簡易檢索 / 詳目顯示

研究生: 賴信川
論文名稱: 運用行動載具輔助空間幾何學習
Apply Mobile Devices to Learn Spatial Geometry
指導教授: 張國恩
Chang, Kuo-En
宋曜廷
Sung, Yao-Ting
學位類別: 碩士
Master
系所名稱: 資訊教育研究所
Graduate Institute of Information and Computer Education
論文出版年: 2006
畢業學年度: 94
語文別: 中文
論文頁數: 68
中文關鍵詞: 行動載具空間幾何視覺化操弄形成性評量
論文種類: 學術論文
相關次數: 點閱:180下載:27
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
  • 學習幾何最有效的方式是在教師的引導下,讓學生主動建構知識;高中數學的空間幾何教學中,常因為缺乏適當的輔具,無法有效的引導學生建立空間幾何概念,教師也不易在課堂中即時瞭解學生的學習狀況,影響空間幾何能力的形成。本研究的目的為發展一套運用手持行動學習載具的空間幾何學習系統,透過在課堂中操弄視覺化空間幾何教材,並輔以即時形成性評量,協助高中生可以更有效建立空間能力,學好立體幾何。實驗結果顯示,運用行動學習載具使用本研究發展的空間幾何學習系統,對於學生空間幾何的學習成效有顯著效果。

    The most effective way for learning geometry is to construct knowledge under teacher’s guidance. For the spatial geometry course of high school mathematics, because of lacking suitable teaching auxiliary, students cannot develop spatial geometry concept effectively. Teachers also cannot easily understand student's learning condition in the classroom immediately. All these will affect the formation of spatial geometry ability. The main purpose of this research was to develop a learning system for spatial geometry which running in mobile device. Students used mobile devices to manipulate the spatial geometry materials according to the teacher’s instructions in the classroom. At the same time, the teacher used mobile devices to carry on formative evaluation in classroom. The experimental result showed that, used this system students had significant result in spatial geometry learning.

    附表目錄 iii 附圖目錄 iv 第一章 緒論 1 1.1 研究背景與動機……………………………………………1 1.2 研究目的……………………………………………………4 1.3 研究假設……………………………………………………5 第二章 文獻探討 6 2.1 空間能力與心像……………………………………………6 2.1.1 空間能力與幾何學習……………………………………6 2.1.2 視覺化與心像……………………………………………11 2.2 形成性評量與幾何學習……………………………………15 2.2.1 評量與教學策略的調整…………………………………15 2.2.2 幾何教學中的評量………………………………………16 2.3 行動科技在教學上的應用…………………………………17 第三章 系統說明 21 3.1 設計理念……………………………………………………21 3.2 系統架構……………………………………………………22 3.2.1 教材內容的開發…………………………………………22 3.2.2 系統平台…………………………………………………23 3.2.3 教材內容…………………………………………………23 3.2.4 頁面規劃…………………………………………………24 3.2.5 系統功能…………………………………………………26 3.3 學習引導機制………………………………………………27 3.3.1 範例的多樣呈現…………………………………………28 3.3.2 即時評量系統……………………………………………32 第四章 研究方法 34 4.1 實驗對象……………………………………………………34 4.2 實驗設計……………………………………………………34 4.3 實驗工具……………………………………………………35 4.3.1「立體幾何動手玩系統」…………………………………35 4.3.2 課程材料…………………………………………………36 4.3.3 自編空間幾何評量試題…………………………………37 4.3.4 自編態度問卷……………………………………………38 4.3.5 行動學習環境……………………………………………39 4.4 實驗程序……………………………………………………39 4.4.1 實驗組的教學活動………………………………………39 4.4.2 對照組的教學活動………………………………………40 第五章 研究結果與討論 42 5.1 學生學習成效分析…………………………………………42 5.1.1 空間構圖部分……………………………………………43 5.1.2 視覺化構圖部分…………………………………………44 5.1.3 視覺化操弄部分…………………………………………45 5.1.4 總分………………………………………………………46 5.2 學生態度問卷分析結果……………………………………48 5.3 討論…………………………………………………………53 第六章 結論與建議 57 6.1 結論…………………………………………………………57 6.2 建議…………………………………………………………58 附錄一 試題對照表 60 附錄二 前測試題 61 附錄三 後測試題 63 附錄四 試題難易度與鑑別度 65 附錄五 學生態度問卷 66 參考文獻 68 附表目錄 表2.1 空間能力因素……………………………………………………6 表3.1 操作引導訊息……………………………………………………26 表4.1 課程材料與高中數學課程對照表………………………………37 表5.1 空間幾何前、後測各個項目成績統計表………………………43 表5.2 空間構圖成績的迴歸係數同質性檢定結果……………………43 表5.3 空間構圖成績的共變數分析結果………………………………44 表5.4 實驗組與控制組在空間構圖部分的成績統計…………………44 表5.5 視覺化構圖成績的迴歸係數同質性檢定結果…………………45 表5.6 視覺化構圖成績的共變數分析結果……………………………45 表5.7 實驗組與控制組在視覺化構圖部分的成績統計………………45 表5.8 視覺化操弄成績的迴歸係數同質性檢定結果…………………46 表5.9 視覺化操弄成績的共變數分析結果……………………………46 表5.10 實驗組與控制組在視覺化操弄部分的成績統計………………46 表5.11 空間幾何評量成績的迴歸係數同質性檢定結果………………47 表5.12 空間幾何評量成績的共變數分析結果…………………………47 表5.13 實驗組與控制組在空間幾何評量總分的成績統計……………47 表5.14 態度問卷五點量表評分百分比統計……………………………48 附圖目錄 圖3.1 教學頁面規劃……………………………………………………25 圖3.2 系統登入畫面……………………………………………………26 圖3.3 管理者畫面………………………………………………………27 圖3.4 文字呈現試題……………………………………………………29 圖3.5 答題的回饋………………………………………………………29 圖3.6 圖形呈現試題……………………………………………………30 圖3.7 動態操弄試題……………………………………………………31 圖3.8 試題解法的圖示…………………………………………………31 圖3.9 指派試題畫面……………………………………………………32 圖3.10 評量試題的作答畫面……………………………………………33 圖3.11 評量結果統計……………………………………………………33

    左台益、王惠中 (2000):動態幾何實驗設計。中華民國第十六屆科學教育學術研討會短篇論文彙編,pp. 337-345。台北市:國立台灣師範大學科學教育研究所。
    左台益、梁勇能(2001):國二學生空間能力與van Hiele幾何思考層次相關性研究。師大學報,46,pp. 1-20。
    朱建正(1997):立體圖形的教材處理。國立嘉義師範學院八十六學年度數學教育研討會。
    宋曜廷、張國恩 (2005):行動載具在教學與學習的應用:近十年研究的批判整合。論文發表於2005學習、教學、與評量國際研討會。6月11-12日。台北。
    李文貞(2003):幼兒幾何型體概念發展研究。國立台灣師範大學人類發展與家庭學系在職進修碩士班學位論文。
    李盛祖(1997):數學診斷測驗編製之探討。測驗與輔導143期。
    林松穎(2004):多媒體輔助兒童幾何學習之設計與應用。國立台灣師範大學資訊教育學系碩士學位論文。
    林淑德、梁成一(2002):「透視陰影概念應用之初探」,創作‧設計‧管理國際研討會論文集。
    林碧珍(1985):數學概念的形成與學習。國教世紀,21卷2期。
    姚晉雯(2002):高三學生平移旋轉解題表現及其相關因素之研究。國立台灣師範大學數學系在職進修碩士班學位論文。
    洪榮昭、劉明洲 (1997):電腦輔助教學之設計原理與應用。增訂一版,台北市,師大書苑。
    張春興、林清山(1989):教育心理學。台灣東華書局,pp.373-408。
    張謙楣(2005):行動載具在支援高中國文科教室教學情境的應用。國立台灣師範大學資訊教育學系碩士學位論文。
    教育部(2003):國民中學九年一貫數學領域綱要。民國92年5月20日修定公佈。
    郭生玉(1996):當前學校教學評量工作的檢討與改進。黃政傑主編:教學評量,pp.157-164。台北:師大書苑。
    陳東陞(1992):國小數學學習困難兒童的教學策略。特殊教育輔導叢書(44)。
    陳俊廷(2002):高中學生空間向量學習困難的診斷測驗工具發展研究。國立高雄師範大學數學系碩士學位論文。
    陳建蒼(2000):高一學生對數函數概念層次教學成效研究。國立高雄師範大學數學系碩士學位論文。
    黃承丞(2003):教室用無線即時形成性評量軟體的設計與應用。國立台灣師範大學資訊教育學系碩士學位論文。
    鄭勝鴻(2004):於動態幾何巨集環境下國中生證明概念與技能發展之研究。國立台灣師範大學數學系碩士學位論文。
    譚寧君(1993):兒童的幾何觀--從Van Hiele幾何思考的發展模式談起,國民教育,33卷5、6期,pp. 12-17。
    Battista, M. T. & Clements, D. H. (1991). Research into practice: Using spatial imagery in geometric reasoning. Arithmetic Teacher, Vol. 39 No.3 pp. 18-21.
    Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, Vol. 21, No. 1. pp. 47-60.
    Battista, M. T. (2002). Learning geometry in a dynamic computer environment. Teaching Children Mathematics, Feb2002, Vol. 8, Issue 6, pp. 333-339.
    Ben-Chaim, D., Lappan, C., & Houang, R. T. (1988). The effect of instruction on spatial visualization skills of middle school boys and girls. American Educational Research Journal, 25(1), pp. 51-71.
    Berta Tünde (2002). Combination of traditional and computer based tools in mathematics education. IS-APMEF 2002.
    Bishop, A. J. (1980). Spatial abilities and mathematics education: A review. Educational Studies in Mathematics, Vol. 11, pp. 257-269.
    Bishop, A. J. (1983). Space and geometry. In Lesh, R. & Landau, M. (eds.), Acquisition of Mathematics concepts and processes. pp. 176-203. New York: Academic Press.
    Bishop, A. J. (1989). Review of research on visualization in mathematics education. Focus on Learning Problems in Mathematics. Winter Edition 1989, Vol. 11. pp.7-16.
    Bishop, A. L. et al. (eds.) (1996). International Handbook of Mathematics Education. The Netherlands: Kluwer Academic Publishers.
    Bishop, C. M. & Tipping, M. E. (1998). A hierarchical latent variable model for data visualization. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No. 3, March 1998.
    Black, P., & William, D. (1998). Assessment and classroom learning, Assessment in Education, 5, pp. 7-75.
    Bloom, B. S. et al. (1971). Handbook on Formative and Summative Evaluation of Student Learning. New York: McGraw-Hill Book Company.
    Chen, Y. S., Kao, T. C., Sheu, J. P., & Chiang, C. Y. (2002). A mobile scaffolding-aid-based bird-watching learning system. In Wireless and Mobile Technologies in Education. Proceedings of the IEEE International Workshop.
    Clements, M. A. (1979). Sex differences in mathematical performance: An historical perspective. Educational Studies in Mathematics, 10, pp. 305-322.
    Crawford, M., Chaffin, & Fittion, L.(1995). Cognition an social context. Learning and Individual Difference, 7(4), pp. 341-362.
    Dempsey, J. V., Driscoll, M. P., & Swindell, L. K. (1993). Text-based feedback. In J. V. Dempsey, & G. C. Sales (eds.), Interactive instruction and feedback, pp. 21-54. NJ: Educational Technology Publications.
    Dixon, J. K. (1997). Computer use and visualization in students’ construction of reflection and rotation concepts. School Science and Mathematics, 97(7), 352-358.
    Duval, R. (1995). Geometrical picture: kinds of representation and specific processes, in Exploiting Mental Imagery with Computers in Mathematic Education (Sutherland & Mason eds.), Springer, pp. 142-157.
    Eliot, J. (1987). Models of psychological space. New York, NY: Springer-Verlag.
    Fennema, E. & Sheman, J. (1977). Sex-related difference in mathematics achievement, spatial visualization and affective factors. American Educational Research journal, Vol 14.
    Freudenthal, H. (1971). Geometry between the devil and the deep sea. Educational Studies in Mathematics 3, pp. 413–435.
    Gardner, H. (1983). Frames of mind: the theory of multiple intelligences. London: Heinemann.
    Gaulin, C., & Puchalska, E. (1983). Representation on paper of 3-dimension shapes. In J. C. Bergeron & N. Herscovics (eds.). Proceedings of the fifth annual meeting of PME-NA, Vol 1 (pp. 322-325). Montreal, Canada: University of Montreal.
    Gay, G., Stefanone, M., Grace-Martin, M., & Hembrooke, H. (2001). The effect of wireless computing in collaborative learning environments. International Journal of Human-Computer Interaction. 13(2), pp. 257-276.
    Geddes, D. & Fortunato, I. (1993). Geometry: research and classroom activities. In D.T.Owens (Eds.), Research Ideas for the Classroom: Middle grades mathematics (pp.199-225). New York: Macmillan Publishing Company.
    Gilbert, et. al. (1982). Students’ conceptions of ideas in mechanics. Physics Education, Vol 17 n2.
    Guay, R. B., McDaniel, E. D., & Angelo, S. (1978). Analytic factors confounding spatial ability measurement. In R. B. Guay & E. D. McDaniel (eds.), Correlates of performance on spatial aptitude tests. pp. 116-128. Lafayette, IN: Purdue University (USArmy Research Institute for the Behavioral and Sciences). Final Report (Grant No: DAHC-19-77-G0019).
    Guttman, R. et al. (1990). A structure theory of spatial abilities. Applied Psychological Measurement, Vol. 14, No. 3, pp. 217-236.
    Hadas, N. and Hershkowitz. (1998). Proof in Geometry as an Explanatory and Convincing Tool. Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education. Stellenbosch (South Africa), Vol 3, pp. 25 – 32
    Hennessy, S. (2000). Graphing investigations using portable (palmtop) technology. Journal of Computer Assisted Learning, 16, pp. 243-258.
    Hershkowitz, R. (1990). Psychological aspects of Learning Geometry. In: P. Nesher and J. Kilpatrick (eds.), Mathematics and Cognition. (pp. 70-95). Cambridge, Cambridge University Press.
    Hoz, R. (1981). The effects of rigidity on school geometry learning. Educational Studies in Mathematics, 12, pp. 171-190.
    Izard, J. (1990). Developing spatial skills with three-dimensional puzzles. Arithmetic Teacher, Vol. 37 No. 6 pp. 44-47.
    Jean, S. & Amy, P. (2002). A report card on handheld computing. Technology & Learning, 22(7), 24-36.
    Kaufmann, H. (2004). Geometry education with augmented reality. in Ph.D. Thesis. Vienna: Vienna.
    Kosslyn, S. M. (1983). Ghosts in the mind's machine : creating and using images in the brain. New York: Norton, 1983.
    Krutetskii, V.A. (1976). The psychology of mathematical abilities in school-children. Chicago: University of Chicago Press.
    Laborde, J. M. & Bellemain, F. (1998). Cabri-Geometry II. Texas Instruments. Copyright Texas Instruments and Université Joseph Fourier, CNRS, 1998. [Online] Available(2006/06/15): http://www-cabri.imag.fr/index-e.html
    Laborde, C. (1998). Visual phenomena in the teaching/learning of geometry in a computer-based environment. In Carmelo Mammana & Vinicio Villani (eds.), Perspectives on the teaching of geometry for the 21th century. pp. 113-121.
    Lee, S. W. (1993). Spatial ability and achievement in geometry among Taiwanese high school students. Ann Arbor, Mich. : UMI, 1993.
    Lord, T. R. (1985). Enhancing the visuo-spatial aptitude of students. Journal of Research in Science Teaching, 22(5), pp. 395-405.
    Luchini, K., Quintana, C., & Soloway, E. (2004). Design guidelines for learner-centered handheld tools. In Dykstra-Erickson, E., & Tscheligi, M. (Chairs), Human factors in computing systems. Proceedings of the SIGCHI conference, Vienna, Austria.
    National Council of Teachers of mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
    Osta, I. (1998). CAD tools and the teaching of geometry. In Carmelo Mammana & Vinicio Villani (eds.), Perspectives on the teaching of geometry for the 21th century. pp. 128-144.
    Owens, D.T. (1990). Research into practice: spatial abilities. Arithmetic Teacher, 37(6), 48-51.
    Presmeg, N.C. (1986). Visualization in high-school mathematics. For the Learning of Mathematics, 6, pp42-46
    Roschelle, J. & Pea, R. (2002). A walk on the WILD side: how wireless handhelds may change CSCL. G. Stahl (Eds.)., Proceedings of CSCL 2002, Boulder, CO, January 7-11, 2000.
    Seddon, G. M., Eniaiyeju, P. A., & Jusoh, I. (1984). The visualization of rotation in diagrams of three-dimensional structures. American Educational Research Journal, 21(1), pp. 25-38.
    Sherman, J. (1980). Mathematics, spatial visualization, and related factors: changes in girls and boys , grades 8-11. Journal of Educational Psychology, 72(4), pp. 476-482.
    Smith, I.M. (1964). Spatial ability. San Diego: Knapp.
    Smith, W. S. & Schroeder, C. K. (1979). Instruction of fourth grade girls and boys on spatial visualization. Science Education, 63(1), pp. 61-66.
    Song, K.S. & Lee, W.Y. (2002). A virtual reality application for geometry classas. Journal of Computer Assisted Learning, Jun2002, Vol. 18 Issue 2, pp.149-156.
    Stanic, G. M. A. & Owen, D. T. (1990). Spatial sense. Arithmetic Teacher, 37(6), pp. 48-51.
    Thomas, N. (2005). Mental imagery. The Stanford Encyclopedia of Philosophy (Fall 2005 Edition), Edward N. Zalta (ed.). [Online] Available(2006/06/15): http://plato.stanford.edu/archives/fall2005/entries/mental-imagery/.
    Trimmel, M. & Bachmann, J. (2004). Cognitive, social, motivational and health aspects of students in laptop classrooms. Journal of Computer Assisted Learning, 20, pp. 151-158.
    Vahey, H. & Crawford, C. (2002). PalmTM education pioneers program: Final evaluation report. [Online] Available(2006/06/15): http://www.palmgrants.sri.com/news.html
    von Glasersfeld, E. (1987). Constructivism. In Husen,T. & Postlethwaite, N.(eds.) International Encyclopedia of Education, Supplement Vol 1, Oxford, Pergamon
    Voyer, D. (1996). The relation between mathematical achievement and gender differences in spatial abilities: A suppression effect. Journal of Educational Psychology 88, pp. 563–571.
    Wheatley, G. H. (1990). Spatial sense and mathematics learning. Arithmetic Teacher, 37(6), pp. 10-11.
    Wheatley, G. H. (1997). Reasoning with images in mathematical activity. In L. D.English (eds.). Mathematical reasoning: Analogies, metaphors, and images. Hillsdale, New Jersey: Lawrence Erlbaum Associates.

    QR CODE