跳到主要內容

臺灣博碩士論文加值系統

(54.172.135.8) 您好!臺灣時間:2022/01/18 14:52
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:王宏哲
研究生(外文):Hong-Zhe Wang
論文名稱:以數學史輔助學習的教學研究
論文名稱(外文):The Teaching Study of Using History of Mathematics to Assist Learning
指導教授:邱守榕邱守榕引用關係
指導教授(外文):Sou-Yung Chiu
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:科學教育研究所
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:153
中文關鍵詞:數學史學習教學合作學習
外文關鍵詞:History of MathematicsLearningTeachingCooperative learning
相關次數:
  • 被引用被引用:9
  • 點閱點閱:965
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:3
本研究旨在探討以數學史為輔的教學實驗中,高職一年級學生的數學認知。以及研究者數學科教學能力的成長。
本研究方法包含行動研究和質性研究。研究者採用數學活動工作單進行教學,並以合作學習的方式,佈置有助於學生解題的環境。在師生互動的過程中,研究者以訊息加工處理法分析學生的數學學習,針對工作單、學習日誌、評量卷、晤談、上課錄影、教學日誌等資料,進行三角校正分析,確保研究效度。
研究發現如下:
一、數學認知方面
(一)學生強記乘法公式而未理解。
(二)以不同策略處理一元二次方程式:除了研究者教導的配方法外,學生也使用十字交乘法、根的公式和試誤法來求解。
(三)在實作中肯定學生的學習:從學生拼湊厚紙板、摺紙和計算網點圖面積中,顯示學生在實作中使用數學知識。
(四)對數學家的軼事感受不同:有人認為數學家成功的事蹟可以做為借鏡,但也有人覺得數學家能成功是因為比一般人更具天分,自己不可能如此。
二、教學能力成長方面
(一)事後反省看到教學盲點:研究者後來重新觀看輔導教學原案,除了晤談後未讓學生實作外,自己也有教學的迷思概念。
(二)編製工作單的能力:在編製工作單中,研究者為了厚植對數學「史實」的理解以及援以「史觀」的精神,閱讀相關的數學史文獻,並採用「分離原則」將課題分割成程序分明且可操作的小段落。
(三)訊息加工處理的能力:為分析學生的數學認知,學生的工作單、評量卷、學生的實作和討論都是訊息加工處理的範疇,研究者越來越熟悉訊息加工處理法的使用。
(四)向學生學習:從學生的學習困難和學習如何編製工作單來引導學生的學習中,研究者瞭解「向學生學習」的重要性。
(五)課室教學策略:利用合作學習的方式,設法營造有利學習的環境,並視情形給予鼓勵與獎賞,都能促進學生學習。
This study is inquired into the mathematical cognition of the first grade students in the vocational school in teaching experiments based on the history of mathematics and raised the growth of teaching ability of the researcher.
The study applied action research and qualitative research. The researcher adopted the work sheets for the mathematical activities to teach and designed an environment to help students to solve problems by cooperative learning. During the interaction of teacher and students, the researcher used the information processing approach to analyze the students’ learning about mathematics and analyzed the triangulation according to work sheets, learning diary, evaluation, interviews, teaching diary, and so on for ensuring the research validity.
The findings of this study are in the following :
The aspect of the mathematical cognition.
1.The students were forced to memorize the multiplicative identities without comprehension.
2.The students dealt with quadratic equation by different ways, such as generate-test method, across-multiplication and formula of root besides the completing the square taught by the researcher.
3.The students’ efforts in learning were confirmed during the manipulation. Some of them pieced up the cardboard, folded the paper and calculated the dot. It stood for that students used mathematical knowledge during the manipulation.
4.The same mathematician’s anecdote gave the students different feelings or meanings. Some of them thought that they would be never as successful as those famous mathematicians since they didn’t have the gifts for mathematics.
The aspect of the growth of teaching ability.
1.The researcher found out the blind spots of teaching by reflection. After reviewing the teaching raw data, the researcher found out his teaching misconception besides no manipulation right away after interviews with students.
2.The researcher improved his ability of making work sheets. During making work sheets, the researcher read documents about the history of mathematics to enhance the events and perspectives, and adopted the separation principle to divide the topics into parts clear and manipulative.
3.The researcher improved his ability of using information processing approach. The reason was that those methods such as students’ manipulation and discussion belonged to the information processing approach’s category and help to analyze students’ mathematical cognition.
4.The researcher realized that the importance of learning from the students. The reason was that learning from students made the researcher knows how to make work sheet to lead student learn from their learning problems and difficulties.
5.The researcher had to use different teaching strategies. The researcher could use cooperative learning or encouragement and reward to design an environment to assist student to learn better.
第壹章 緒論
第一節 研究背景與研究動機……………………………………1
第二節 研究目的與待答問題……………………………………4
第三節 名詞解釋…………………………………………………4
第四節 研究的基本假設與限制…………………………………6
第貳章 文獻探討
第一節 以數學史輔助數學教學…………………………………7
第二節 鷹架理論…………………………………………………19
第三節 合作學習…………………………………………………25
第四節 認知觀點…………………………………………………28
第參章 研究方法
第一節 研究對象…………………………………………………33
第二節 研究者的教學經驗………………………………………35
第三節 研究工具…………………………………………………36
第四節 研究流程…………………………………………………42
第五節 資料收集與分析…………………………………………45
第肆章 研究發現與討論
第一節 輔導教學原案……………………………………………48
第二節 學生的錯誤類型…………………………………………75
第三節 數學科教學能力的成長…………………………………76
第伍章 結論與展望
第一節 結論………………………………………………………106
第二節 檢討與展望………………………………………………109
參考文獻
中文書目………………………………………………………………114
西文書目………………………………………………………………115
附錄
附件一 「一元一次方程式」測驗卷………………………………119
附件二 「一元二次方程式」測驗卷………………………………120
附件三 <乘法公式>工作單………………………………………121
附件四 <乘法公式>工作單修改版………………………………124
附件五 <配方法>工作單…………………………………………128
附件六 <解一元二次方程式的幾何模式>工作單………………132
附件七 <解一元二次方程式>工作單……………………………135
附件八 <哪裡出錯了>工作單……………………………………137
附件九 <桑雅˙卡巴列夫斯基-土星、對稱和求解>工作單…139
附件十 <關孝和-解決不可解的問題>工作單…………………143
附件十一 <印度國寶-拉瑪奴江>工作單………………………146
附件十二 <印度國寶-拉瑪奴江>工作單修改版………………150
附件十三 <十字交乘表>…………………………………………151
中文書目
于富雲(2001):從理論基礎探究合作學習的教學效益。教育資料與研究,第三十八期。
水木耳譯(1995):科學中的數學方法。新竹:凡異出版社。譯自Polya(1977):Mathematical methods in science.
牛頓雜誌(1998),第178期。台北市:牛頓出版社。
李秀卿(1997):二次方程式的幾何思維之歷史研究:以中國與回教世界為例。國立台灣師範大學數學研究所碩士論文。
林清山譯(2000):教育心理學-認知取向。台北市:遠流出版社。譯自Mayer, R. E.(1987):Educational Psychology.
邱守榕(1992):關於數學學習研究。科學發展月刊,第二十卷,第五期。
邱守榕(1996):數學教育。行政院國家科學委員會:學門資源整合規劃資料。
邱守榕、黃鴻博、梁崇惠和陳正賢(1999):數學教學活動設計與表演賽推廣手冊。國立彰化師範大學數學系。
邱守榕(2000):數學史與數學教育史在數學師資教育改革中的實質作用II-史實與史觀對數學活動設計與分析的啟示。行政院國家科學委員會專題研究計畫成果報告,計畫編號NSC 89-2511-S-018-010。
吳大任譯(1996)(Felix Klein原著):高觀點下的初等數學,第一卷。台北市:九章出版社。
岳修平譯(1998):教學心理學-學習的認知基礎。台北市:遠流出版公司。譯自Gangé, E. D., Yekovich, C. W. & Yekovich, F. R. (1993) The Cognitive Psychology of School Learning.
洪蘭譯(1999):心理學。台北市:遠流出版社。譯自Gleitman, H. (1991) Psychology.
洪萬生(1998):HPM台北通訊,第一卷第一期。
洪萬生(1999):HPM台北通訊,第二卷第四期。
洪萬生(2000):HPM台北通訊,第三卷第六、七期。
梁崇惠編(1999):數學史作業彙編。
梁崇惠編(1999):心裡有數-數學週刊。
梁鑑添和蕭文強(1995):一門與數學發展史有關的課程。刊登於蕭文強編香港數學教育的回顧與前瞻,梁鑑添博士榮休文集,香港大學出版社。
許志逸(1999):淺談合作學習。建構與教學,第十四期。
陳瑞姬和魏慶榮譯(1975):邏輯與教學,數學傳播季刊。
教育部(2000):國民教育九年一貫課程「數學」課程綱要。台北市:教育部。
張菀珍(1997):鷹架理論在成人教學實務之應用。成人教育,40,43-52。
蕭文強(1976):數學發展史給我們的啟發。抖擻,17,19-25。
戴文賓(1999):國一學生由算術領域轉入代數領域呈現的學習現象與特徵。國立彰化師範大學科學教育研究所碩士論文。
歐陽絳(1999):數學的藝術。台北市:九章出版社。
歐陽絳譯(1997):數學史概論。台北市:九章出版社。譯自 Howard Eves (1989) An introduction to the history of mathematics.
閻育蘇譯,張公緒校(2000):怎樣解題。台北市:九章出版社。譯自Polya, G.(1957) How to Solve It.
Alcoze, et al. (1993). Multiculturalism in Mathematics, Science, and Technology. New York:Addison-Wesley Publishing Company.
Athen, H. & Heinz, K. (1977). Proceedings of the Third International Congress on Mathematical Education. Karlsruhe:The Organizing Committee of the Third International Congress on Mathematical Education.
Bagni, G. T. (2000). Difficulties with series in history and in the classroom. In John Fauvel, Jan van Maanen (Eds.), History in mathematics education: the ICMI study. Dordrecht: Kluwer. 179-184.
Berk, L. E. & Winsler, A. (1995). Scaffolding Children’s Learning:Vygotsky and Early Childhood Education. Washington, DC:National Association for the Education of Young Children.
Bruner, J. S. (1966). Toward A Theory of Instruction. New York:W. W. Norton & Company.
Crabill, C. D. (1990). Small-Group Learning in the Secondary Mathematics Classroom. In N. Davison (Ed.), Cooperative Learning in Mathematics-A Handbook for Teachers, New York:Addison-Wesley Publishing Company.
Ellis, E. S. (1994). Research Synthesis on Effective Teaching Principles and the Design of Quality Tools for Educators. Executive Summary. Technical Report No. 6. ERIC:ED386854.
Fauvel, J. (1991). Using History in Mathematics Education. For the Learning of Mathematics, 11(2), 3-6.
Furinghetti, F. (2000). The Long Tradition of History in Mathematics Teaching:An old Italian Case. In Katz J. (Ed.), Using History to Teach Mathematics: An International Perspective, Washington: MAA. 49-58
FitzSimons, G. E. (2000).Alternative educational pathways:adult learners returning to mathematics education, vocational education and training. In John Fauvel, Jan van Maanen (Eds.), History in mathematics education: the ICMI study. Dordrecht: Kluwer. 179-184.
Glass, A. L. & Holyoak, K. J. (1986). Cognition ( 2nd ed. ). Singapore:McGraw-Hill Book Company.
Grugnetti, L. (2000). The History of Mathematics and its Influence on Pedagogical Problems. In Katz J. (Ed.), Using History to Teach Mathematics: An International Perspective, Washington: MAA. 29-35.
Hogan, K. & Pressley, M. (1997). Scaffolding scientific competencies within classroom communities of inquiry. In K. Hogan & M. Pressley (Eds.), Scaffolding student learning: Instructional approaches & Issues (pp. 74-107). Cambridge, MA:Brookline Books.
Howson, A. G. (1973). Developments in Mathematical Education-Proceedings of the Second International Congress on Mathematical Educational. Cambridge, London:Cambridge University Press.
Johnson, D.W. & Johnson, R.T. (1990). Using Cooperative Learning in Math. In N. Davison (Ed.), Cooperative Learning in Mathematics-A Handbook for Teachers, New York:Addison-Wesley Publishing Company.
Katz, V. (1997). Some ideas on the use of history in the teaching of mathematics. For the Learning of Mathematics, vol. 17, no. 1, 62-63.
McCarthey, S. J. & McMahon, S. (1995). From Convention to Invention:Three Approaches to Peer Interaction During Writing. In Interaction in Cooperative Groups:The Theoretical Anatomy of Group Learning, edited by R. Hertz-Lazarowitz, N. Miller, p.17-35. Cambridge:Cambridge University Press.
Patton, M. Q. (1990). Qualitative Evaluation And Research Methods (2nd Ed.), Newbury Park:Sage.
Radford, L. & Guerette, G. (2000). Second Degree Equations in the Classroom:A Babylonian Approach. In Katz J. (Ed.), Using History to Teach Mathematics: An International Perspective, Washington: MAA. 69-75.
Rogers, L. (1974). History of Mathematics at Teachers Conferences in England, Exeter 1974. Historia Mathematica, Vol. 1, No. 1.
Schoenfeld, A. H. (1985). Mathematical Problem Solving. NY:Academic.
Schoenfeld, A. H. (1987). Cognitive Science and Mathematics Education:An Overview. In A. H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp.1-31), New Jersey:LEA.
Silver, E. A. (1987). Foundations of Cognitive Theory and Research for Mathematics Problem-Solving. In A. H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp.33-60), New Jersey:LEA.
Steffe, L. P. & D’Amborosio, B.S. (1996). Using teaching experiments to enhance understanding of students’ mathematics. In Treagust, D.F., Duit, R., & Fraser, B.J. (Eds), Improving teaching and learning in science and mathematics. NY:Teachers College Press. 65-76.
Shulman, L. S. (1986).Those Who Understand:Knowledge Growth in Teaching. Stanford University. American Educational Research, 15(2), 4-14.
Swetz, F. (2000a). Mathematical Pedagogy:An Historical Perspective. In Katz J. (Ed.), Using History to Teach Mathematics: An International Perspective, Washington: MAA. 11-16.
Swetz, F. (2000b). Problem Solving from the History of Mathematics. In Katz J. (Ed.), Using History to Teach Mathematics: An International Perspective, Washington: MAA. 59-65.
Tzanakis, C., Arcavi, A., Correia, C., Isoda, M., Chi-kai Lit, Niss, M., Pitombeira, J., Rodriguez, M., & Man-Keung Siu (2000). Integrating history of mathematics in the classroom: an analytic survey. In John Fauvel, Jan van Maanen (Eds.), History in mathematics education: the ICMI study. Dordrecht: Kluwer. 201-240.
Vygotsky, L. S. (1978). Mind in Society. Cambridge, MA:Harvard University Press.
Wood, D., Bruner, J. & Ross, G. (1976). The Role of Tutoring in Problem Solving. Journal of Child Psychology and Psychiatry and Allied Disciplines, 17, 89-100.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top