研究中界定的證明方法特徵含：

（一）證明使用的物件之特徵。
1. 主要是用抽象符號來證明
2. 主要是用特例來證明
3. 主要是用運算的方式來證明
4. 主要是用圖形的方式來證明
5. 主要是用實際數字來證明

（二）證明步驟與銜接之特徵。
6. 步驟的銜接自然
7. 步驟很多
8. 用了很多符號
9. 想法很難

（三）證明效度、嚴謹度、一般性之特徵。
10. 要證明不等式都可以用這樣的想法
11. 證明是有效的
12. 證明是嚴謹的
13. 證法可以套用到一般的狀況（如：所有正數、所有圖形……）

研究結果發現，學生較喜歡的證法應有效而且能用在其他同類型的數學證明中，但是，其想法不能太難，步驟也不能太多，特別是不要以實際數字作為證明的主要內容。

中文部分
1. 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。國立臺灣師範大學數學系碩士論文。
2. 林福來（民90）。青少年的數學概念學習研究－－子計劃十四：青少年數學論證能力發展研究。行政院國家科學研究委員會專題研究計劃期中報告。
3. 林福來，吳家怡（民84）。數學證明的瞭解(II)。行政院國家科學研究委員會專題研究計劃期末報告。
4. 曾政清（民92）。高中生透過局部推理活動以發展數學證明能力之教學實驗。國立臺灣師範大學數學系碩士論文。
5. 楊凱琳（民93）。建構中學生對幾何證明閱讀理解的模式。國立臺灣師範大學數學系博士論文。
6. 蕭文強（民87）。數學證明。新竹：凡異。
7. 羅昭強。教育統計講義－－SPSS 12.0版。未出版。

英文部分
1. Alibert, D. & Thomas, M. (1991). Research on mathematical proof. In D. Tall (ed.), Advanced Mathematical Thinking. 215-230.
2. Alibert, D. (1988). 'Towards New Customs in the Classroom', For the Learning of Mathematics, 8(2), 31-35.
3. Arnhiem, R. (1969). Visual Thinking, Berkley: University of California Press.
4. Balacheff, N. (1987). Processus de Prevue et Situations de Validation. Educational Studies in Mathematics, 18(2), 147-176.
5. Bell, A. (1976). A study of pupils' proof-explanations in mathematical situations. Educational Studies in Mathematics, 7, 23-40.
6. Chazan, D. (1993). High School Geometry Students' Justification for their Views of Empirical Evidence and Mathematical Proof. Educational Studies in Mathematics 24, 359-387.
7. Davis, R. B. (1986). Algebra in elementary schools. Proceedings of the 5th In ternational Cogress on Mathematical Education, Birkhauser, Bosten.
8. de Villiers, M. (1999). Rethinking proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press.
9. Ersoz, F. A. (2009). Proof in different mathematical domains. Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education, vol. 1, 160-165.
10. Fischbein, E. & Kedem, I. (1982). Proof and certitude in development of mathematical thinking. In A. Vermandel (ed.), Proceedings of the 6th PME Conference, Universitaire Instelling Antwerpen, pp. 128-132.
11. Hanna, G. (1983). Rigorous proof in mathematics education. Toronto: OISE Press.
12. Hanna, G. (1989). Moore than formal proof. For the learning of mathematics 9, 20-30.
13. Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13.
14. Hanna, G. (1997). The ongoing value of proof. Journal Mathematik Didaktik, 18, 171-185.
15. Healy, L. & Hoyles, C. (1998). Justifying and proving in school mathematics. Teacher Report in The National Wide Survey, Institute of Education, University of London.
16. Healy, L. & Hoyles, C. (2000). A Study of Proof Conceptions in Algebra. Journal for Research in Mathematics Education, 31(4), 396-428.
17. Hoyles, C. (1997). The Curricular Shaping Students' Approaches to Proof. For the Learning of Mathematics, 17(1), 7-16.
18. Knuth, E. J. (2002). Secondary School Mathematics Teachers' Conceptions of Proof, Journal for Research in Mathematics Education, 2002, vol. 33, No. 5, 379-405.
19. Kondratieva, M. (2009). Geometrical Sophisms and Understanding of Mathematical Proofs, Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education, vol 2, 3-8.
20. Leron, U. & Zaslavsky, O. (2009). Generic Proving: Reflections on Scope and Mathod, Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education, vol 2, 53-58.
21. Lin, F. L. (1988). Societal differences and their influences on children's mathematics understanding. Educational Studies in Mathematics, 19, 471-497.
22. Mamona-Downs, J. & Downs, M. (2009). Proof Sataus from a perspective of Articulation, Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education, vol 2, 94-99.
23. Mason, J., Burton, L., & Stacey, K. (1982). Thinking Mathematically. Reading, MA: Addision-Wesley.
24. Polya, G. (1945). How to solve it. Princeton, New Jersy: Princeton University Press.
25. Porteous, K. (1990). What do children really believe? Educational Studies in Mathematics, 21, 589-598.
26. Stylianides, A. J. (2007). Proof and Proving in School Mathematics, Journal for Research in Mathematics Education, 38(3), 289-321.
27. Tall, D. (1991). The psychology of advanced mathematical thinking. In D. Tall (ed.), Advanced Mathematical Thinking. The Netherlands, Kluwer Academic Publishers.
28. Tall, D. O. (1979), 'Cognitive aspects of proof, with special reference to the irrationality of √2,' Proceedings of PME 3, Warwick, 203-205.
29. Vinner, S. (1988). 'Visual Considerations in College Calculus - Students and Teachers', Theory of Mathematics Education Proceedings of the Third International Conference, Antwerp, 109-116.
30. Wilder, R. L. (1968). Evolution of Mathematical Concepts, John Wiley.
31. Yang, K. L. & Lin, F. L. (2009). Reading Perspective on Learning Mathematics Proofs, Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education, vol 2, 274-279.