本研究目的在於「設計二次函數課程的數位教學環境」，以幫助高中學生學習二次函數概念，並探討在此學習環境下，其學生的二次函數之概念結構與表徵整合能力。
本研究共分成兩部分，第一部份透過內容分析法來分析國高中二次函數課程素材結構，及設計問卷以分析國中生二次函數概念結構。再根據數學概念的多重表徵理論以及分析的結果，發展高中二次函數的數位教學活動，以進行第二部分的準實驗教學研究。兩組變因在於呈現多重表徵的環境不同，實驗組進行動態鏈結多重表徵的數位教學，而對照組則以靜態海報呈現多重表徵的教學。研究結果顯示，依據本研究的設計所進行的高中二次函數教學活動，均有助於兩組學生形成高中二次函數概念。而特別對中等程度學生而言，動態鏈結多重表徵的教學效果顯著地優於靜態圖形海報的教學。從學生作答情形與訪談資料進一步分析，我們可以發現動態鏈結多重表徵的數位教學方式呈現有助於學生：
1. 掌握二次函數的概念定義。
2. 進行二次函數的概念膠囊化與解膠囊化過程。
3. 對二次函數的圖形變動產生動態心像並能說明代數式係數變動意義。
4. 能增長二次函數代數結構與圖形表徵的轉移以幫助理解二次函數的正定性。
動態鏈結多重表徵的教學環境設計，能夠將數學概念中表徵的連結關係以連續、即時性的方式具體的呈現出來，此呈現方式有助於學生連結及形成整合多重表徵能力，用以解決問題。

一、中文部分
王石番(1991)。傳播內容分析法：理論與實證。臺北：幼獅。
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，第九卷第三期，281-297。
左台益、蔡志仁(2001)。動態視窗之橢圓教學實驗。師大學報：科學教育類，46(1,2)，21-42。
左台益、黃哲男(2001)。動態幾何環境國二生心像建構研究。中華民國第十七屆科學教育學術研討會。
楊孝濚(1978)。內容分析。載於楊國樞、文崇一、吳聰賢、李亦園（編）。社會及行為科學研究法（下冊）（809-833頁）。臺北：東華。
教育部(2003)。國民中學九年一貫課程綱要。臺北市：教育部。
林義男（譯）(1989)。內容分析法導論。（原作者：Weber, R. P.）。臺北：巨流。（原著出版年：1985）。
歐用生(1991)。內容分析法。教育研究法（229-254頁）。臺北：師大書苑。
南一書局（民97）。國中數學課本第六冊。臺南市，南一。
南一書局（民97）。國中數學教師手冊第六冊。臺南市，南一。
南一書局（民99）。高中數學課本第一冊。臺南市，南一。
南一書局（民99）。高中數學教師手冊第一冊。臺南市，南一。
翰林書局（民99）。高中數學課本第一冊。高雄市，翰林。
翰林書局（民99）。高中數學教師手冊第一冊。高雄市，翰林。
 
二、英文部分
Achenbach, T. M. (1991). Integrative guide for the 1991 CBCL/4-18, YSR, and TRF profiles. Burlington: Department of Psychiatry, University of Vermont.
Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183-198.
Bernard, B. (1952). Content analysis in communication research. Hafner.
Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247-285
DiSessa, A. (1987). Phenomenology and the Evolution of Intuition. In C. Janvier, (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, pp.83-96. New Jersey, Lawrence Erlbaum Associates, Inc.
Dreyfus, T., & Halevi, T. (1988, July-August). Quadfun-A case study of pupil computer interaction. Paper presented to the theme group on Microcomputers and the Teaching of Mathematics at the Sixth International Congress on Mathematical Education, Budapest, Hungary.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall(Ed.), Advanced mathematical thinking(pp.95-123). London: Reidel.
Dubinsky, E. (1992). Development of the process conception of function. Educational Studies in Mathematics, 22, 247-258.
Duval, R (1995). Geometrical Pictures: Kinds of Representation and Specific Processings. In R. Sutherland and J. Mason (Eds), Exploiting Mental Imagery with Computers in Mathematics Education. Berlin: Springer.
Duval, R (1998). Geometry from a Cognitive Point of View. In C. Mammana and V. Villani (Eds), Perspectives on the Teaching of Geometry for the 21st Century: an ICMI study. Dordrecht: Kluwer.
Duval, R. (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics, Volume 61 (1-2), Springer Netherlands.
Duval, R. (2007). Cognitive Functioning and the understanding of mathematical processes of proof. In Boero, P. (Ed.), Theorems in School: From History,
Eraslan, A. (2005). A qualitative study: Algebra Honor students' cognitive obstacles as they explore concepts of quadratic functions.
Even, R.(1990). Subject matter knowledge for teaching and the case of function. Educational Studies in Mathematics, 21, 521-544.
Freudenthal, H. (1983). Didactical Phenomenology of Mathematics Structures. Dordrecht, The Netherlands: D. Reidel.
Goldin, G. A. (1987). Cognitive Representational Systems for Mathematical problem solving. In C. Janvier, (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, pp.125-145. New Jersey, Lawrence Erlbaum Associates, Inc.
Gray, E.M. & Tall, D.O.(1994). Duality, ambiguity, and flexibility: A proceptual view of elementary arithmetic. Journal for Research in Mathematics Education,26(2),114-141.
Hennessy, S. (1993). Situated cognition and cognitive apprenticeship: Implications for classroom learning.
Hiebert, J. (Ed.). (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum.
Janvier, C. (1987a). Translation Processes in Mathematics Education. In C. Janvier (Ed.) Problems of Representation in the Teaching and Learning of Mathematics (PP. 27-31). Hillsdale, NJ: Lawrence Erlbaum.
Janvier, C. (1987b) 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. 27-31). Hillsdale, NJ: Lawrence Erlbaum
Kaput, J. J. (1987a). Representation Systems and Mathematics. In Janvier, C. (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, 67-71. USA, LEA.
Kaput, J. J. (1987b). Towards a Theory of Symbol Use in mathematics. In Janvier, C. (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, 67-71. USA, LEA.
Kaput, J. J. (1989). Linking representations in the symbol systems of Algebra. In Wagner, S. & Kieran, C. (Eds.), Research issues in the learning and teaching of Algebra, 4, 167-194.
Kieran, C. (1993). Functions, Graphing, and Technology: Integrating Research on learning and Instruction. In Romberg, T. A. & Fennema, E. & Carpenter, T. P. (Eds.), Integrating Research on the Graphical Representation of Functions,101-130. London, LEA.
Krippendorff, K.(1980). Content Analysis: An Introduction to Its Methodology. Beverly Hills, Calif.: Sage.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. Problems of representation in the teaching and learning of mathematics, 33-40.
Lovell, K. (1971). Some aspects of the growth of the concept of a function. MF Rosskopf, LP Steffe et S. Taback éds.), Piagetian Cognitive Development Research and Mathematical Education, 12-33.
Lu, Y. W. (2008). The use of mathematical software in secondary mathematics teaching - A new challenge for young teachers. Paper presented at the meeting of ICME 11, Monterrey, Mexico
Markovits, Z., Eylon, B., & Bruckheimer, M. (1988). Difficulties Students Have with the Function Concept. In A. F. Coxford, (1988 yearbook Ed.), The ideas of algebra, K-12, pp.43-60. University of Michigan.
Markovits, Z. (1982). Understanding of the concept of function among grade 9 students. Unpublished masters’ thesis, Weizmann Institute, Rehovot, Israel.
Moschkovich, J. Schoenfeld, A. H. & Arcavi, A. (1993). Aspects of Understanding: On Multiple Perspectives and Representations of Linear Relations and Connections Among Them. In T. A. Romberg, E. Fennema, & T. P. Carpenter, (Eds.), Integrating research on the graphical representation of functions, pp.69-100. Hillsdale, New Jersey, Lawrence Erlbaum Associates, Inc.
National Council of Teachers of Mathematics. Commission on Standards for School Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Natl Council of Teachers of.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (Vol. 1). Natl Council of Teachers of.
National Council of Teachers of Mathematics, (2009). Focus in High School Mathematics: Reasoning and Sense Making. Reston, VA: National Council of Teachers of Mathematics
Posner, G. J. (1989). Field experience: Methods of reflective teaching. New York: Longma.
Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of'well-taught'mathematics courses. Educational psychologist, 23(2), 145-166.
Schwarz, B. B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 362-389.
Seufert, T. (2003). Supporting coherence formation in learning from multiple representations. Learning and Instruction, 13(2), 227-237.
Sfard, A. (1987). Two Conceptions of Mathematical Notions: Operational and Structural. In Proceedings of the Eleventh International Conference of PME, 3, 162-169.
Sfard, A. (1989). Transition from Operational to Structural Conception: the Notion of Function Revisited. In Proceedings of the Thirteenth International Conference of PME, 3, 151-158.
Sfard, A. (1991). The Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of The Same Coin. Educational Studies in Mathematics, 22, 1-36.
Sweller, J., van Merrienboer, J. J. G.., & Paas, F. G. W. C. (1998). Cognitive architechture and instructional design. Educational Psychology Revies, 10, 251-296
Tall, David. "Natural and formal infinities." Educational Studies in Mathematics48.2-3 (2001): 199-238.
Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematics in Science and Technology, 14(3), 293-305.
Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. The concept of function: Aspects of epistemology and pedagogy, 25, 195-213.
Vygotsky, L. S.(1978). Mind in society: The development of higher mental processes, eds. & trans. M. Cole, V. John-Steiner, S. Scribner, & E. Souberman. Cambridge, MA: Harvard University Press.
Yerushalmy ,M. (1988). Effect of graphic feedback on the ability to transform algebraic expression when using computers (Interim report submitted to the Spencer Fellowship of the National Academy of Education). Haifa, Israel: University of Haifa.
Zaslavsky, O. (1997). Conceptual obstacles in the learning of quadratic function. Focus on Learning Problems in Mathematics, 19(1), 20-25
Zazkis, R., Liljedahl, P., & Gadowsky, K. (2003). Conceptions of function translation: Obstacles, intuitions, and rerouting. The Journal of Mathematical Behavior, 22(4), 435-448.