研究生: |
李芳庭 |
---|---|
論文名稱: |
國三學生學習教師幾何推理證明的情形之研究 |
指導教授: | 謝豐瑞 |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2008 |
畢業學年度: | 96 |
語文別: | 中文 |
論文頁數: | 153 |
中文關鍵詞: | 學生習得 、幾何證明 、幾何推理 |
論文種類: | 學術論文 |
相關次數: | 點閱:213 下載:146 |
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 |
本研究要探討的是學生對於課堂中教師作的幾何推理證明的學習情形,並且試圖從教師的教學中尋找影響學生學習的可能原因?
本研究進入學校數學課堂,實地觀察並拍攝教學實錄,作為分析教師教學對學生學習之影響的資料,並設計兩式開放程度不同的問卷,收集學生主動憶取和被動憶取教師所做推理證明的表現。
本研究藉由學生對於教師所做推理證明中所含的主要成分、局部推理、邏輯序列、重要轉折的抓取情形,來分析學生習得教師的推理證明的情形。
此外,除了分析各觀察班級學生習得幾何推理證明之情形,本研究試圖比較三個觀察班級中,學生程度相當的學生在習得教師推理證明情形之差異,再分析教師課堂教學,探討教師教學對學生習得情形差異之可能影響為何?
主要的研究結果有:第一、學生對於教師作的是「證明」或是「說明」的重視程度不同。學生較容易抓取到形式化證明的結構,而說明解釋方式的推理證明,學生反而不易抓取到主要成分。第二、學生對於應用已經形成概念之性質的局部推理,常出現的是僅寫出結論的斷言形式,或是直接應用在其他局部推理中,而不會做出該局部推理。第三、學生在憶取教師的推理證明時,鮮少與教師完全相同,有時會嵌入學生自己的局部推理、自創的紀錄格式、可接受但不同於教師的邏輯序列,也就是說某種程度可以看到學生將教師推理證明內化為自己的推理證明的現象,而不僅是完全地模仿教師的推理證明。第四、國中教師的幾何推理證明教學,仍是以講述教學為主,若能搭配問答,提出開放度較高的問題、多利用板書和圖形、避免過高的教學主題密度、提供學生重複經歷相同或相似的推理證明歷程…等教學手法及教學內容安排,應能幫助學生習得教師所做的幾何推理證明。
中文部份:
吳慧真(民86)。幾何證明探究教學之研究。國立臺灣師範大學數學系碩士班碩士學位論文,未出版,台北市。
李士錡(2001)。 PME: 數學教育心理。上海華東師範大學出版社,p22-p63。
李宜芬(民 90)。國三學生突破因附圖造成之論證障礙的學習歷程之研究。國立臺灣師範大學科學教育研究所碩士學位論文,未出版,台北市。
黃哲男(民 90)。於動態幾何環境下國中生動態心像建構與幾何推理之研究。國立臺灣師範大學科學教育研究所碩士學位論文,未出版,台北市。
楊弢亮(1982)。中學數學教學法通論。台北市,九章。
詹玉貞(民 88)。波利亞的解題步驟對國中數學資優生學習幾何證明成效之研究。國立臺灣師範大學科學教育研究所碩士學位論文,未出版,台北市。
蕭文強(民87)。數學證明。新竹市:凡異。
英文部份:
Battista,M.T.,&Clements,D.H.(1995).Geometry and Proof. The mathematics Teacher,88(1),48-54
Boero,P.(1999). Argumentation and mathematical proof:A complex, productive. unavoidable relationship in mathematics and mathematics education. International Newsletter on the Teaching and Learning of mathematical proof,7/8
Boero,P.(2007)(ed.), Theorems in school:from History, epistemology and Cognition to Classroom practice, Sensepublisher.
Lin,F.L(2005).MODELING STUDENTS’ LEARNING ON MATHEMATICAL PROOF AND REFUTATION, Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education ,Vol. 4, pp. 3–18. Melbourne: PME.
Duval, R. (1998). Geometry from a cognitive of view.Perspectives on the Teaching of Geometry for the 21st century.An ICMI Study. (pp.37-52)
Duval,R.(2002).Proof understanding in MATHEMATICS:What ways for STUDENTS?Proceedings of 2002 International Conference on Mathematics:Understanding Proving and Proving to Understand,pp.61-77
Hann,G.,&Lajnke,H.N.(1996).Proof and Proving. In A.J.Bishop,K.Clements,C. Keitel,J.Kilpatrick,&C.Laborde(Eds.),International handbook of mathematics education(pp.877-908).Dordrecht,Netherlands:Kluwer Academic Publishers.
Hoyles.C.(1997). The Curricular Sharping of Students’ Approaches to Proof. For the learning of mathematics, 17(1),7-16
Harel, G. and Sowder, L.(1998). Students’ proof schemes: Results from Exploratory Studies,in E. Dubinsky, A. H. Schoenfeld and J. J. Kaput (eds.), Research on Collegiate Mathematics Education, Vol. III, AmericanMathematical Society, Providence, RI, USA, pp. 234–283.
Hearly,L.&Hoyles,C.(1998). Justifying and Proving in School Mathematics. Technical report on the nationwide survey. Institute of education, University of London
Heinze,A.(2004). THE PROVING PROCESS IN MATHEMATICS CLASSROOM-METHOD AND RESULT OF A VIDEO STUDY. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education,Vol 3,pp41-48
Heinze,A.,&Ufer,S.(in press).Development of geometric proof competency from grade 7 to 9:a longitudinal study.
Moore, R. C.(1994). Making the transition to formal proof, Educational Studies in
Mathematics 27(3), 249–266
McCrone,S.S.&Martin,T.S.(2001).INVESTIGATING THE TEACHING AND LEARNING OF PROOF:FIRST YEAR RESULTS, Proceeding of the Annual Meeting of the North American Charter of the International Group for the Psychology of Mathematics Education, pp585-594.
McCrone,S.S.&Martin,T.S.(2002).Assessing high school student’s understanding of geometric proof. mathematics and technology education, Canadian Jounral for Science, Mathematics, and Technology Education 4(2),223-242
Martin,T.S., McCrone,S.S., Bower,M.W. and Dindyal,J(2005).THE INTERPLAY OF TEACHER AND STUDENT ACTIONS IN THE TEACHING AND LEARNING OF GEOMETRIC PROOF, Educational Studies in Mathematics 60,95-124
National Council of Teachers of Mathematics.(2000). Principles and standards for school mathematics. Reston, VA:Author.
Pedemonte,B.(2007).How can the relationship between argumentation and proof be analysed?,Educational Studies in Mathmetics,66, 23-41
Reiss, K., Hellmich, F., & Reiss, M. (2002). Reasoning and proof in geometry: prerequisites of knowledge acquisition in secondary school students. In A.D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 113–120). Norwich: University of East Anglia.
Senk,S.L.(1985).How well do students write geometry proofs?Mathematics Teacher,78(6),448-456
Senk,S.L.(1989).Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education,20(3),309-321
Stylianides, A.J.(2007). Proof and Proving in School Mathematics. Journal for Mathematics Education, 38(3),289-321
Usiskin,Z.(1982). Van Hiele levels and achievement in secondary school geometry. Chicago:University of Chicago Press.