本研究的目的在了解同一學校內在職數學教師組成一個討論小組，利用課餘時間討論自己有興趣的教學問題所促進的教師自我專業成長情況。教師所討論的教學問題聚焦在關心學生的學習，解決教學問題的中心想法則是培養數學感的教學及診斷教學。
研究採詮釋性研究法，參予的教師有四位，他們與研究者任教於同一學校。本文僅對三年之中，全程參與的兩位進行報導，不對第三年才參與的兩位教師進行報導。參與教師的選取是當研究者向同事表明想經由教師間共同討論教學問題，以了解教師的教學是否改變時，兩位教師表示願意參加，此外並無特定標準。資料收集包括教師互動錄音、教師教學錄影與錄音、教學札記、教師深度訪談、學生感想寫作、學生訪談、以及教學講義。資料信度採三角校正，除將研究者所轉錄原案內容拿給參予教師確認外，資料分析的編碼並與第三者形成共識。資料效度分析除採教學錄影的生態效度之外，並參照教師的言談、教學行為，以及學生的反應進行相互印證。
經過三年的校內同事互動，發現兩位教師在教學專業知識和教學態度已有改變。在教學知識方面：參與教師釐清了一些以前從未觸及的數學學科內容知識。他們原本從不去注意學生容易犯的錯誤概念，和不去了解學生犯錯的原因，轉而注意與了解學生容易犯的錯誤，並探究學生犯錯的原因。他們的教學法實作也產生了質變，他們從偏向講述的單一教學取向轉變為多元教學取向。改變的關鍵是因為同事互動促使他們關心學生的需求和考量學生的學習問題，而在互動兩個月後開始第一階段的改變 -- 嘗試多種教學策略；經過些許的取捨之後，在第一年末開始第二階段的改變 -- 持續使用多種教學策略；由於參與教師沒有機會深刻體認或批判教學策略的適用性，而在第三年處於保守使用多種教學策略的第三階段。在教學信念與態度方面：兩位教師教學信念的改變並不明顯，但他們的教學態度比互動前更關心學生的學習。
研究發現，參與教師之所以能進行專業發展，是由於注入關心學生學習需求的同事互動引動教師在教室內進行師生互動，而師生互動的經驗又為同事互動引入活水。同事互動與師生互動就像是引動教師內在專業成長的一個外部循環系統，而教師本身對教學問題的反覆察覺、解決與反思所形成的關心學生學習需求的內在循環就是被外環引動的教師專業成長的內涵。外循環與內循環間又相互連動創造了教師專業發展的學生中心互動模式。
研究者試著從這個教師專業發展的互動模式推廣Schön(1983)的反思理論，發現教師獨自察覺、反思、解決教學問題所引發的是教師對教學行動的自我性反思，同事互動引發教師對教學行動的社會性反思。至於師生互動則引發教師在教學行動中的反思。
這一個互動模式同時也蘊涵了林福來(民87)所提出的教師專業發展機制理念。當教師碰到教學問題時，教師能遞迴，並利用對教學行動的社會性反思、自我性反思或在教學行動中反思而調整、再前進。
本文最後從研究結果和啟示中，擬出一份建議書給想利用學生中心互動模式進行專業發展的教師。

王秋絨(民80)：教師專業社會化理論在教育實習設計上的蘊義(再版)。台北：師大書苑。
行政教育改革審議委員會(民84a)：行政院教育改革審議委員會第一期諮議報告書。行政院教育改革審議委員。
行政教育改革審議委員會(民84b)：行政院教育改革審議委員會第二期諮議報告書。行政院教育改革審議委員。
呂玉琴(民83)：國小教師分數教學之相關知識研究。國立台灣師範大學科學教育研究所博士論文。
林福來（民83）：八十三年度基礎科目數學考科試題研發工作計劃研究報告。大學入學考試中心。
林福來(民86)：教學思維的發展：整合數學教學知識的教材教法(1/3)。行政院國家科學委員會專題研究計劃成果報告。
林福來(民87)：學生教師的數學教學概念化初探。邀請演講「1998年國際數學學術研討會」，台師大數學系，12月18-21日。
林福來(民88)：教學思維的發展：整合數學教學知識的教材教法(3/3)。行政院國家科學委員會專題研究計劃成果報告。未發表。
林福來、郭汾派、林光賢(民84)：比例推理的錯誤診斷與補救。科教研討會論文彙編。
林碧珍(民86)：數學教師在教師成長計劃下的知識成長 -- 個案研究。第十三屆科學教育學術研討會。pp.399-405。
高華強(民77)：社會變遷與教育革新。師大書苑。
陳舜芬、丁志仁、洪儷瑜(民85)：師資培育與教師進修制度的檢討。行政院教育改革審議委員會。
梁淑坤(民88)：擬題與課程之融合：教師在推廣專案中為主動研究者。1999數學教師教育國際學術研討會。國立台灣師範大學。1999年5月10-14日。
黃光雄等譯(民72)：情意領域目標分類。輔導叢書(11)。台灣省立新竹師範專科學校附設新竹區國民教育輔導中心編印。
黃坤錦(民80)：各國教師專業之比較研究。發表於「國際比較師範教育學術研討會論文集」，中華民國師範教育學會主編。師大書苑。
黃桂妮(民86)：國中數學教師的數學教學知識之分析－關於文字符號的使用，國立高雄師範大學碩士論文。
張宏志、柳賢(民84)：數學科實習教師實習期間之教學相關技能，教學態度及價值觀的改變分析研究。行政院國家科學委員會專題研究計劃成果報告。
張維玲(民85)：反省取向的師資培育學程研究。國立台灣師範大學教育研究所博士論文。
楊思偉(民85)：在職進修教育的趨勢與做法。研習資訊，13 卷 6 期。pp.24-27。
劉牡丹(民80)：基本溝通技巧--專注行為、尊重、反映、具體。諮商與輔導，64期，pp.27-30。
劉鍚麒(民84)：合作省思教學模式在國小數學教室中的協同行動研究。行政院國家科學委員會專題研究計劃成果報告。
蔡敏玲，陳正乾譯(民86)：社會中的心智：高層次心理過程的發展。心理出版社，台北。
蔡碧璉(民82)：國民中學教師專業成長與其形象知覺之研究。國立政治大學教育研究所博士論文。
鍾靜(民85)：小學數學課程改革下之教師成長研究 II。行政院國家科學委員會專題研究計劃成果報告。
Becker，J.R. & Pence，B.J.(1996). Mathematics teacher development：Connections to change in teachers' beliefs and practices. PME20 vol I. pp.103-118.
Bell，A.W.(1989). Teaching for the test. The Times Educational Supplement. Outlines the Shell Centre's research into diagnostic teaching methods.
Bell，A.W.(1992). Diagnostic teaching. Selected Lectures from the 7th lnternational Congress on Mathematical Education. pp.19-34.
Bell，A.W.(1994). Some experiments in diagnostic teaching. Educational Studies in Mathematics，24(1)，pp115-137.
Bell，A.W.；Costello，J. & Kuchemann，D.(1983). Research on learning and teaching，N.F.E.R.—Nelson.
Blackman，C.A.(1989). Issue in professional development：The continuing agenda. In M.L. Holly & C.S. McLoughlin(eds.)(1989). Perspectives on the teacher professional development. New York：The Falmer Press.
Booth，L.R.(民76). 診斷教學理念，Booth 專題演講，蔡淑貞整理，科學教育月刊第100 期，pp.41-48.
Booth，L.R.(1984). Algebra：Children's strategies and error. N.F.E.R. Nelson.
Boufi，A.(1994). A case study of a teacher's chance in teaching mathematics. PME XVIII，vol II. pp.120-127.
Brown，C.A. & Borko，H.(1992). Becoming a mathematics teacher. In D.A. Grouws(ed.) (1992). Handbook of research on mathematics teaching and learning，National Council of Teachers of Mathematics，Macmillan Publishing Company，New York. pp.209-242.
Case，R.(1978). The developmentally based theory and technology of instruction. Review of Educational Research，48(3). Pp.439-463.
Chapman，O.(1993). Facilitating in-service mathematics teachers self- development. PME XVII，vol I，pp.228-235.
Chin ,C.(金鈐)(1995). Mathematics teachers' beliefs，their classroom practices and influences on student learning：Four case studies. The University Cambridge PHD.
Cobb, P.(1999). Supporting teacher’s learning in social and institutional context. Proceedings of the 1999 International Conference of Mathematics Teacher Education.Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. II. pp.7-76.
Cobb，P.；Wood，T. & Yackel，E.(1990). Classrooms as learning environments for teachers and researches，In R. Davis，C. Maher & N. Noddings(eds.)(1990). Constructivist views on the teaching and learning of mathematics JRME Monograph #4. Reston，VA：NCTM.
Cobb，P.；Yackel，E. & Wood，T.(1991). Curriculum and teacher development：Psychological and anthropological perspectives. In Fennema，E.；Carpenter，T.P. & Lamon，S.J.(1991). Integrating research on teaching and learning mathematics. State University of New York Press. pp.83-119.
Cooney，T.(1994). Research and teacher education：In search of common ground. Journal for Research in Mathematics Education，25. pp.608-636.
Cooney, T.(1999). Considering the paradoxes, perils, and purposes of conceptualizing teacher development. Proceedings of the 1999 International Conference of Mathematics Teacher Education.Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. pp.1-33.
Cooney，T.J. & Shealy，B.E.(1994). Conceptualizing teacher as field of inquiry：Theoretical and practical implications. PME XVIII. Vol. II. Pp.225-232.
Denny，M.(unpressed)(1998). Student-teachers’ professional development.
Edwards，T.G.(1994). Using a model to understand the process of change in a middle school mathematics teacher. Paper presented at the Annual Meeting of National Council of Teachers of Mathematics (72nd，Indianapolis，IN，April 12，1994).
Ernest，P.(1988). The impact of beliefs on the teaching of mathematics. Paper presented for ICME Vi，Budapest，Hungary.
Ernest，P.(1994a). What is social constructivism in the psychology of mathematics education？ PME XVIII，vol.II. pp.304-311.
Ernest，P.(eds)(1994b). Constructing mathematical knowledge：Epistemology and mathematics education，London：The Falmer Press.
Even，R.；Tirosh，D. & Markovits，Z.(1996). Teacher subject matter knowledge and pedagogical content knowledge：Research and development. PME 20，vol. 1. pp.119-134.
Fennema，E. & Franke，M.L.(1992). Teachers' knowledge and its impact. In D.A. Grouws(ed.)(1992). Handbook of research on mathematics teaching and learning， National Council of Teachers of Mathematics，Macmillan Publishing Company，New York. pp.147-162.
Frick，T. & Semmel，M.I.(1978). Observer agreement and reliabilities of classroom observational measures. Review of Educational Research，48，1，pp.157-184.
Fuller，R.A.(1994). Change in teachers' conceptions and practice. Paper presented at the Meeting of the Mid-Western Educational Research Association (Chicago，IL，October 13，1994).
Fuller，F. & Bown，O.(1975). On becoming a teacher. In K. Ryan(ed.)(1975). Teacher Education(The 74th Yearbook of the National Society for the Study of Education. pp.25-52). University of Chicago Press.
Garnett，P. J.；Tobin，K.(1989). Teaching for understanding：Exemplary practice in high school chemistry. Journal of Research in Science Teaching；v26 n1 pp.1-14.
Goffree, F. & Oonk, W.(1999). When real teaching practice can be (digitally) represented in colleges of education: The MILE project. Proceedings of the 1999 International Conference of Mathematics Teacher Education. Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. pp.34-75.
Grant，C.E.(1984). A study of the relationship between secondary mathematics teachers' beliefs about the teaching-learning process and their observed classroom behavior. Dissertation Abstracts International 46，DA8507627.
Hart，K.M.(1984). Ratio：Children's strategies and errors. N.F.E.R. Nelson.
Hensen, K.T.(1996). Teachers as researchers. In John Sikula(Ed.). Handbook of research on teacher educator(p.56). Macmillan.
Horan，M.(1991). Attributes of exemplary community college teachers：A review of the literature. GEOGRAPHIC SOURCE：U.S.；Florida.
Jaworski, B.(1999). Development mathematics teaching: teachers, teacher-educator and researchers as co-learners. Proceedings of the 1999 International Conference of Mathematics Teacher Education. Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. pp.226-261.
Jones，G.A.，Lubinski，C.A.，Swafford，J.O. & Thornton，C.A.(1994). A framework for the professional development of K-12 mathematics teachers. In Aichele，D.B. & Coxford，A.F.(1994). Professional development for teachers of mathematics. 1994 Yearbook，NCTM.
Kesler，R. Jr.(1985). Teachers' instructional behavior related to their conceptions of teaching and mathematics and their level of dogmatism：Four case studies. Unpublished Doctoral Dissertation，University of Georgia，Athens.
Kieran，C.(1994). Dinog and seeing things differently：A 25-year retrospective of mathematics education research on learning. Journal for Research in Mathematics Education，Vol.25，No.6，pp.583-607.
Koehler，M.S. & Grouws，D.A.(1992). Mathematics teaching practices and their effects. In D.A. Grouws(ed.) (1992). Handbook of research on mathematics teaching and learning，National Council of Teachers of Mathematics，Macmillan Publishing Company，New York. pp.115-126.
Knowles, J.G.(1995). Life-History accounts as mirrors: A practical avenue for the conceptualization of reflection in teacher education. In Calderhead, J. & Gates, P.(1995). Conceptualizing reflection in teacher development. The Falmer Press. pp. 70-92.
Krainer, K.(1999). Learning from Gisela- or: Finding a bridge between classroom development, school development, and the development of educational system. Proceedings of the 1999 International Conference of Mathematics Teacher Education.Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. pp.76-95.
Krainer，K；Krainz-Durr，M.；Piber，C.；Posch，P；& Rauch，F.(1998). The CAPE project – constructing activities for peer-education. PME 1998. Vol.I.pp.105-112.
Learman, S.(1999). A review of research perspectives on mathematics teacher education. Proceedings of the 1999 International Conference of Mathematics Teacher Education.Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. pp.110-133.
Lin, F.L.(1999). Re-designing mathematrics teacher ecucation. Journal of Mathematics Teacher Education. Vol. II. To be press.
Livingston. C. & Borko，H.(1990). High school mathematics review lessons：Expert-novice distinctions. Journal for Research in Mathematics Education，21. pp.372-387.
Markovits，Z. & Even，R.(1994). Teaching situations：Elementary teacher' pedagogical content knowledge. In J. P. da Ponte & J.F. Matos(eds.)(1994). Proceedings of the 18th International Conference for Psychology of Mathematics Education，vol 3. pp.239-246.
McGalliard，W.A. Jr.(1983). Selected factors in the conceptual systems of geometry teachers：Four case studies. Dissertation Abstracts International 44，1364A.
Mitchell，J. & Williams，S.E.(1993). Expert/novice difference in teaching with technology. Paper presented at the Annual Meeting of the American Educational Research Association (Atlanta，GA，April 12-16，1993).
NAEP(1988). Mathematics objectives: 1990 assessment. National Assessemnt of Educational Progress, Princeton, NJ.
NCTM.(1989). Curriculum and evaluation standards for school mathematics. National Council of Teachers of Mathematics，Reston，VA：Author.
NCTM.(1990). Professional standards for teaching mathematics. National Council of Teachers of Mathematics，Reston.
Nodding，N.(1992). Professionalization and mathematics teaching. In D.A. Grouws(ed.) (1992). Handbook of research on mathematics teaching and learning，National Council of Teachers of Mathematics，Macmillan Publishing Company，New York. pp.197-208.
Onslow，B.A.(1986). Overcoming conceptual obstacles concerning rates：Design and implementation of a diagnostic teaching unit. The University of Nottingham for the degree of Doctor of Philosophy.
Penick，J.E.；Yager，R.E. & Bonnstetter，R.(1986). Teachers make exemplary programs. Educational Leadership; v44 n2，pp.14-20.
Raymond，A.M.(1995). Mathematics teacher development：Lessons learned from two collaborative action research partnerships. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (17th，Columbus，OH，October 21-24，1995).
Resnick，L.B.(1989). Defining，assessing，and teaching number sense. In J.T. Sowder & B.P. Schappelle(Eds.) Establishing foundations for research on number sense and related topics：Report of a Conference(pp.35-39.). San Diego State University Center for Research in Mathematics and Science Education.
Ropo，E.(1987). Teachers' conceptions of teaching and teaching Behavior：Some differences between expert and novice teachers. Paper presented at the Annual Meeting of the American Educational Research Association (Washington，DC，April 20-24，1987).
Schön，D.A.(1983). The reflective practitioners：How professionals think in action. Basic Books，Inc.，USA.
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.
Shaw，K.(1989). Contracts of teacher ideal and actual beliefs about mathematics understanding：Three case studies. Unpublished Doctoral Dissertation，University of Georgia，Athens.
Shaw，K. & Jakubowski，E.(1991). Teachers changing for changing times. Focus on Learning Problems in Mathematics，13(4). pp.13-20.
Simon，M.A. & Schifter，D.(1991). Towards a constructivist perspective：An intervention study of mathematics teacher development. Educational Studies in Mathematics 22：pp.309-331.
Skemp，R.R.(民72). 談教師在職教育，林褔來譯. 國立台灣師範大學數學系. pp.29-30.
SLO/NVORWO (1994). Standards for primary mathematics teacher education. Utrecht：Freudenthal Institute.
Sowder，J.(1994). Estimation and number sense. In D.A. Grouws(ed.)(1992). Handbook of research on mathematics teaching and learning，National Council of Teachers of Mathematics，Macmillan Publishing Company，New York.pp.371-389.
Sullivan, P.(1999). Thinking teaching: Seeing an active role for mathematics teacher. Proceedings of the 1999 International Conference of Mathematics Teacher Education.Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. pp.205-225.
Thompson，A.(1984). The relationship of teachers' conceptions of mathematics teaching to instructional practice. Educational Studies in Mathematics，15. pp.105-127.
Tirosh, D. & Stavy, R.(1999). The intuitive rules theory and inservice teacher education. Proceedings of the 1999 International Conference of Mathematics Teacher Education. Department of Mathematics National Taiwan Normal University. Taipei, Taiwan. pp.205-225.
Tobin，K.；Fraser，B. J.(1988). Investigations of exemplary teaching in Australian mathematics classes. Australian Mathematics Teacher；v44 n1 pp.5-8.
Tobin，K.；Fraser，B. J.(1990). What does it mean to be an exemplary science teacher? Journal of Research in Science Teaching；v27 n1 pp.3-25.
Watson，G.A.(1995). Middle school mathematics teacher change：Social constructivism climbs a step. Paper presented at the Annual Meeting of the National Council of Teachers of Mathematics，73rd，Boston，MA.
Wood，T.；Cobb，P. & Yackel，E.(1990). The contextual nature of teaching：Mathematics and reading instruction in one secondary-grade classroom. Elementary School Journal，90(5). pp.497-513.
Wood，T.；Cobb，P. & Yackel，E.(1991). Changes in teaching mathematics：A case study. American Educational Research Journal，28(3)，pp.587-616.
Vygotsky，L.(edited by A. Kozulin)(1996). Thought and language. The MIT Press Cambridge，Massachusetts London，England.