本研究的研究目的是探討優秀中學數學教師在概念引入時提供給學生何種有意義學習的機會。研究實際進入課堂觀察教師的教學活動，蒐集資料後歸納分析，為保持學習環境的真實與自然，並未設計實驗或干預教師的教學，完全配合教師進行資料收集，而且關注教師的教學過程，以自然探究法進行。屬於質的研究。
本研究界定出四位高中優秀數學教師作為研究對象，並選取高一至高三的教學內容共十四節課來做分析。研究結果的報導分四個部分：第一、教師在概念引入時出現的教學方式，及如何使用這些教學方式。第二、教師在教師建立意義所使用的教學手法及如何使用這些教學手法。第三、數學意義的來源。第四、教師提供的意義類型。

中文部分
1. Mayer, R. E.（1997）：教育心理學：認知取向(林清山譯)。台北市：遠流出版公司。
2. Patton, M. Q.（1995）：質的評鑑與研究(吳芝儀、李奉儒譯）。台北：桂冠圖書股份有限公司。
3. Skemp, R. R.（1995a）：數學學習心理學(陳澤民譯，民84)。台北市：九章出版社。
4. Skemp, R. R.（1995b）：智性學習(許國輝譯)。香港：公開進修學院出版社。
5. 丁斌悅（民90）：國二學生學習線型函數時的概念表徵發展研究。國立台灣師範大學數學研究所碩士論文。
6. 朱敬先（1987）：教學心理學。台北：五南。
7. 宋玉如（民 97）。中學數學教師應有的數學教學特質研究─學生觀點，尚未發表。國立台灣師範大學數學研究所碩士論文。
8. 余民寧（民86）：有意義的學習：概念構圖之研究。台北：商鼎文化。
9. 林寶山（1988）：教學原理。台北：五南。
10. 林寶山（1990）：教學論。台北：五南。
11. 施良方（1996）。學習理論。高雄：麗文文化公司。
12. 張春興（2000）：教育心理學：三化取向的理論與實踐 (重訂版 ed.). 台北市：東華書局.
13. 張春興（1998）：張氏心理學辭典(二版)。台北：東華書局股份有限公司。
14. 張新仁（1993）：奧斯貝的學習理論與教學應用，教育研究，82.08 。
15. 陳建誠（1998）：面積表徵的轉換。國立台灣師範大學數學研究所碩士論文。
16. 教育部國語推行委員會（編）（1994）：重編國語辭典修訂本網路版。取自於http://dict.revised.moe.edu.tw。
17. 楊龍立（2006）：講述式教導及接受式學習的實施-前導組織的探討。科學教育研究與發展季刊，2006專刊，64-74。
18. 蔡志仁（民 89）。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。
19. 謝豐瑞（民 97）：中學數學教師專業發展指標之研究－子計畫四：中學教師數學教學能力專業發展研究(3/3) ，進行中尚未發表。行政院國家科學委員會專題研究計畫。
20. 謝豐瑞，等（民 96）：國中數學領域教師教學專業發展工作坊成果彙編。國立台灣師範大學數學系。
21. 魏世台（民70）：奧素伯認知教學理論之分析研究。台北師範大學教育研究所碩士論文。
英文部分
1. Ausubel, D. P.（1963）. The psychology of meaningful verbal learning. New York : Grune & Stratton.
2. Ausubel, D. P.（1968）. Educational psychology: A cognitive view. New York: Holt, Rinehart & Winston.
3. Ausubel, D. P. & Robinson F. G.（1969）. School learning – an introduction to educational psychology. N. Y. : Holt, Rinehart & Winston.
4. Ausubel, D.P., Novak,.J .D., & Hanesian,H.（1978）.Education psychology.（2nd ed）N. Y. : Holt, Rinehart & Winston.
5. Barnes, B.R. & Clawson, E. U. （1975） .Do advance organizers facilitate learning? Recommendations for further research based on analysis of 32 studies. Review of educational research,1975, 45,637-659.
6. Dickey, E.M.（1993）. The Golden Ratio: A Golden Opportunity to Investigate Multiple Representations of a Problem. The Mathematics Teacher, 86(7), pp.554-557.
7. Dubinsky, E., Elterman, F.,＆Gong C.（1988）.The student’s construction of quantification. For the Learning of Mathematics—An International Journal of Mathematics Education ,8, pp. 44–51.
8. Goldin, G. A.（1987）.Cognitive Representational Systems for Mathematical problem solving. Problems of representation in the teaching and learning of mathematics. Edited by Claude Janiver,pp.125-145.
9. Goldin, G. A. （1998）.Representational systems, learning, and problem solving in mathematics. Journal of mathematical behavior, 17(2), p137-165.
10. Hiebert, J. & Lefevre, P. （1987）.Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis, ed. Hiebert,J. Conceptual and Procedural Knowledge: The Case of Mathematics. Hillsdale, NJ:Erlbaum.
11. Herscovics, N.（1979）.A learning model for some algebraic concepts. In K. Fuson, ＆ W. Geeslin, (Eds.), Explorations in the modelling of the learning of mathematics, pp.98-116. Columbus.
12. Hirsch, C.R.（1976）.Making Mathematical Induction Meaningful. School Science and Mathematics, 76(1), 27-31.
13. Howson, G.（2005）.“Meaning” and School Mathematics. Meaning in Mathematics Education.(pp.17-38) Springer.
14. Janvier, C.（1987a）.Representation and Understanding: The Notion of Function as an Example. In Janvier, C. (ed), Problems of Representation in the Teaching and Learning of Mathematics, 67-71. USA, LEA.
15. Janvier, C.（1987b）.Representation and Understanding: The Circle as an Example. In Janvier, C. (ed), Problems of Representation in the Teaching and Learning of Mathematics, 67-71. USA, LEA.
16. Janvier, C.（1987c）.Translation progress in mathematics. In Janvier, C. (ed), Problems of Representation in the Teaching and Learning of Mathematics, 27-32. USA, LEA.
17. Joyce, B. & Weil, M.（1986）.Models of teaching. N. J.：Prenitce-Hall.
18. Joyce, B., Weil, M., &Calhoun, E.（2004）.Models of teaching. Boston : Allyn and Bacon.
19. Kaput,J.J.（1987a）.Representation Systems and Mathematics. Problems of representation in teaching and learning mathematics. Edited by Claude Janvier:Lawrence Erlbaum,Hillsdale,NJ.pp.19-26.
20. 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.
21. Kaput, J.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. Erlbaum, Hillsdale, NJ (1989), pp. 167–194.
22. Karmiloff-Smith, A.（1984）.Children’s problem solving. In M.E. Lamb, A.L. Brown, & B. Rogoff (Eds.), Advances in Developmental Psychology, vol.3 (pp.39-90). Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
23. Karmiloff-Smith, A.（1986）."Stage/structure versus phase/process in modeling linguistic and cognitive development". In I. Levin (Ed.) Stage and Structure: Reopening the debate. New York: Ablex, 164-190.
24. Kember, D.（1991）.Instructional design for meaningful learning. Instructional Science, 20, 289–310.
25. Kieran, C.（2007） .Learning and teaching algebra at the middle school through college levels - building meaning for symbols and their manipulation. The Second Handbook of Research on Mathematics Teaching and Learning Vol.3, 707-762.NCTM.
26. Kilpatrick, J., Hoyles, C. & Skovsmose, O.（2005）.Meanings of Meaning of Mathematics. Meaning in Mathematics Education.(pp.9-16) Springer.
27. Kinnear, J.（1994）.What Science Education Really Says about Communication of Science Concepts. Paper presented at the Annual Meeting of the International Communication Association (44th, Sydney, New South Wales, Australia, July 11-15, 1994).
28. Lave, J. & Wenger, E.（1991）.Situated Learning: Legitimate Peripheral Participation. New York: Cambridge University Press.
29. Lesh, R.（1979）.Mathematical learning disabilities: Consideration for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, & M. G.Kantowski (Eds.). Applied mathematics problem solving. (pp.235-264) Columbus.
30. Lesh, R.（1981）.Applied Mathematical Problem Solving. Educational Studies in Mathematics, v12 n2, p235-264.
31. 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. Edited by Claude Janiver,(pp.33-40).
32. 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.
33. Mayer, R. E.（1979）.Can Advance Organizers Influence Meaningful Learning？Review of Educational Research, v49 n2 p371-83
34. Mayer, R. E.（1987）.Educational psychology: a cognitive approach. Lawrence Earlbaum.
35. Mayer, R. E.（1992）.Thinking, problem solving, cognition. New York : W.H. Freeman.
36. Mayer, R. E.（2002）.Rote versus meaningful learning. Theory into Practice, 41(4), 226.
37. Meira. L.（1996）.Students' early algebraic activity: Sense making and the production of meanings in mathematics. In L. Puig and A. Gutierrez (eds). Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3. p.377-384.
38. Royer, J. M. & Cable, G. W.（1975）.Facilitated learning in connected discourse. Journal of Educational Psychology, 67, 116-123.
39. National Council of Teachers of Mathematics.（2000）.Principles and standards for school mathematics. Reston, VA : NCTM
40. Noss, R. & Hoyles, C.（1996）.Windows on Mathematical Meanings: learning cultures and computers. Kluwer, Dordrecht.
41. Radford, L.（2004）.Syntax and meaning. In M. J. Hoines and A. B. Fuglestad (eds.), Proceedings of the 28 Conference of the international group for the psychology of mathematics education (PME 28), Vol. 1, pp. 161-166. Norway: Bergen University College.
42. Rubenstein & Thompson（2001）. Learning Mathematical Symbolism: Challenges and Instructional Strategies. Mathematics Teacher, v94 n4, p265-71 ,Apr 2001.
43. Rumelhart, D. E. & Norman, D. A.（1978）.Accretion, tuning, and restructuring: three modes of learning. In J. W. Cotton & R. L. Klatzky (Eds.). Semantic factors in cognition (pp.37-53). Hillsdale, NJ: Lawrence Erlbaum Associates.
44. Skemp,R. R.（1989）.Mathematics in the primary school. London : Routledge.
45. Shuell, T. J.（1990）.Phases of Meaningful Learning. Review of Educational Research, 60(4), 531. .
46. Sigurdson , S. E. & Olson, A. T.（1992）. Teaching Mathematics with Meaning. Journal of Mathematical Behavior, 11(1),37-57.
47. Skovsmose, O.（2005）.Meaning in Mathematics Education. Meaning in Mathematics Education (pp.83-100). Springer.
48. Spiro, R. J., Coulson, R. L., Feltovich,P. J. & Anderson, D. K.（1988）.Cognitive flexibility theory: Advanced knowledge acquisition in ill-structured domains(Tech. Rep. No.5). Springfield, IL: Southern Illinois University School of Medicine, Conceptual Knowledge Research Project.
49. Usiskin, Z.（1996）. Mathematics as a language. Communication in Mathematics k-12 and Beyond:1996 yearbook(pp.231-243). Reston, VA:NCTM.
50. Wall’s, G.（1926）. The art of thought. New York：Harcourt Brace Jovanovich.