳玫瑤(民90),教學對高中生學習函數概念的影響。國立台灣師範大學數學研究所碩士論文。
    10.吳淑琳(民90),國中生線型函數概念發展之個案研究。國立台灣師範大學數學研究所碩士論文。
    11.林文俊(民91),線型函數概念在國中數學課程中發展的脈絡。國立台灣師範大學數學研究所碩士論文。
    12.林生傳(民83),教育心理學。台北,五南圖書出版公司。
    13.林星秀(民90),高雄市國二函數課程GSP輔助教學成效之研究。國立高雄師範大學數學研究所碩士論文。
    14.林寶山(民80),教學原理。台北,五南圖書出版公司。
    15.邱津芳(民79),國二資優生線型函數概念之研究。國立彰化師範大學科學教育研究所碩士論文。
    16.姚如芬(民82),高雄地區高中一年級學生數學學習態度與其數學學習成就之相關研究。國立高雄師範大學數學研究所碩士論文。
    17.孫文先、陳碧真【編】(民71),簡明數學百科全書。台北,九章出版社。
    18.高毓婷(民90),多元評量對國中數學學習的影響與研究。國立台灣師範大學數學研究所碩士論文。
    19.教育部(民91),國民中小學九年一貫課程暫行綱要。台北,教育部。
    20.陳盈言(民90),國二學生變數概念的成熟度對其函數概念發展的影響。國立台灣師範大學數學研究所碩士論文。
    21.陳英娥(民81),電腦輔助教學在國中數學科學習成效之研究。國立高雄師範大學數學教育研究所碩士論文。
    22.國立編譯館【主編】(民91a),國民中學數學(第三冊)。台北,國立編譯館。
    23.國立編譯館【主編】(民91b),國民中學數學教師手冊(第三冊)。台北,國立編譯館。
    24.張靜嚳(民85),建構教學:採用建構主義,如何教學?建構與教學,7,頁13-22。
    25.張春興(民81),張氏心理學辭典。台北,東華書局。
    26.葉倩亨(民87),建構取向教學在國中一年級數學課程之實驗研究。國立政治大學教育研究所碩士論文。
    27.鄭維誠(民91),線型函數的學習對國二學生變數概念發展的影響。國立台灣師範大學數學研究所碩士論文。
    28.謝豐瑞、陳材河(民86),函數的一生。科學教育月刊,第199期,頁34-43。
    29.戴仁欽(民87),建立模型教學法對學生概念學習與計算解題之影響。國立台灣師範大學科學教育研究所碩士論文。
    30.羅汝惠(民82),台灣南區國中一年級數學科解題導向教學法與傳統教學法教學成效之比較研究。國立高雄師範大學數學教育研究所碩士論文。
    西文部分
    1.Abrams, P. J. (2001). Teaching Mathematical Modeling and the Skills of Representation. In A. A. Cuoco, & F. R. Curcio, (2001 yearbook Eds.), The Roles of Representation in School Mathematics, pp. 173-185. Reston, Va.: NCTM.
    2.Ainsworth, S. E., Bibby, P. A., & Wood, D. J. (1998). Analysing the costs and benefits of multi-representational learning environments. In M. W. van Someren, P. Reimann, H. P. A. Boshuizen, & T. de Jong, (Eds.), Learning with Multiple Representations, pp. 120-134. Oxford, U. K.: Elsevier Science.
    3.Burghes, D. H., & Borrie, M. S. (1979). Mathematical modelling:a new approach to teaching applied mathematics. Physics Education, Vol. 14, pp. 82-86.
    4.Clement, L. L. (2000). What Do Students Really Know about Functions? Mathematics Teacher, Vol. 94, No. 9, pp. 745-748.
    5.Coulombe, W. N., & Berenson, S. B. (2001). Representation of patterns and functions tools for learning. In A. A. Cuoco, & F. R. Curcio, (2001 yearbook Eds.), The Roles of Representation in School Mathematics, pp. 173-185. Reston, Va.: NCTM.
    6.Dreyfus, T., & Eisenberg, T. (1982). Intuitive functional concepts: A baseline study on intuitions. Journal for Research in Mathematics Education, 13(5), pp.360-380.
    7.Even, R. (1990). Subject matter knowledge for teaching and the case of function. Educational Studies in Mathematics, 21, pp. 521-544.
    8.Friedlander, A., & Tabach, M. (2001). Promoting multiple representations in algebra. In A. A. Cuoco, & F. R. Curcio, (2001 yearbook Eds.), The Roles of Representation in School Mathematics, pp. 173-185. Reston, Va.: NCTM.
    9.Galbraith, P. L., & Clatworthy, N. J. (1990). Beyond Standard Models- Meeting the Challenge of Modelling. Educational Students in Mathematics, 21, pp. 137-163.
    10.Halloun, I., & Hestenes, D. (1987). Modeling instruction in mechanics. American Journal of Physics, 55(5), pp. 455-462.
    11.Halloun, I. (1996). Schematic Concepts for Schematic Models of the Real World: The Newtonain Concept of Force. Science Education, Manuscript No. 6205, Draft II, January 5, 1997.
    12.Hestenes, D., Wells, W., & Swackhamer, G. (1992). Force Concept Inventory. The Physics Teacher, 30, pp. 141-158.
    13.Izsák, A. (2003). ” We want a statement that is always true”: Criteria for good algebraic representations and the development of modeling knowledge. Journal for Research in Mathematics Education, 34(3), pp. 191-227.
    14.Janvier, C. (1987a). Representation and Understanding: The Notion of Function as an Example. In C. Janvier, (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, pp. 67-71. New Jersey, Lawrence Erlbaum Associates, Inc.
    15.Janvier, C. (1987b).Translations processes in mathematics education. In C. Janvier, (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, pp. 27-32. New Jersey, Lawrence Erlbaum Associates, Inc.
    16.Kaput, J. J. (1989). Linking representations in the symbol systems of Algebra. In S. Wagner, & C. Kieran , (Eds.), Research issues in the learning and teaching of Algebra, pp. 167-194.
    17.Lange, J. D. (1996). Using and Applying Mathematics in Education. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick,& C. Laborde, (Eds.), International Handbook of Mathematics Education, pp. 49-98. Kluwer Academic Publishers.
    18.Larnarus, M. (1974). Mathophobia: Some personal speculations. National Elementary Principal, 53, pp. 16-22.
    19.Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2002). Model Development Sequences. In H. Doerr,& R. Lesh, (Eds.), Beyond constructivism: models and modelling perspective on mathematical problem solving, learning and teaching. Mahwah, N.J.: Lawrence Erlbaum.
    20.Lovell, K. (1971). Some aspects of the growth of the concept of function. In M. F. Rosskopf, L. P. Steffe, & S. Taback, (Eds.), Piaget’s cognitive-development research and mathematical education, pp.12-33. Washington, DC: National Council of Teachers of Mathematics.
    21.Malone, T. W., & Lepper, M. R. (1987). Making learning fun: A taxonomy of insrinsic motivations for learning. In R. E. Snow, & M. J. Farr, (Eds.), Aptitude, Learning, and Instruction: Volume 3: Conative and Affective Process Analyses, pp. 223-253. Hillsdale, NJ: Lawrence Erlbaum.
    22.Markovits, Z. (1982). Understanding of the concept of function among grade 9 students. Unpublished master’s thesis, Weizmann Institute, Rehovot, Israel.
    23.Markovits, Z., Eylon, B., & Bruckheimer, M. (1986). Functions Today and Yesterday. For the Learning of Mathematics, Vol. 6, No. 2, pp. 18-28.
    24.Markovits, Z., Eylon, B., & Bruckheimer, M. (1988). Difficulties Students Have with the Function Concept. In A. F. Coxford, (1988 yearbook Ed.), The ideas of algebra, K-12, pp. 43-60. University of Michigan.
    25.Mcleod, D. B. (1992). Research on affect in mathematics education: a reconceptualization. In D. A. Grouws, (Ed.), Handbook of Research on Mathematics Teaching and Learning, pp. 575-596. N. Y.: Macmillan.
    26.Meyer, M. R. (2001). Representation in Realistic Mathematics Education. In A. A. Cuoco, & F. R. Curcio, (2001 yearbook Eds.), The Roles of Representation in School Mathematics, pp. 173-185. Reston, Va.: NCTM.
    27.National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston, Va.: NCTM, 2000.
    28.Niss, M. (1987). Applications and Modelling in the Mathematics Curriculum. International Journal of Mathematical Education in Science and Technology, Vol. 18, No. 4, pp. 487-505.
    29.Pirie, S. E., & Kieren, T. (1989). A Recursive Theory of Mathematical Understanding. For the learning of mathematic, 9(3), pp. 7-11.
    30.Pirie, S. E., & Kieren, T. (1991a). The Characteristics of the Growth of Mathematical Understanging. Paper presented at the meeting of AERA, Chicago, IL.
    31.Pirie, S. E., & Kieren, T. (1991b). Recursion and the Mathematical Experience. In L. P. Steffe (Ed), Epistemological Functions of Mathematical Experience, pp. 78-101. New York: Springer Verlag.
    32.Pirie, S. E., & Kieren, T. (1994). Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It ? Educational Studies in Mathematics, 26, pp. 165-190.
    33.Renshaw, P. (1996). A sociocultural view of the mathematics education of young children. In H. Mansfield, N. A. Pateman, & N. Bednarz et al. (Eds.), Mathematics for Tomorrow’s Young Children, pp. 59-78. Kluwer Academic Publishers.
    34.Reynolds, A. & Wheatley, G. (1996). How do social interaction among children contribute to learnig? In H. Mansfield, N. A. Pateman, & N. Bednarz et al. (Eds.), Mathematics for Tomorrow’s Young Children, pp. 59-78. Kluwer Academic Publishers.
    35.Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19(6), pp. 551-554.
    36.Salomon, G., & Globerson, T. (1987). Skills may not be enough: The role of mindfulness in learning and transfer. Internation Journal of Educational Research, 11(6), pp. 626-637.
    37.Schwarz, B.B., & Hershkowitz, R. (1999). Prototypes: Brakes or Levels in Learning the Function Concept? The Role of Computer Tools. Journal for Research in Mathematics Education, Vol. 30, No. 4, pp.362-389.
    38.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, pp.1-36.
    39.Sigurdson, S. E., & Olson A. T. (1992). Teaching mathematics with meaning. Journal of Mathematical Behavior, 11, pp. 37-57.
    40.Steffe, L., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory and application. New York, NY: Praeger.
    41.Swetz, F. (1989). When and How Can We Use Modeling? Mathematics Teacher, December 1989, pp. 722-726.
    42.Thomas, D. (1975). The concept of function. In M. F. Rosskopf, (Ed.), Children’s mathematical concepts: Six Piagetian studies in mathematics education. New York: Teachers College Press.
    43.Treffers, A. (1987). Framework for Instruction Theory. In A. Treffers, ( Ed.), Three Dimensions, pp.239-296. Netherlands: D. Reidel.
    44.Treffers, A. (1991). Didactical background of a mathematics program for primary education. In L. Streefland et al. (Ed.), Realistic Mathematics Education in Primary School, pp. 21-56. Freudenthal Institute, Utrecht.
    45.Wheatley, G. (1991). Constuctivist perspectives on mathematics and science learning. Science Education, 75(1), p. 9-12.
    46.Yerushalmy, M., & Shternberg, B. (2001). Charting a Visual Course to the Concept of Function. In A. A. Cuoco, & F. R. Curcio, (2001 yearbook Eds.), The Roles of Representation in School Mathematics, pp. 173-185. Reston, Va.: NCTM.

    QR CODE