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研究生: 林恆理
論文名稱: 八位學生教師數學教學知識的個案研究:以無限概念為例
指導教授: 金鈐
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2006
畢業學年度: 94
語文別: 中文
論文頁數: 201
中文關鍵詞: 學生教師教師專業發展教師的數學教學知識無限概念
論文種類: 學術論文
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  • 本研究是以國立台灣師範大學數學系教材教法的課程為場景,透過問卷調查法,從其中一班38位修課學生中篩選出8位個案,進行為期一年的個案追蹤研究。本研究採用個案研究法,搭配問卷、訪談與教室觀察的方式,探討相關學生教師在學習教數學的第一年裡,數學教學知識的內涵與發展。透過分析數學層次和教學層次的知識,瞭解學生教師理解無限概念的深度、廣度與完全性,以及教學使用的問話、類比與操作性活動的表徵方式,並以Wenger (1998) 的實務社群(community of practice)理論作為個案數學教學知識發展的脈絡。

    研究結果顯示,個案學生教師的模擬教學與理想中的教學有相當的落差,他們有不同層次的迷失概念,可以進一步區分成「數學層次的迷思」、「教學層次的迷思」與「數學與教學層次的迷思」。此外,個案對於自己教學問題的察覺與反思,呈現出「沒察覺沒反思」、「有察覺沒反思」與「有察覺有反思」三種狀態。由於學生教師普遍無法精確掌握無限數學概念的內涵,因此,個人認為「精確性」應該可以作為「對基礎數學有深刻理解」(Ma, 1999)的第四個面向。培育活動中採用的案例教學,也對部分個案產生一定程度的影響,而學習型實務社群的功能雖然有部分的限制,但是仍有助於瞭解個案數學教學知識發展的脈絡。

    這個階段的研究結果反應出學生教師在學習教數學時的個別差異,接續的研究可以從瞭解迷思教學概念產生的原因、如何克服與修正這些迷思概念以及如何進一步促使學生教師產生更深層的察覺與反思等幾個方向著手。最終,希望所培育出的中學數學教師,不僅對數學內容有深刻的理解,也能適切地將其轉換成對於不同能力與背景的學生有意義、有效且合適的理解形式(Shulman, 1987)。

    The research is one-year case study on the students who participate the method course for secondary mathematics. Eight student cases from the thirty-eight participants were selected in terms of question survey, and followed by interview and classroom observation to understand the content and development of the student teachers’ pedagogical knowledge in mathematics in the process of learning to teach mathematics. By analyzing mathematical and pedagogical knowledge, the author tries to investigate the depth, broad and thoroughness of the concept of infinity of the eight student teachers, and the representation of teacher questioning, analogy and manipulatives used in microteaching. The theoretical context for situating their knowledge development is based on Wenger’s theory of community of practice.

    The results show that there were distinct differences between microteaching and ideal teaching among cases. They have misconceptions of mathematic and pedagogy. The eight cases also reflect three states of awareness, including no awareness and no reflection, awareness but no reflection, or awareness and reflection. Due to most of the student teachers could not understand fully the mathematical concept of infinity, the author adds a fourth element “accurateness” to the Ma’s notion of profound understanding of fundamental mathematics. The method course of the teacher education program seems to have potential influences on the cases, while the theory of learning community supports those cases to develop their pedagogical knowledge in mathematics.

    The study results reflects also some individual differences among the student cases when they are learning to teach, and the future research is expected to understand the causes and adjustments of the misconceptions, also to stimulate deeply the reflection and awareness of student teachers. Finally, the author also expects that the well–trained secondary mathematics teachers can not only understand profoundly mathematical content but also transform the content knowledge into forms that are pedagogically powerful and yet adaptive to the variations in ability and background presented by the students (Shulman, 1987)

    第一章 緒論...................1 第一節 研究動機...................1 第二節 研究目的...................7 第二章 文獻探討...................9 第一節 數學教師的專業發展...................9 第二節 數學教師的知識內涵...................21 第三節 無限的概念...................35 第四節 本研究的詮釋性架構...................44 第三章 研究方法...................47 第一節 研究場域與對象...................47 第二節 個案研究法...................52 第三節 研究設計...................55 第四節 資料分析...................61 第五節 研究限制...................66 第四章 研究結果...................71 第一節 群組X...................72 第二節 群組Y...................83 第三節 群組Z...................92 第四節 八位個案的綜合分析...................101 第五章 省思和討論...................107 第一節 學生教師數學教學知識的內涵...................107 第二節 學生教師數學教學知識的發展...................110 第三節 研究的困難與挑戰...................116 第六章 結論和建議...................119 第一節 階段性的結論...................119 第二節 接續研究的建議...................121 參考文獻...................127

    一、中文部分

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    朱綺鴻和譚克平(2000)。現職教師對數教導數學歸納法意見初探。科學教育月刊,232,2-15。
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    李源順(1999)。數學教師在校內互動促進自我專業發展的個案研究。國立台灣師範大學博士論文(未出版)。
    沈亞梵(1995)。師資培育多元化與教師品管之研究。台北市:師大書苑。
    林恆理(2003)。中學數學科實習教師的教學知識研究。行政院國家科學委員會補助大專學生專題研究計劃成果報告。國立台灣師範大學數學系。
    林碧珍(2001)。發展國小教師之學生數學認知知識:理論結合實務研究取向的教師專業發展。台北市︰師大書苑。
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    林福來、郭汾派和林光賢(1995)。比例推理與錯誤診斷補救。行政院國家科學委員會補助專題研究計劃成果報告。國立台灣師範大學數學系。
    林曉雯(1994)。國中生物教師教學表徵的詮釋性研究。國立台灣師範大學博士論文(未出版)。
    林靜雯和邱美虹(2005)。整合類比與多重表徵研究取向探索多重類比設計對兒童電學概念學習之影響。科學教育學刊,13(3),317-345。
    金鈐(2005)。職前中學數學教師教學信念和價值的評量研究(2/3)。行政院國家科學委員會補助專題研究計劃期中進度報告。國立台灣師範大學數學系。
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    陳松靖(2002)。三位學生教師數學教學概念轉變歷程的個案研究。國立台灣師範大學碩士論文(未出版)。
    陳長城(2003)。數學史話。台北市:台灣東華。
    陳恆迪(1993)。國中學生物理概念類比學習之研究。國立彰化師範大學碩士論文(未出版)。
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    鄭英豪(2000)。實習教師數學教學概念的學習:以「概念啟蒙例」的教學概念為例。國立台灣師範大學博士論文(未出版)。
    鄭智馨(2000)。個案研究─影響教師類比選用之因素以及教師的類比對學生學習之影響。國立台灣師範大學碩士論文(未出版)。
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    Ginsburg, H. P. (1997). The clinical interview in psychological research and practice. Cambridge: Cambridge University Press. [謝如山譯(2004)。進入兒童心中的世界。台北市:五南圖書。]
    Maxwell, J. A. (1996). Qualitative research design: An interactive approach. Thousand Oaks: Sage. [高熏芳、林盈助和王向葵合譯(2001)。質化研究設計:一種互動取向的方法。台北市:心理。]
    Robert, K. Y. (1994). Case study research design and methods. Thousand Oaks: Sage. [尚榮安譯(2001)。個案研究法。台北市:弘智文化。]
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    二、英文部分

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