研究生: |
卓益安 Cho, Yi-An |
---|---|
論文名稱: |
臺灣高中數學教師專門數學知識與眼界數學知識的個案研究 The Case Studies of Taiwanese High-school Mathematics Teachers’ Specialized Content Knowledge and Horizon Content Knowledge |
指導教授: |
金鈐
Chin, Chien 楊文金 Yang, Wen-Gin |
學位類別: |
博士 Doctor |
系所名稱: |
科學教育研究所 Graduate Institute of Science Education |
論文出版年: | 2016 |
畢業學年度: | 104 |
語文別: | 中文 |
論文頁數: | 227 |
中文關鍵詞: | 教學用數學知識 、教學用數學任務 、專門數學知識 、眼界數學知識 |
英文關鍵詞: | mathematical knowledge for teaching, mathematical task for teaching, specialized content knowledge, horizon content knowledge |
DOI URL: | https://doi.org/10.6345/NTNU202203745 |
論文種類: | 學術論文 |
相關次數: | 點閱:142 下載:6 |
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 |
本研究採用詮釋性個案研究法,探索三位高中典型數學教師專門數學知識(Specialized Content Knowledge,簡稱SCK)與眼界數學知識(Horizon Content Knowledge,簡稱HCK)的特徵。依據Ball、Thames與Phelps(2008)提出的教學用數學知識(mathematical knowledge for teaching,簡稱MKT)的理論架構下,收集和分析三位個案教師在拉格朗日插值多項式與數學歸納法兩個教學單元的實徵資料。
資料收集的範圍包括參與觀察的場域筆記、上課教材、課堂錄影和訪談。研究者一方面依據文獻資料歸納個案教師課堂使用的數學任務(簡稱教學用數學任務),另一方面修改LMT (2007)的「教學的數學品質(mathematical quality of instruction,簡稱MQI)」編碼詞彙表,建立課堂教學錄影的分析工具。修改分析工具的原則有兩個:一是基於文獻資料的輔助,將編碼歸類至SCK與HCK兩個操作型定義;二是依照個案教師實際的課堂活動,刪減、增加與修訂部分編碼。
主要的研究發現有二:第一是,三位個案教師的SCK在提供數學解釋上展現,例如,教師解釋數學名詞、特殊主題的數學想法、解題歷程等。教學用數學任務的數學內涵更深也更廣,展現了數學知識在數學課堂教學中扮演的關鍵角色,也更能夠使研究者理解個案教師在不同數學主題展現的SCK特徵。第二是,個案教師在不同單元顯現出的HCK中眼界(Horizontal)、周邊(Peripheral)與從入門透視進階(Elementary-on-Advanced)三個面向的特徵都不太一樣。HCK幫助教師察覺數學主題的關鍵核心概念,也幫助學生看到特定主題的數學結構。
This study combines interpretive case study data with the quantitative video analysis to explore three exemplar high-school mathematics teachers’ characteristics of specialized content knowledge (SCK) and horizon content knowledge (HCK). Firstly, the researcher focused on these two mathematical topics of Lagrange interpolation polynomial and mathematical induction. Based on the theoretical framework of mathematical knowledge for teaching (MKT), the researcher collected and analyzed three case teachers’ emperical data including field notes, teaching material, videos of classroom teaching and follow-up interviews. Secondly, the researcher modified the coding system of Mathematical Quality of Instruction (MQI) developed by Learning Mathematics to Teaching (2007), and categorized the codes into two operational definition of SCK and HCK. The two major priciples of modification include the suggestions of literature and the three case teachers’ actual classroom teaching.
There are two major findings. One is that three teachers’ SCK was founded in the mathematical explanation of mathematical definions and noun, key ideas of specific mathematics topics and problem-solving. The content of these mathematical tasks for teaching was more borader and deeper, which played the critical role in the classroom teaching. And these mathematical tasks for teaching help the researcher to understand the characteristics of SCK in different mathematical topics. The other is that HCK has three different characteristics, including horizontal, peripheral and elementary-on-advanced dimension. The HCK not only helps teachers be aware of the key and core concept of mathematics topic, but also helps students see the mathematical sturcture of the specific topics.
一、 中文部分:
王國華、段曉林、張惠博(1998)。國中學生對科學教師學科教學之知覺。科學教育學刊,6(4),363-381。
沈湘媛(2012)。高中數學教師教學專業知識的個案研究。國立台灣師範大學碩士論文,台北市。
邱美虹、江玉婷(1997)。初任與資深國中地球科學教師學科教學知識之比較。科學教育學刊,5(4),419-460。
林培棠(2012)。兩位資深高中數學教師專門內容知識之嵌入式設計的混合方法研究。國立台灣師範大學碩士論文,台北市。
范良火(2003)。教師教學知識發展研究。上海市:華東師範大學出版社。
張世忠、李俊毅、謝幸芬 (2013)。一個同儕教練為基礎之發展模式對國中科學教師PCK之影響:以「熱與溫度」單元為例。科學教育學刊,21(1), 1-24。
張世忠、蔡孟芳、陳鶴元 (2012)。國中科學教師的學科教學知識與科學教學導向之探討。科學教育學刊,20(5),413-433。
鈕文英(2007)。教育研究方法與論文寫作。台北: 雙葉書廊。
教育部(2012)。中華民國師資培育白皮書。台北市:教育部。
教育部、國科會(2010)。【教育部、國科會新聞稿】國際教育成就調查,我國數學師資培育排名第一。2013年8月31日,取自http://tedsm.math.ntnu.edu.tw/news/20100416.html
陳亭瑋(2011)。資深高中數學教師教學知識與教學構思的個案研究。國立臺灣師範大學數學研究所碩士論文,臺北市。
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。
曾名秀(2011)。資深高中數學教師教學相關知識的個案研究。國立臺灣師範大學數學研究所碩士論文,臺北市。
黃政傑(1997)。課程改革的理念與實踐。台北:漢文。
謝豐瑞(2012)。臺灣數學師資培育跨國研究結論與建議。載於謝豐瑞(主編),臺灣數學師資培育跨國研究Taiwan TEDS-M 2008(305-316頁)。臺北:國立臺灣師範大學數學系。
饒見維(1996)。教師專業發展-理論與實際。台北市:五南。
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.
Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93 (4), 373-397.
Ball, D. L. (2010, April). Knowing mathematics well enough to teach it: From teachers' knowledge to knowledge for teaching. Presented at the Institute for Social Research Colloquium, Ann Arbor, MI, April 27, 2010.
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., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 annual meeting of the Canadian Mathematics Education Study Group (pp. 3-14). Edmonton, Alberta, Canada: Canadian Mathematics Education Study Group (Groupe Canadien d’étude en didactique des mathématiques).
Ball, D. L., & Bass, H. (2009). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners’ mathematical future. Paper presented on a keynote address at the 43rd Jahrestagung für Didaktik der Mathematik held in Oldenburg, Germany, March 1-4, 2009.
Ball, D. L., Thames, M. H., Bass, H., Sleep, L., Lewis, J., &Phelps, G. (2009). A practice-based theory of mathematical knowledge for teaching. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 1 (pp. 95-98). Thessaloniki, Greece: PME.
Ball, D. L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
Berliner, D. C. (1986). In pursuit of the expert pedagogue. Educational Researcher, 15(7), 5-13.
Bishop, A. J., Seah, W. T., & Chin, C. (2003). Values in mathematics teaching-the hidden persuaders? In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second International Handbook of Mathematics Education (pp. 717-765). Dordrecht: Kluwer.
Bogdan, R. C., & Biklen, S. K. (1998). Qualitative research for education: An introduction to theory and methods (3rd ed.). Boston: Allyn and Bacon.
Bromme, R. (1994). Beyond subject matter: A psychological topology of teachers' professional knowledge. In Biehler, R.; Scholz, R.W.; Strasser, R.; Winkelmann, B. Didactics of Mathematics as a Scientific Discipline (pp. 73 - 88). Dordrecht: Kluwer Academic Publishers.
Brown, C. & Borko, H. (1992). Becoming a mathematics teacher. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 209-239). New York: Macmillan.
Carpenter, T.P., Fennema. E., & Franke, M.L. (1996). Cognitively Guided instruction: A knowledge base for reformn in primnary mathematics instruction. Elemnentary School Journal, 97(1), 1-20.
Carter, K. (1990). Teachers' knowledge and learning to teach. In W. R. Houston (Ed.), Handbook of research on teacher education (pp. 291-310). New York: Macmillan.
Charalambous, Y. C. (2008). Preservice teachers' mathematical knowledge for teaching and their performance in selected teaching practices: Exploring a complex relationship. Unpublished doctoral dissertation, State University of Michigan, East Lansing, MI.
Chin, C. (1995). Mathematics teachers' beliefs, their classroom practices and influences on student learning: Four case studies. Unpublished Ph.D Thesis, University of Cambridge
Chinnappan, M. & Lawson, M. (2005). A framework for analysis of teachers’ geometric content knowledge and geometric knowledge for teaching. Journal of Mathematics Teacher Education, 8, 197-221.
Clark, C. M., & Peterson, P. L. (1986). Teachers’ thought processes. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 255-296). New York: Macmillan.
Cochran, K. F., DeRuiter, J. A., and King, R. A. (1993). Pedagogical content knowing: an integrative model for teacher preparation. Journal of Teacher Education, 44(4), 263–272.
Cooney, T. J. (1994) Research and Teacher Education: In Search of Common Ground. Journal for Research in Mathematics Education, 25(6), 608-636.
Cooney, T. J. (1994). Teacher education as an exercise in adaptation. In D. B. Aichele, &A. F. Coxford (Eds.), Profession development: 1994 yearbook (pp. 9-22). Reston, VA:National Council of Teachers of Mathematics.
Davis, B., & Renert, M. (2009) Mathematics for teaching as shared, dynamic participation. For the Learning of Mathematics, 29(3), 37–43.
Davis, B., & Renert, M. (2013). Profound understanding of emergent mathematics: broadening the construct of teachers’ disciplinary knowledge. Educational Studies in Mathematics, 82(2), 245-265.
Davis, B., & Simmt, E. (2006) Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293–319.
Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). “Mathematical knowledge for teaching”: adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171-197.
Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Education Studies in Mathematics, 21(6), 521-544.
Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29, 1-20.
Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan
Fennema, E., T. P. Carpenter, M. L. Franke, L. Levi, V. Jacobs, and S. Empson. (1996) “Learning to Use Children’s Thinking in Mathematics Instruction: A Longitudinal Study.” Journal for Research in Mathematics Education 27 (4): 403–434.
Fenstermacher, G. D (1986). Philosophy of research on teaching: Three aspects. In M. C. Wittrock, Ed., Handbook of research on teaching (3rd ed., pp. 37-49). New York: Macmillan.
Feiman-Nemser, S. (2008). Teacher Learning. How do Teachers learn to teach? In CochranSmith, M, Feiman-Nemser, S., McIntyre, D. (Eds.). Handbook of research on Teacher Education. Enduring Questions in Changing Contexts. New York/Abingdon: Routledge/ Taylor & Francis.
Figueiras, L., Ribeiro, M., Carrillo, J., Fernández, S. & Deulofeu, J. (2011) Teachers’ advanced mathematical knowledge for solving mathematics teaching challenges: a response to Zazkis and Mamolo. For the Learning of Mathematics, 31(3), 26-28.
Foster, C. (2011) Peripheral mathematical knowledge. For the Learning of Mathematics, 31(3), 24-26.
Frick, T., &Semmel, M. I. (1978). Observer agreement and reliabilities of classroom observational measures. Review of Educational Research, 48(1), 157-184.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students‘ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte, NC: Information Age Publishers.
Hill, H. C. (2010). The nature and predictors of elementary teachers’ mathematical knowledge for teaching. Journal for Research in Mathematics Education, 41(5), 513-545.
Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s Mathematics Professional Development Institutes. Journal of Research in Mathematics Education, 35, 330-351.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26, 430-511.
Hill, H. C., Rowan, B., &Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal ,42, 371-406.
Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers' mathematical knowledge: what knowledge matters and what evidence counts? In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 111-155). Charlotte, NC: Information Age Publishing.
Huillet, D. (2009). Mathematics for teaching: an anthropological approach and its use in teacher training. For the Learning of Mathematics, 29(3), 4-10.
Klein, H. K., and Myers, M. D. ìA Set of Principles for Conducting and Evaluating Interpretive Field Studies in Information Systems,î MIS Quarterly (23:1), March 1999, pp. 67-94.
Learning Mathematics for Teaching (LMT) Project (2006). A coding rubric for measuring the mathematical quality of instruction. Retrieved September 25, 2013, from http://sitemaker.umich.edu/lmt/files/lmt-mqi_description_of_codes.pdf
Learning Mathematics for Teaching (LMT) Project (2007). Mathematical quality of instruction video coding glossary. Retrieved September 25, 2013, from http://sitemaker.umich.edu/lmt/files/lmt-mqi_glossary_1.pdf
Learning Mathematics for Teaching (LMT) Project (2011). Measuring the mathematical quality of instruction. Journal of Mathematics Teacher Education, 14(1), 25-47.
Leinhardt, G. (1983). Novice and expert knowledge of individual students’ achievement. Educational Psychologist, 18(3), 165-179.
Leinhardt, G. & Simth, D. A. (1985). ‘Expertise in Mathematics Instruction: Subject Matter knowledge’. Journal of Educational Psychology, 77(3), 247-371.
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Beverly Hills, CA: Sage.
Livingston, C. and Broko, H. (1989), Expert- novice diffences in teaching: a cognitive analysis and implications for teacher education, Journal of Teacher Education, 040(004), 0036-0042.
Ma, L. (1996). Profound understanding of fundamental mathematics: What is it ,why is it important, and how is it attained? Unpublished doctoral dissertation, Stanford University, Stanford.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics. Mahwah, NJ: Lawrence Erlbaum.
Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3–11.
McDiarmid, G.WE. & Clevenger-Bright, M. (2008). Rethinking teacher capacity. In Demers, K., Cochran-Smith, M. Feiman-Nemser, S. & John McIntyre, D. (Eds), Handbook of research on teacher education: Enduring questions in changing contexts. (3rd Ed.). (pp. 134-156). Abingdon: Taylor & Francis.
McEwan, H., &Bull, B. (1991). The pedagogic nature of subject matter knowledge. American Educational Research Journal, 28, 316-334.
McIntyre, D. I. (1980). Systematic observation of classroom activities. Educational Analysis, 2(2), 3-30.
National Council of Teachers of Mathematics.(1991). Professional standards for teaching mathematics. Reston, VA: Author.
Patton, M. Q. (1987). How to use qualitative methods in evaluation. Newbury Park, CA: Sage.
Petrou, M., & Goulding, M. (2011). Conceptualizing teachers’ mathematical knowledge in teaching. In Rowland T. & Ruthven K. (Eds.), Mathematical knowledge in teaching (pp. 9- 25). London: Springer.
Rosenshine, B., & Furst, N. (1973). The use of direct observation to study teaching. In R. M. W. Travers (Ed.), Second handbook of research on teaching (pp. 122-183). Chicago: Rand McNally.
Rowland, T. (2008). Researching teachers’ mathematics disciplinary knowledge. In P. Sullivan, &T. Wood (Eds.), The international handbook of mathematics teacher education Vol. 1 (pp. 273-298). Rotterdam, The Netherlands: Sense Publishers.
Rowland, T., Huckstep, P. & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255-281.
Ruthven K. (2012). Conceptualising mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical Knowledge in Teaching (pp. 83-96). New York: Springer.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
Sim, J., & Wright, C. C. (2005). The kappa statistic in reliability studies: use, interpretation, and sample size requirements. Physical therapy, 85(3), 257-268.
Sleep, L. (2009). Teaching to the Mathematical Point: Knowing and Using Mathematics in Teaching. Unpublished doctoral dissertation, State University of Michigan, East Lansing, MI.
Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection. Mathematics Teaching in the Middle School, 3, 268-275.
Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11(4), 307-332.
Thames, M. H. (2009). Coordinating mathematical and pedagogical perspectives in practice-based and discipline-grounded approaches to studying mathematical knowledge for teaching (K-8). Unpublished dissertation. University of Michigan, Ann Arbor.
Vale, C., McAndrew, A., & Krishnan, S. (2011). Connecting with the horizon: developing teachers’ appreciation of mathematical structure. Journal of Mathematics Teacher Education, 14(3), 193-212.
Wilson, S. M., Shulman, L. S., & Richert, A. E. (1987). “150 different ways of knowing: Representations of knowledge in teaching.” In J. Calderhead (Ed.), Exploring teachers’ thinking (pp. 104–124). Sussex: Holt, Rinehart, & Winston.
Yin, R. K. (1994). Case study research: design and methods (2nd ed.). Thousand Oaks, CA: Sage
Zazkis, R. & Momolo, A. (2011) Reconceptualizing knowledge at the mathematical horizon. For the Learning of Mathematics, 31(2), 8-13.
Zazkis, R. & Zazkis, D. (2011). The significance of mathematical knowledge in teaching elementary methods courses: perspectives of mathematics teacher educators. Education Studies in Mathematics, 76(3), 247-263.