動態幾何軟體對於數學幾何概念及概念心像的建構有正面助益，唯因環境與硬體支援的缺乏，使得其僅淪為精緻的繪圖與展示工具。行動載具的發展，讓軟體、硬體整合數學課堂教學有了新的契機，透過科技輔助讓靜態幾何教學成為可動態操弄圖形的實驗科學。
Sfard提出學習者透過具體化操弄得到概念的存在性，Dubinsky認為概念發展的步驟為行動、心智程序、物件與基模。鑑於此，本研究開發動態幾何教學系統，融合平版電腦與代數幾何軟體GeoGebra於數學課堂教學中，提供可即時操弄的動態多重表徵與視覺化模組。研究結果對橢圓學習、概念發展及運用多重表徵解題有顯著成效。

Dynamic geometry software helps us to construct the mathematics geometric concepts and concept images. However, due to the lack of the environment and hardware support, it just becomes a fine drawing board and a display tool. The development of mobile technology creates new opportunities on integration of software, hardware, and traditional mathematics classroom teaching. Therefore, technology enables the static geometry teaching become experimental science.
Sfard proposes that the existence of the concept can be obtained through learners' concrete manipulation. Dubinsky indicated that the steps of concept development are actions, processes, objects and schemas. Therefore, this research aims to develop dynamic geometry teaching system in order to integrate TablePC and GeoGebra on mathematics classroom instruction. The system provides real-time dynamic module with multiple representations and visualization. The findings of this study are better learning effect, conceptual development, problems solving by using multiple representations.

一、中文部份
左台益(2008)。概念工具與動態表徵。論文發表於2008國科會數學教育研究經驗傳承研討會。6月20日。台南縣。

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。

左台益、蔡志仁(2001)。高中生建構橢圓多重表徵之認知特性。科學教育學刊， 9(3)，281-297。

李昂哲(民97)。高二學生圓錐曲線之橢圓方程式解題歷程之分析研究。國立高雄師範大學數學教學碩士班論文，高雄市。

宋曜廷、侯惠澤、張國恩（2005）。資訊科技融入教學：借鏡美國經驗，反思台灣發展。教育研究集刊，51卷，31-62。

林德威(民97)，高一學生學習二次函數圖形與配方法錯誤類型之研究。國立高雄師範大學數學教學碩士班論文，高雄市。

教育部高中數學學科中心(民97)。98普通高級中學數學科課程綱要。教育部高中數學學科中心，台北市。(http://camel.ck.tp.edu.tw/xoops/)

國立台灣師範大學教育研究中心(民96)。職業學校98數學科科課程綱要草案。國立台灣師範大學教育研究中心，台北市。

梁新正(民85)。 高雄地區高二學生數學解題之基模知識與歷程之分析研究。國立高雄師範大學數學研究所論文，高雄市。

陳吟汝 (民95) 。台南地區高二學生圓錐曲線單元錯誤類型之分析研究。國立高雄師範大學數學研究所碩士論文，高雄市。

陳彥良 (民95)。電腦數學實驗運用在高中數學統計單元教學之研究—以「大數法則」、「常態分佈」及「信賴區間」等單元為例。國立交通大學理學院碩士在職專班，新竹市。

陳創義 (民97)。數學與動態幾何學習網。http://140.122.140.4/~cyc/_private/m1.htm

張國恩(1999)。資訊融入各科教學之內涵與實施。資訊與教育，72，2-9。

温安榮(民96) 。GSP 融入數學教學對高二學生數學學習成效影響之研究-以「圓錐曲線」單元為例。國立高雄師範大學數學教學碩士班論文，高雄市。

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。國立台灣師範大學數學研究所碩士論文，台北市。

黃美玲 (民95)。橢圓標準式解題歷程與錯誤類型之分析。國立彰化師範大學科學教育研究所，彰化市。

蔡志仁(民88)。動態連結多重表徵視窗環境下橢圓學習之研究。國立台灣師範大學數學研究所碩士論文，台北市。

賴信川(民95)。運用行動載具輔助空間幾何學習。國立臺灣師範大學資訊教育學系在職進修碩士班論文，台北市。

謝宗霖(民94) 。合作式概念圖學習對高中生數學學習成效研究－以「圓錐曲線」單元為例。國立高雄師範大學數學研究所論文，高雄市。

謝世杰(民95)。有關三角函數圖形的平移和單向伸縮變換之電腦輔助補救教學之相關研究。國立台灣師範大學數學研究所碩士論文，台北市。

蕭燕玲 (民97)。高工學生圓錐曲線的概念與運算及應用錯誤類型之研究。國立高雄師範大學數學教學碩士班論文，高雄市。

二、英文部份
Adam,R.D., & Victor,M.(1993). Principales of Neurology(5th ed.). McGraw-Hill, New York.

Akpinar, A., & Hartley, J. R. (1996). Designing interactive learning environments. Journal of Computer Assisted Learning, 12, 33-46.

Baki, A. (2002). Computer based mathematics teaching. Istanbul: Ceren Publishing.

Baki, A., & Guveli, E. (2008). Evaluation of a web based mathematics teaching material on the subject of functions . Computers & Education, 51,854-863.

British Educational Communications and Technology Agency. (2003). What the Research Says about Using ICT in Maths. UK. Becta ICT Research.

Becker, H., Ravitz, J., & Wong, Y., (1999). Teacher and Teacher-Directed Student Use of Computers, Teaching, Learning, and Computing: 1998 National Survey Report #3. University of California Irvine, Centre for Research on Information Technology and Organizations.

Chang, K. E., Liu, S. H., & Chen, S. W. (1998). A testing system for diagnosing misconceptions in DC electric circuits. Computers & Education,31(2),195-210.

Chang, K. E., Chen, S. F., & Sung, T. C. (2001). Learning through computer-based concept mapping with scaffolding aid. Computer-Assisted Learning, 17(1), 21-33.

Chang, K. E., Sung, Y. T. & Lee, C. L. (2003). Web-based collaborative inquiry learning. Computer-Assisted Learning,19(1), 56-69.

Chang, K. E., Lin, S. C., & Sung, Y. T. (2005). A new assessment for computer-based concept mapping. Educational Technology and Society, 8(3), 138-148.

Chang, K. E., Sung,Y. T., & Lin, S. F. (2006). Computer-assisted learning for mathematical problem solving. Computers & Education 46(2), 140-151.

Chang, K. E., Sung, Y. T., Ho, H. T. (2006). Web-based Tools for Designing and Developing Teaching Materials for Integration of Information Technology into Instruction. Educational Technology and Society, 9(4), 139-149.

Chang, K. E., Sung, Y. T., & Lin, S. Y., (2007). Developing Geometry Thinking through Multimedia Learning Activities. Computers in Human Behavior, 23(5), 2212-2229.

Chang, K. E., Chen, Y. L., & Sung, Y. L. (2008). Effects of learning support in simulation-based physics learning. Computers & Education,51(4), 1486-1498.

Chang, K. E., Sung, Y. T., Chen, Y. L., & Huang, L., H. (2008). Learning Multiplication through Computer-Assisted Learning Activities. Computers in Human Behavior, 24(6), 2904-2916.

Cuban, L. (1989). Neoprogressive visions and organizational realities. Harvard Educational Review, 59(2), 217–222.

Cuban, L., Kirkpatrick, H., & Peck, C. (2001). High access and low use of technologies in high school classrooms: Explaining an apparent paradox. American Educational Research Journal, 38(4), 813–834.

Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: beginning with a coordinated process schema. Journal of Mathematical Behavior, 15,167-192.

Derry, S. J., & LaJoie, S. P. (1993). A middle camp for (un)intelligent instructional computing: An introduction. In S. P. LaJoie & S. J. Derry (Eds.), Computers as cognitive tools (pp. 1-11). Hillsdale, NJ: Lawrence Erlbaum Associates.

Dubinsky, E. (1991). Reflective Abstraction in Advanced Mathematical Thinking, In D. Tall (Ed.), Advanced mathematical Thinking, Dordrecht, Kluwer Academic Press (pp. 95-123).

Dubinsky, E. (1992). Development of the process conception of function. Educational Studies in Mathematics, 22, 247-258.

Engstro¨m, L. (2004). Examples from teachers’ strategies using a dynamic geometry program in upper secondary school. Paper presented at ICME-10. http://www.icme-organisers.dk/tsg10/articulos/Lil_Engstrom.doc.

Fister, K. R., McCarthy, & Maeve, L. (2007). Mathematics instruction and the tablet PC. International Journal of Mathematical Education in Science and Technology,39 (3),285–292.

GeoGebra ORG.. http://www.geogebra.org/

Hershkowitz, R. (1989). Visualization in geometry-Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61-76.

Hiebert, J. Lefevre, P. (1987). Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis. In Hiebert,J. (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics. Hillsdale, NJ:Erlbaum.

Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: who gets an opportunity to learn what? British Educational Research Journal, 28(4), 567–590.

Hew, k. F., & Brush, T. (2007). Integrating technology into K-12 teaching and learning: current knowledge gaps and recommendations for future research. Educational Technology, Research and Development, 55(3), 223-252.

Ittigson, R.J. & Zewe, J.G. (2003). Technology in the mathematics classroom. In L.A. Tomei (Ed.), Challenges of Teaching with Technology Across the Curriculum: Issues and Solutions(pp. 114-133.) Hershey: Information Science Publishing.

Janvier, C. (1987). Representation and Understanding: The Notion of Function as an Example. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 67-72). Hillsdale: NJ: Lawrence Erlbaum Associates.

Jonassen, D. H., Howland, J., Moore, J., &Marra, R. (2003). Learning to solve problems with technology: A constructivist perspective (2nd ed.). Upper Saddle: Prentice Hall.

Jonathan ,B. & David,B. (2003) Mathematics by Experiment : Plausible Reasoning in the 21st Century. A K Peters, Limited.

Jones, A. (2004). A Review of the Research Literature on Barriers to the Uptake of ICT by Teachers. UK: Becta.

Kaput, J. (1987). Toward a theory of symbol use in mathematics. In C. Janvier(Ed.), Problem of representations in mathematics learning and problem solving (pp. 159-196). Hillsdale, NJ:Lawrence Erlbaum Associates.

Kaput, J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167-194). Reston, VA: National Council of Teachers of Mathematics & Lawrence Erlbaum Associates.

Kaput, J. (1992) Technology and mathematics education. In Grouws, D (Ed.), Handbook of research on mathematics teaching and learning (pp. 515-556). New York. Macmillan.

Keong, C.C., Horani, S., & Daniel, J. (2005). Constructions of dynamic geometry：A Study on the Use of ICT in Mathematics Teaching. Malaysian Online Journal of Instructional Technology,2(3),43-51.

Kommers, P., Jonassen, D. H., & Mayes, T. (1992). Cognitive tools for learning. Springer-Verlag: Heidelberg.

Kong, S. C. (2008). The development of a cognitive tool for teaching and learning fractions in the mathematics classroom: A design-based study. Computers & Education, 51, 886-899.

Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.

Lampert, M. (1993). Teachers’ thinking about students’ thinking about geometry: The effects of new teaching tools. In J. Schwartz, M. Yerushalmy, & B. Wilson (Eds.), The Geometric Supposer: What is it a case of? Hillsdale NJ: Lawrence Erlbaum.

Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In: C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics, (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum Associates

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics, VA Reston.

Office for Standards in Education (2001). ICT in schools：The impact of government initiatives. London: UK.

Office for Standards in Education (2002). ICT in schools: Effect of government initiatives Secondary Mathematics. London: UK.

Office for Standards in Education (2004). ICT in schools：The impact of government initiatives Secondary mathematics. London: UK.

Oldknow, A. (2004). ICT and Mathematics: a guide to learning and teaching mathematics 11-19. UK. The Mathematical Association. http://www.m-a.org.uk/

Olive, J. (2002). Implications of using dynamic geometry technology for teaching and learning. In: M. Saraiva, J. Matos, & I. Coelho (Eds.), Ensino e Aprendizagem de Geometria. Lisbon: SPCE. http://www.spce.org.pt/sem/JO.pdf.

Olivier, W. (2005, Nov 25th – Dec 1st). Teaching Mathematics: Tablet PC Technology adds a new dimension. The Mathematics Education into the 21st Century Project Universiti Teknologi Malaysia Reform, Malaysia.

Remillard, J. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2),211–246.

Rogers, Y. (2007). Using External Visualizations to Extend and Integrate Learning in Mobile and Classroom Settings. In J.K. Gilbert, M. Reiner, & M. Nakhleh (Eds.), Visualization: Theory and Practice in Science Education,(pp. 89–102). Springer Netherlands.

Ruthven, K., Hennessy,S., & Deaney, R. (2008). Constructions of dynamic geometry：A study of the interpretative flexibility of educational software in classroom practice. Computers & Education ,51,297-317

Scher, D. (2000). Lifting the curtain: The evolution of the Geometer’s Sketchpad. The Mathematics Educator, 10(1), 42–48.

Schwarz, B. & Hershkowitz, R.(1999). Prototypes: Brakes or Levers in Learning the Function Concept? The Role of Computer Tools. Research in Mathematics Education, 30(4), 362-389.

Sfard, A.(1991). On the dual nature of mathematical conceptions:Reflection on process and objects as different sides of the same coin. Educational Studies in Mathematics,22,1-36.

Sivin-Kachala, J., & Bialo, E. R. (2000). Research report on the effectiveness of technology in schools. Washington, DC: Software and Information Industry Association.

Tall, D. O. & Vinner, S.(1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.

Van Hiele,P.M. (1986). Structure and insight : A theory of mathematics education. Orlando, FL：Academic Press.

Vinner, S. (1983). Concept definition, concept images and the notion of function. International Journal Mathematics Educational Science Technolology, 14(3), 293-305.

Vinner, S., & Hershkowitz, R(1983). On concept formation in geometry. Zentralblatt fur Didaktik der Matematik, 83(1), 20-25.

Wiske, M. S., & Houde, R. (1993). From recitation to construction: Teachers change with new technologies. In J. Schwartz, M. Yerushalmy, & B. Wilson (Eds.), The geometric supposer: What is it a case of? Hillsdale, NJ: Lawrence Erlbaum.

Wong, M. L., & Li, S. C. (2006). Is ICT a Lever for Educational Change? A Study of the Impact of ICT Implementation on Teaching and Learning in Hong Kong. Informatics in Education: An International Journal, 5(2).