Basic Search / Detailed Display

Author: 王淳華
WANG,CHUN-HUA
Thesis Title: 探討國中數學教師平均數知識、觀感及其教學實務間的關係之個案研究
Explore the Relationship of Average Knowledge、Concepts and Teaching Practice in Mathematics Teacher Case Study
Advisor: 楊凱琳
Yang, Kai-Lin
Degree: 碩士
Master
Department: 數學系
Department of Mathematics
Thesis Publication Year: 2013
Academic Year: 101
Language: 中文
Number of pages: 150
Keywords (in Chinese): 平均數知識平均數觀感對於學習者知識教學
Thesis Type: Academic thesis/ dissertation
Reference times: Clicks: 203Downloads: 48
Share:
School Collection Retrieve National Library Collection Retrieve Error Report
  • 本研究以兩位不同背景的國中數學教師為對象,探討個案教師的平均數知
    識、觀感及其實務間的關係進行初步探討。本研究採用個案研究法,透過教學
    觀察、課前課後訪談和學生問卷來蒐集相關資料。從教師所具備的知識、觀感;
    在課程中實施與否以及改變與否等三個面向來了解教師實施統計課程的情形。
    結果發現一位教師對於平均數的內容知識以及學習者的知識相當充足,但其
    教學知識並不足夠甚至有錯誤的地方,對於平均數的內容觀感俱備正確性、真
    實性以及有效性,認為統計教學應該要多讓學生去感受統計數字背後的含意,
    並且指出學生對於統計應該是感到喜歡並具有實用性;另一位教師在平均數
    的教學知識的部分較為充足,但因對抽樣概念較為缺乏,使得對於內容知識以
    及學習者的知識較為不足,對於平均數的內容觀感俱備正確性、真實性以及有
    效性,認為統計教學應該要避免大量的計算,同時也指出學生對於統計應該是
    感到不排斥具有實用性。
    在課室的呈現上,一位教師較偏向傳統的課程實施,談到的平均數性質以
    教科書內容為主,不會因對於學習者的知識而有所改變,其教學知識並沒有完
    全展現在課程之中並且輔以大量舉例的方式來傳達 T1 本身的觀感;T2 則較偏
    向開放討論的方式,因此談到的平均數性質較教課書內容多,其教學知識並沒
    有完全展現在課程之中,也是輔以大量舉生活例的方式來傳達 T2 本身的觀感。
    在受到改變的情況上,T1 大部分的知識與觀感並不會因教學而受到改變,
    僅教學法知識會受到實務中(時間點、學生反應)影響,而產生了一些消弱反應;
    T2 大部分的知識與觀感並不會因教學而受到改變,但教學法知識會明顯受到
    實務中(與學生一起討論)而明顯增強。

    第壹章 緒論 1 第一節 研究背景 1 第二節 研究目的與待答問題 6 第三節 名詞界定 6 第貳章 文獻探討 7 第一節 統計教學所需的知識 7 第二節 統計教學所需的觀感 19 第三節 統計教學的知識、觀感與教學實務的實徵性研究 25 第參章 研究方法 29 第一節 研究對象的背景與選擇 29 第二節 研究設計與流程 32 第三節 研究工具 37 第四節 資料蒐集與分析 46 第五節 研究的信效度 49 第肆章 研究結果 51 第一節 個案教師T1在非課室與課室呈現的平均數相關知識與觀感 51 第二節 個案教師T2在非課室與課室呈現的平均數相關知識與觀感 73 第三節 兩名個案在非課室與課室的平均數相關知識與觀感之展現 95 第四節 兩名個案在非課室與課室的平均數相關知識與觀感之變化 110 第伍章 結論與建議 115 第一節 結論 115 第二節 討論 116 第三節 建議 119 參考文獻 123 中文部分 123 英文部分 125 附錄 131

    中文部分
    丁興祥、張慈宜和曾寶瑩(譯)(2006)質性心理學一研究方法的實務指南(原作者:Smith)。台北市:遠流。(原著出版年:2003)
    方吉正 (1998)。教師信念研究之回顧與整合一六種研究取向。教育資料與研究,20,36-44。

    任眉眉 (2004)。機率統計之概念暨網路學習研究—子計畫二:統計概念與應用網路學習研究。行政院國家科學委員會專題研究計畫成果報告。(編號:NSC92-2511-S-006-001),未出版。

    張少同、王建都、呂小娟(2003)。青少年的數學概念學習研究—子計畫七:青少年的統計概念學習研究。行政院國家科學委員會專題研究計畫成果報告。(編號:NSC 91-2521-S-003-007),未出版。

    吳芝儀、李奉儒(譯)(1995)。質的評鑑與研究(原作者:Patton, M. Q.)。台北:桂冠。(原著出版年:1990)

    吳柏林、葉倩亨 (2002)。由自然潛能與數學生活化探討國中數學的統計與機率領域課程設計。教育研究月刊,101,90-104。

    卓明惠 (2011)。探討高中數學教師在統計單元教學之個案研究(未出版之碩士論文)。國立彰化師範大學科學教育研究所。彰化市。

    香港特別行政區教育局 (1999)。中學課程綱要數學科。取自http://www.edb.gov.hk/tc/curriculum-development/kla/ma/curr/sec-math-1999.html

    高中數學學科中心 (2009)。普通高級中學必修科目「數學」課程綱要。取自http://mathcenter.ck.tp.edu.tw/MCenter/Center/CourseOutline.aspx

    國民教育司 (2011)。國民中小學九年一貫課程綱要數學學習領域修正草案對照表。取自http://140.111.34.54/EJE/content.aspx?site_content_sn=15326

    教育部(2011)。國民教育階段九年一貫課程綱要總綱。教育部,台北。

    熊召弟、王美芬、段曉林、熊同鑫(譯)(1996)。科學學習心理學(原作者:Glynn, S. M., Yeany, R. H., & Britton, B. K.)。台北:心理。(原著出版年:1991)。

    陳宜良(2005)。中小學數學科課程綱要評估與發展研究-我國與美國加州、英國、新加坡、日本、中國大陸、南韓之跨國比較。2011年12月29日,取自http://www.math.ntu.edu.tw/~chern/mathedu/Comparison.pdf

    陳幸玫 (2006)。國小統計課程之內函與教學理念。科學教育月刊,287,2-12。

    新加坡教育局 (2012)。中一、中二數學綱要。取自http://www.moe.gov.sg/cpdd/syllabuses.htm

    黃精裕(2008)。高中數學教師數學教學相關知識之初探─以集中與離散趨勢量數為例(未出版之碩士論文)。國立臺北教育大學數學教育研究所,臺北市。

    蘇國樑 (2000)。統計對象的抽象原則。科學教育月刊,233,19-26。

    鄭天澤 (2011)。機率統計之概念暨網路學習研究—子計畫三:高中教師對機率統計課程認知之現況了解與改進研究。行政院國家科學委員會專題研究計畫成果報告。(編號:NSC 89-2511-S-004-001),未出版。

    楊凱琳(2012)。探討中學數學教師的統計教學知能。行政院國家科學委員會專題研究計畫成果報告。(編號:NSC 98-2511-S-003-009 -M),未出版。

    英文部分
    Ball, D. L. (1991). Teaching mathematics for understanding: What do teachers need to know about subject matter? In M. Kennedy (Ed.), Teaching academic subjects to diverse learners (pp. 63–83). New York: Teachers College Press.
    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.
    Ball, D. L., Hill, H. H., & Bass, H. (2005, Fall). Knowing mathematics for teach-ing: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, pp. 14-46.
    Batanero, C., Godino, J. D., & Roa, R. (2004). Training teachers to teach probability. Journal of Statistics Education, 12(1). Online:www.amstat.org/publications/jse.
    Begle, E. I (1979). Critical variables in mathematics education:Finding from a survey of the empirical literature. Washington, DC:Mathematical Association of America and National Council of Teachers of Mathematics.
    Brown, S. I. (1985). Problem-solving and Teacher Education:The Humanism twixt Models and Muddles. In:R. Morris (ed.), Studies in Mathmatics Education. Vol. 4 The Education of Secondary School Teachers of Mathmatics, pp. 3-28. Paris, Unesco.
    Burgess, T. A. (2008). Teacher knowledge for teaching statistics through investigations. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).
    Carpenter, T. P., Fennema, E., Peterson, P. L., & Carey, D. (1988). Teachers' pedagogical content knowledge of students' problem solving. Journal of Research in Mathematics Education, 19, 385-401.
    Chick, H. L., & Pierce, R. U. (2008). Teaching statistics at the primary school level: Beliefs, affordances, and pedagogical content knowledge. In C. Batanero, G. Burrill, C. Reading.
    Clark, C, & Yinger, R. (1979). Teachers' thinking. In P. Peterson & H. Walberg (Eds.), Research on teaching. Berkeley, Calif.: McCutchan.

    Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382-393.
    Deborah L MacCullough. (2007), A Study of Experts' Understanding of Arithmetic Mean.
    Denzin, N.K. (1978). The research act: A theoretical introduction to sociological methods. New York: McGraw-H.
    Dietz, E. J. (1993). A Cooperative Learning Activity on Methods of Selecting a Sample, The American Statistician, 47, 104-108.
    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. 147-162). New York, NY: National Council of Teachers of Mathematics.
    Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124 e 158.
    Garfield, J., & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: implications for research. Journal for Research in Mathematics Education, 19(1), 44-63.
    Garfield, J. and Ben-Zvi, D. (2004). Statistical literacy, reasoning, and thinking: goals, definitions, and challenges. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 3-16). Dordrecht, the Netherlands: Kluwer Academic Publishers.
    Garfield, J. and Ben-Zvi, D. (2007). How Students Learn Statistics Revisited: A Current Review of Research on Teaching and Learning Statistics,"International Statistical Review, 75, 372 – 396.
    Groth, R. E., & Bergner, J. A. (2005). Preservice elementary school teachers' metaphors for the concept of statistical sample. Statistics Education Research Journal, 4(2), 27-42.
    Guimarães, Gitirana, Marques & dos Anjos (2010). The Conecpt of Mean by Primary School Students. ICOTS8 (2010) Contributed Paper.
    Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’mathematical knowledge for teaching on student achievement.American Education Research Journal, 42(2), 371-406.
    Lajoie, S. P., Lavigne, N. C., & Lawless, J. (1993). The use of hypercard for facilitating assessment : A library of exemplars for reifying statistical concepts. Paper presented at the American Educational Research Association Conference, Atlanta ,GA.
    Magel, R. C. (1998), Using Cooperative Learning in a Large Introductory Statistics Class, Journal of Statistics Education, 6, http://www.amstat.org/publication
    Marton, F. (1988). Phenomenography: A research approach to investigating different understandings of reality. In R. R. Sherman & R. B. Webb (Eds.), Qualitative research in education: Focus and methods (pp. 141-161). New York: The Falmer Press.understandings of reality. In R. R. Sherman & R. B. Webb (Eds.), Qualitative research in education: Focus and methods (pp. 141-161). New York: The Falmer Press.
    McDiarmid, G. W., Ball, D., and Anderson, C. (1989). Why staying ahead one chapter just won'twork: Subject-specific pedagogy. In M. Reynolds (Ed.), Knowledge base for beginning teachers. Washington, DC: American Association of Colleges of Education.
    Mevarech, Z. R. (1983). A deep structure model of students' statistical misconceptions. Educational studies in mathematics, 14, pp415-429.
    Mokros, Jan ,& Russell, Susan Jo(1992). Children’s Concepts of Average and Representativeness.
    National Council of Teachers of thematics. (1989). Curriculum and Evaluation Standards for Shool Mathematics. Reston, VA: NCTM.
    National Council of Teachers of thematics.(2000).Principles and Standards for School Mathematics. printed in U Piaget , J .(1973). To understand is to invent :The future of education. New eston, VA: NCTM.
    The National Commission on Teaching and America’s Future (2002).取自http://nctaf.org/
    Patton, M. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Beverly Hills, CA: Sage.
    Pollatsek, S. Lima, A. D. Well (1981) . Concept or Computation: Students' Understanding of the Mean. Educational Studies in Mathematics , 12 . pp. 191-204
    Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior, 22, 405–435.
    Qualification and Curriculum Authority (1999). Mathematics, the National Curriculum for England.
    Ra ̇de, L. 1985. Statistics. In: R. Morris (ed), Studies in Mathematics Education. Vol. 4: The Education of Secondary School Teachers of Mathematics, pp.97-107. Paris, Unesco
    Rebecca.B Corwin, & Susan Jo Russell (1990). A unit of study for grades 3-4 from Used Numbers: Real Data in the Classroom. Developed at Technical Education Research Centers and Lestey Collage.
    Roschelle, J. (2000). Choosing and using video equipment for data collection. In: R. Lesh (Ed.), Handbook of research data design in mathematics and science education (pp. 709–731). Mahwah, NJ: Lawrence Erblaum Associates.
    Sachs, J. (1997). Reclaiming the agenda of teacher professionalism: An Australianexperience. Journal of Education for Teaching, 23, 263–275.
    Scheaffer R. L.(1988). Statistics in the schools: The past, present and future of the quantitative literacy project. Proceedings of the American Statistical Association from the Section on Statistical Education, 71-78.
    Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 465-494). New York: Macmillan.
    Shulman, L. S. (1985). An emerging model for the study of knowledge growth in teaching. Paper presented at the annual meeting of the American Educational Research Association, Chicago.
    Shulman, L. S.(1986). Those who understand: Knowledge Growth in Teaching. Educational Researcher, 15(1), 4-14.
    Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 51, 1-22.
    Stake, R. (1995). The art of case research. Newbury Park, CA: Sage Publications.
    Steinbring, H. (1989). The Interaction between Teaching Practice and Theoretical Conceptions A Cooperative Model of In-Service Training in Statistics for Mathematics Teachers (Grades 5-10). Studies in mathematics education,7,202-214
    Stella, C. A. (2003). Um estudo sobre o conceito de média com alunos do Ensino Médio. São Paulo, 2003. 181p. Master Dissertation (Master degree in Mathematics Education), Pontifícia Universidade Católica de São Paulo.
    Strauss, S., &. Bichler, E. (1988). The development of children’s concepts of the arithmetic average. Journal for Research in Mathematics Education, 19(1), 64-80.
    Valli, L. (1992). Reflective teacher education: Cases and critiques. Albany: State University of New York Press.
    Vermette,Gattuso& Bourdeau(2005).Data analysis or how high school students “read” statistics.
    Watson, J., Callingham, R., & Nathan, E. (2009). Probing Teachers’ Pedagogical Content Knowledge in Statistics: “How will Tom get to school tomorrow?” In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides (Proceedings of the 32 nd annual conference of the Mathematics Education Research Group of Australasia, Wellington, NZ, Vol. 2, pp. 563-570), Palmerston North, NZ: MERGA.
    Watson, J. M., & Moritz, J. B. (1999). The development of concepts of average. Focus on Learning Problems in Mathematics, 21 (4) 15–39.
    Wilson, S. & Cooney, T. (2002). Mathematics teacher change and development: The role of beliefs. In G.C. Leder, E. Pehkonen, & G. Törner (Eds.) Beliefs: A Hidden Variable in Mathematics Education. pp. 127-147.
    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). London: Cassell.
    Yang, K. L. (2012). Investigating Mathematics teachers thoughts of statistical inference. Research in Mathematics Education, 14(3), 299-300. (Current Report)

    下載圖示
    QR CODE