本研究利用第一年(張繼元，2005)所篩選出的六位個案，以不同實習學校的實務社群(Community of Practice) (Wenger, 1998)為場景，進行為期一年的個案第三年追蹤研究。本研究採用個案研究法，並搭配教室觀察、個案晤談及文件資料收集，探討六位數學科實習教師在實習學校中數學教學相關知識的轉變。作者以實務社群作為個案學習和發展數學教學知識的脈絡，透過分析教學實作中所呈現的不同知識面向，以及與輔導老師互動後的知識遷移情形，嘗試瞭解數學實習教師在一年實習過程的教學相關知識轉變，並以Valsiner (1987)的學習發展理論來詮釋個案階段性的教學專業發展。

研究結果顯示，個案在實習之初的數學教學知識是不足的，在不同社群脈絡下，由於受到實習環境和輔導老師的影響而促使其知識有不同內涵和程度的轉變與發展。其中，輔導老師的輔導策略與態度對個案教學知識的影響是最為顯著的，但是，也必須考量到個案的學習領悟(learning-to-see)才能促成最佳的發展。此外，研究也發現，個案的外顯教學行為與內在思想觀念是與教學實作相互牽引的，這同時也會伴隨著身份的協商和教學信念的改變。

本研究結果應有助於數學師資培育者，進一步掌握數學實習教師的教學知識學習軌跡，並且，瞭解輔導老師的輔導策略、理念與方式對數學實習教師的可能影響。也有助於師資培育機構，更深入瞭解實習過程對師資培育的重要性，以及實習環境與制度的建構對實習教師的實際影響。

Abstract

This research followed the six student teacher cases that Zhang (2005) studied for one academic year in their probationary period. Wenger’s (1998) theory of community of practice is used as the theoretical basis. Case study method with classroom observations and interviews was adopted to explore six mathematical probationary teachers’ transition of the relevant knowledge of mathematics teaching in their site-based schools. The author sees community of practice as the context of the learning and developing knowledge of mathematical teaching, and then analyzes different knowledge faces of the six studied cases in classroom teaching practice and the relevant pedagogical knowledge that are transformed within the school context while interacting with his or her mentor teachers. Besides, the author used Valsiner’s (1987) theory of learning and concept development to interpret the six cases’ development of professional knowledge of/for teaching secondary mathematics.

The research results revealed that the knowledge bases for teaching secondary mathematics of the six cases are insufficient. When they were under different community of practice and influenced by the environment and the mentors, their pedagogical knowledge would be forced to change in different orientations. The tactics and attitudes of mentors had enormous effect on the development of professional knowledge for the six cases, the mentors should also think about how to facilitate the cases’ knowledge development through learning-to-see. In addition, the result also showed that external teaching behaviors and the internal ideas or conceptions that the cases develop are interactive and built through classroom teaching practice, and this also goes with the process of negotiating identity and belief change.

The research results may contribute to the training of mathematics teachers in grasping the pre-service teacher’s learning-to-teach process, and understand the possible influences that mentors could have on the probationary mathematics teachers. Besides, this result can also help the teacher education institutions to understand more about how to provide the courses for site-based schools and the environment and system influences on the pre-service teachers.

參考文獻

一、中文部分
方炎明（1979）。主要國家教育實習制度概述。載於師大學生實習指導委員會（編印），67學年度師範院校實習研討紀錄(pp.18-39)。台北市：國立台灣師範大學。
何妤珩（2004）。國小實習教師實務知識發展之研究。國立台中師範學院國民教育研究所碩士論文，台中市。
李維（譯）（2000）。L. S. Vygotsky著。思維與語言（Thought and Language）。台北市：昭明。
吳芝儀、李奉儒（譯）（1995）。M. Q. Patton著。質的評鑑與研究（Qualitative Evaluation and Research Methods）。台北市：桂冠。
吳芝儀、廖梅花（譯）（2003）。A. Strauss 及 J. Corbin著。質性研究入門：紮根理論研究方法（Basics of Qualitative Research: Techniques and Procedure for Developing Grounded Theory）。台北市：濤石。
林恆理（2005）。八位學生教師數學教學知識的個案研究：以無限概念為例。國立台灣師範大學數學系碩士班碩士論文，台北市。
金鈐（2004）。行政院國家科學委員會補助專題研究計畫報告—職前中學數學教師教學信念與價值的評量研究（1/3）。台北市：國立台灣師範大學數學系。
金鈐（2005）。行政院國家科學委員會補助專題研究計畫報告—職前中學數學教師教學信念與價值的評量研究（2/3）。台北市：國立台灣師範大學數學系。
金鈐（2007）。行政院國家科學委員會補助專題研究計畫報告—職前中學數學教師教學信念與價值的評量研究（3/3）。台北市：國立台灣師範大學數學系。
金鈐（2007）。中學數學教師專業發展指標之研究—子計畫五：中學數學教師後設認知專業發展指標之研究（1/3）。台北市：國立台灣師範大學數學系。
尚榮安（譯）（2001）。個案研究法（Case study research design and methods）。台北市：弘智文化。
范良火（2003）。教師教學知識發展研究。上海：華東師範大學出版社。
高薰芳、林盈助、王向葵（譯）（2001）。J. A. Maxwell著。質化研究設計：一種互動取向的方法（Qualitative Research Design: An Interactive Approach）。台北市：心理。
教育部（1995）。高級中等以下學校及幼稚園教師資格檢定及教育實習辦法。1995年11月16日，取自http://www.ntnu.edu.tw/csd/dois/dois_index.php?l=law_dois /law_dois_1/law_dois_1。
教育部（1995）。師資培育法。1995年2月22日，取自http://www.tec.stu.edu.tw /teacher01.htm。
教育部（2003）。國民中小學九年一貫課程綱要數學學習領域。台北市：教育部。
教育部（2005）。師資培育之大學辦理教育實習作業原則。2005年9月7日，取自http://www.ntnu.edu.tw/csd/dois/dois_index.php?l=law_dois/law_dois_1/law_ dois_1。
許秀聰（2005）。一位資深高中數學教師重構教學概念的行動研究。國立台灣師範大學碩士論文，台北市。
張繼元（2005）。六位學生數學教師教學價值認同的個案研究。國立台灣師範大學碩士論文，台北市。
陳英娥和林福來（2004）行動研究促進初任數學教師的教學成長。科學教育月刊，12（1），83-105。
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，台北市。
陳國泰（1999）。國小初任教師實際知識發展之研究。國立高雄師範大學教育研究所博士論文，高雄市。
陳霓慧（2006）。八位學生數學教師教學認知和情意面互動的個案研究。國立台灣師範大學碩士論文，台北市。
黃光雄（主譯）（2003）。R. C. Bogdan 及 S. K. Biklen著。質性教育研究理論與方法（Qualitative Research for Education: An Introduction to Theory and Method）（3rd ed.）。台北市：濤石。
黃政傑（主編）（1997）。教學原理。台北市：師大書苑。
黃凱旻（2002）。一個輔導中學數學實習教師教學概念轉變的行動研究。國立台灣師範大學碩士論文，台北市。
黃凱旻、金鈐（2003）。一個輔導中學數學實習教師教學概念轉變的行動研究。國立台灣師範大學學報：科學教育類，48（1），21-44。
黃炳煌（1981）。師範院校教育實習之探討。台灣教育，372，7-18。
楊銀興（1993）。師範學院結業實習教師工作及生活困擾問題之研究。台北市：師大書苑。
廖俊傑(2007)。六位學生數學教師教學價值實踐的個案研究。立台灣師範大學碩士論文，未出版，台北市。

二、英文部分
An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145-172.
Artzt, A. & Thomas, E. (1999). A cognitive model for examining teachers’ instructional practice in mathematics: A guide for facilitating teacher reflection. Educational Studies in Mathematics, 40, 211-235.
Ball, D.L. (1990b). Prospective elementary and secondary teachers’ understandings of division. Journal for Research in Mathematics Education, 21(2), 132-144.
Ball, D.L. & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning (pp.83-104). London: Ablex Publishing.
Ball, D.L., Lubienski S.T., & Mewborn D.S. (2001). Research on Teaching Mathematics: The Unsolved Problem of Teachings’ Mathematical Knowledge. In Virginia, Richardson (Ed.), Handbook of Research on Teaching (4th ed.) (pp.433-455). Washington, D.C.: AERA.
Blanton, M.L., Westbrook, S., ＆ Carter, G. (2005). Using valsiner’s zone theory to interpret teaching practices in mathematics and science classroom. Journal of Mathematics Teacher Education, 8, 5-33.
Boaler, J. (1998). Open and Closed Mathematics: Student Experiences and Understands. Journal for Research in Mathematics Education, 29(1), 41-62.
Boaler, J. (1999). Participation, knowledge and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40, 259-281.
Boaler, J., & Greeno, J.G. (2000). Identity, agency, and knowing in mathematics worlds. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning (pp.171-200). London: Ablex Publishing.
Boaler, J. (2002). The Development of Disciplinary Relationships: Knowledge, Practice and Identity in Mathematics Classrooms. For the Learning of Mathematics, 22(1). Canada, Kingston: FLM Publishing Association.
Brown, S., Cooney, T., & Jones, D. (1990). Mathematics teacher education. In W.R. Houston (Ed.), Handbook of Research on Teacher Education (1st ed.) (pp.469-497). New York: Macmillan.
Brown, C.A., & Borko, H. (1992). Becoming a mathematics teacher. In A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 209-239), NY: Macmillan.
Christensen, D. (1996). The professional knowledge-research base for teacher education. In W.R. Houston (Ed.), Handbook of Research on Teacher Education (2nd ed.) (pp.38-52). New York: Macmillan.
Cooney, T.J. (1994). Teacher education as an exercise in adaptation. In D.B. Aichele and A.F. Coxford (Eds.), Professional Development for Teachers of Mathematics: 1994 Year Book (pp.9-22). Reston: NCTM
Cooney, T.J. (2001). Considering the paradoxes, perils, and purposes of conceptualizing teacher development. In F.L. Lin and T.J. Cooney (Eds.), Making Sense of Mathematics Teacher Education (pp.9-31). Netherlands: Kluwer Academic Publishers.
Cooney, T.J., & Wiegel, H.G. (2003). Examining the mathematics in mathematics teacher education. In Alan J. Bishop, M.A. Clements, Christine, Keitel, Jeremy Kilpatrick, & Frederick K.S. Leung (Eds.), Second International Handbooks of Mathematics Education (Part Two, pp.795-828). Dordrecht: Kluwer Academic Publishers.
Elbaz, F. (1983). Teacher thinking: A study of practical knowledge. New York: Nichols.
Elliott, B., & Calderhead, F. (1993). Mentoring for Teacher Development: Possibilities and Caveats. In D. McIntyre, H. Hagger, & M. Wilkin (Eds.), Mentoring: perspectives on school-based teacher education. London, Philadelphia: Kogan Page.
Fennema, E., & Franke, M.L. (1992). Teachers’ knowledge and its impact. In A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 147-164), NY: Macmillan.
Furlong, J., & Maynard, T. (1995). Mentoring student teachers: The growth of professional knowledge. London: Routledge.
Goos, M. (2005). A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology. Journal of Mathematics Teacher Education, 8, 35-59.
Jaworski, B., & Watson, A. (1994). Mentoring, co-mentoring and inner mentor. In B. Jaworski, & A. Watson (Eds.), Mentoring in mathematics teaching (pp.124-138). London: The Falmer Press.
Jones, M.G., & Vesilind, E.M. (1996). Putting practice into theory: Changes in the organization of pre-service teachers’ pedagogical knowledge. American Educational Research Journal, 33(1), 91-117.
Leinhardt, G. (1988). Expertise in instructional lessons: An example from factions. In D. Grouws, T. Cooney, & D. Jones (Eds.), Perspectives on research on effective mathematics teaching (pp.47-66). Reston, VA: National Council of Teachers of Mathematics.
Leinhardt, G., & Greeno, J.C. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 2, 75-95.
Lerman, S. (2001). A review of research perspectives on mathematics teacher education. In F.L. Lin and T.J. Cooney (Eds.), Making Sense of Mathematics Teacher Education (pp.9-31).Dordrecht, The Netherlands: Kluwer Academic Publishers.
Lerman, S. (2002). Situating research on mathematics teachers’ beliefs and on change. In G.C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A Hidden Variable in Mathematics Education? (pp.233-243). Dordrecht: Kluwer Academic Publishers.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: Lawrence Erlbaum Publishers.
Munby, H., Russell, T., & Martin, A. (2001). Teachers’ knowledge and how it develops. In Virginia, Richardson (Ed.), Handbook of Research on Teaching (4th ed.) (pp.877-904). Washington, D. C.: AERA.
National Council of Teachers of Mathematics. (2000). Professional standards for teaching mathematics. Reston, VA: Author.
Nickerson, S.D., & Moriarty, G. (2005). Professional communities in the context of teachers’ professional lives: A case of mathematics specialists. Journal of Mathematics Teacher Education, 8, 113-140.
Noddings, N. (1992). Professionalization and mathematics teaching. In D.A. Grovws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp.209-239). New York: Macmillan.
Peterson, P.L. (1988). Teachers’ and students’ cognitional knowledge for classroom teaching and learning. Educational Researcher, 17(5), 5-14.
Russell, T. (1988). From pre-service teacher education to first year of teaching: A study of theory and practice, in J. Calderhead (Ed.), Teachers’ professional learning. London: The Falmer Press.
Schwab, J.J. (1978). Science, curriculum and liberal education. Chicago: University of Chicago Press.
Shulman, L.S. (1983). Autonomy and obligation: The remote control of teaching. In L.S. Shulman & G. Sykes (Eds.). Handbook of teaching and policy. New York: Longman.
Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Research, 15(2), 4-14.
Shulman, L.S. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1-23.
Simon, M. (1994). Learning mathematics and learning to teach: Learning cycles in mathematics teacher education. Educational studies in Mathematics, 26, 71-94.
Skott, J. (2001). The emerging practices of a novice teacher: The roles of his school mathematics images. Journal of Mathematics Teacher Education, 4, 3-28.
Thompson, A.G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp.127-146). New York: Macmillan.
Tirosh, D., & Graeber, A.O., (2003). Challenging and Changing Mathematics Teaching Classroom Practices. In Alan J. Bishop, M.A. Clements, Christine, Keitel, Jeremy Kilpatrick, & Frederick K.S. Leung (Eds.), Second International Handbooks of Mathematics Education (pp.643-687). Dordrecht: Kluwer Academic Publishers.
Tzur, R. (2001). Becoming mathematics teacher-educators: Conceptualizing the terrain through self-reflective analysis. Journal of Mathematics Teacher Education, 4, 259-283.
Valsiner, J. (1987). Culture and the development of children’s actions: A cultural-his-torical theory of developmental psychology. New York: John Wiley & Sons.
Wenger, E. (1998). Communities of practice-learning, meaning, and identity. Cambridge: Cambridge University Press.
Wilson, M., & Cooney, T.J. (2002). Mathematics teacher change and development. In G.C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A Hidden Variable in Mathematics Education? (pp.127-147). Dordrecht: Kluwer Academic Publishers.
Wilson, P.S., Cooney, T.J., & Stinson, D.W. (2005). What constitutes good mathematics teaching and how it develops: nine high school teachers’ perspectives. Journal of Mathematics Teacher Education, 8, 83-111.
Zaslavsky, O., Chapman, O., ＆ Leikin, R. (2003). Professional development of mathematics educators: Trends and tasks. In Alan J. Bishop, M.A. Clements, Christine, Keitel, Jeremy Kilpatrick, & Frederick K.S. Leung (Eds.), Second International Handbooks of Mathematics Education (pp.877-917). Dordrecht: Kluwer Academic Publishers.