1 |
Thomas, D. R. (2006). A general inductive approach for analyzing qualitative evaluation data. American Journal of Evaluation, 27(2), 237-246.
DOI
|
2 |
Alcock, L., & Inglis, M. (2008). Doctoral students' use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69, 111-129.
DOI
|
3 |
Aristotle. (n.d.). Be a free thinker and don't accept everything you hear as truth. Be critical and evaluate what you believe in. Retrieved August 20, 2020from https://www.azquotes.com/quote/1397505
|
4 |
Australian Curriculum, Assessment and Reporting Authority. (2015). Australian curriculum: Mathematics. Retrieved November 20, 2020 from https://australiancurriculum.edu.au/f-10-curriculum/mathematics/
|
5 |
Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. In D. En Pimm (Ed.), Mathematics, teachers and children (pp. 216-235). London, UK: Hodder & Stoughton.
|
6 |
Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71-80.
DOI
|
7 |
Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1/2), 5-23.
DOI
|
8 |
Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L. I. Tatsien (Ed.), Proceedings of the international congress of mathematicians (Vol. III) (pp. 907-920). Beijing, China: Higher Education Press.
|
9 |
Begle, E. G. (1973). Some lessons learned by SMSG. The Mathematics Teacher, 66(3), 207-214.
DOI
|
10 |
Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351-382.
DOI
|
11 |
Brown, S. I., & Walter, M. I. (2014). Problem posing: Reflections and applications. Hillsdale, NJ: Psychology Press.
|
12 |
Department for Education. (2014). Mathematics programme of study: Key stage 4 (National curriculum in England). Retrieved March 17, 2020, from https://www.gov.uk/government/uploads
|
13 |
Cai, J., & Cirillo, M. (2014). What do we know about reasoning and proving? Opportunities and missing opportunities from curriculum analyses. International Journal of Educational Research, 64, 132-140.
DOI
|
14 |
Chazan, D. (1993). High school geometry students' justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359-387.
DOI
|
15 |
Coe, R. & Ruthven, K. (1994). Proof practices and construct of advanced mathematics students. British Educational Research Journal, 20, 41-53.
DOI
|
16 |
Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington DC: Authors.
|
17 |
Creswell, J. W., & Poth, C. N. (2016). Qualitative inquiry and research design: Choosing among five approaches. Thousands Oaks, CA: Sage Publications.
|
18 |
de Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17-24.
|
19 |
Ellis, A. B., Ozgur, Z., Vinsonhaler, R., Dogan, M. F., Carolan, T., Lockwood, E., Lynch, A., Sabouri, P., Knuth, E., & Zaslavsky, O. (2019). Student thinking with examples: The criteriaaffordances-purposes-strategies framework. The Journal of Mathematical Behavior, 53, 263-283.
DOI
|
20 |
Epstein, D., & Levy, S. (1995). Experimentation and proof in mathematics. Notices of the AMS, 42(6), 670-674.
|
21 |
Lockwood, E., Ellis, A., & Knuth, E. (2013). Mathematicians' example-related activity when proving conjectures. In Brown, S., Karakok, G., Roh, K., & Oehrtman, M. (Eds.). Proceedings for the Sixteenth Annual Conference on Research on Undergraduate Mathematics Education (Vol. 1, pp. 16-28). Denver, CO: Northern Colorado University.
|
22 |
Knuth, E. J. (2002a). Teachers' conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5, 61-88.
DOI
|
23 |
Knuth, E. J. (2002b). Proof as a tool for learning mathematics. Mathematics Teacher, 95(7), 486-490.
DOI
|
24 |
Knuth, E. J. (2002c). Secondary school mathematics teachers' conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405.
DOI
|
25 |
Knuth, E., Zaslavsky, O., & Ellis, A. (2019). The role and use of examples in learning to prove. The Journal of Mathematical Behavior, 53, 256-262.
DOI
|
26 |
Knuth, E., Zaslavsky, O., Vinsonhaler, R., Gaddis, D., & Fernandez, L. (2019). Proving-related activities. In S. Otten, A. G. Candela, Z. Araujo, C. Haines, & C. Munter (Eds.). Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1718-1722). St. Louis, MO: University of Missouri.
|
27 |
Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510-524.
DOI
|
28 |
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428.
DOI
|
29 |
Hanna, G., & Jahnke, N. (1996). Proof and proving. In A. Bishop, et al. (Eds.), International handbook of mathematics education (pp. 877-908). Dordrecht: Kluwer.
|
30 |
Harel, G., & Sowder, L. (1998). Students' proof schemes: Results from exploratory studies. Research in Collegiate Mathematics Education III, 7, 234-282.
|
31 |
Iannone, P., Inglis, M., Mejia-Ramos, J. P., Simpson, A., & Weber, K. (2011). Does generating examples aid proof production? Educational Studies in Mathematics, 77, 1-14.
DOI
|
32 |
Kim, H. (2020). Problem posing as a tool for students to engage in proving. In Sacristan, A. I., Cortes-Zavala, J. C. & Ruiz-Arias, P. M. (Eds.). Mathematics education across cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 2082-2086), Mazatlan, Sinaloa: Mexico.
|
33 |
Maher, C. A., & Martino, A. M. (1996). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 27(2), 194-214.
DOI
|
34 |
Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41-51.
DOI
|
35 |
Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in mathematics, 27(3), 249-266.
DOI
|
36 |
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
|
37 |
Polya, G. (1954). Mathematics and plausible reasoning: Induction and analogy in mathematics (Vol. I). Princeton, NJ: Princeton University Press.
|
38 |
Schoenfeld, A. H. (1994). What do we know about mathematics curricula? The Journal of Mathematical Behavior, 13(1), 55-80.
DOI
|
39 |
Porteous, K. (1990). What do children really believe? Educational Studies in Mathematics, 21(6), 589-598.
DOI
|
40 |
Lockwood, E., Ellis, A., Knuth, E., Dogan, M. F., & Williams, C. (2013). Strategically chosen examples leading to proof insight: A case study of a mathematician's proving process. In Martinez, M. & Castro Superfne, A. (Eds.). Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 245-252). Chicago, IL: University of Illinois at Chicago.
|
41 |
Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4-36.
DOI
|
42 |
Rowland, T. (2002). Generic proofs in number theory. In S. R. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 157-183). Westport, CT: Ablex Publishing.
|
43 |
Schoenfeld, A. H. (1979). Explicit heuristic training as a variable in problem-solving performance. Journal for Research in Mathematics Education, 10(3), 173-187.
DOI
|
44 |
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
|
45 |
Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11(4), 307-332.
DOI
|
46 |
Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237-253.
DOI
|
47 |
Stylianides, G. J. (2009) Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258-288.
DOI
|
48 |
Varghese, T. (2009). Secondary-level student teachers' conceptions of mathematical proof. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-14.
|
49 |
Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40(3), 314-352.
DOI
|
50 |
Thompson, D. R., & Senk, S. L. (2014). The same geometry textbook does not mean the same classroom enactment. ZDM, 46(5), 781-795.
DOI
|
51 |
Ozgur, Z., Ellis, A. B., Vinsonhaler, R., Dogan, M. F., & Knuth, E. (2019). From examples to proof: Purposes, strategies, and affordances of example use. The Journal of Mathematical Behavior, 53, 284-303.
DOI
|
52 |
Remillard, J. T., & Bryans, M. B. (2004). Teacher's orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 33(5), 352-388.
DOI
|
53 |
Schoenfeld, A. H. (1983). Beyond the purely cognitive: Belief systems, social cognitions, and metacognitions as driving forces in intellectual performance. Cognitive science, 7(4), 329-363.
DOI
|
54 |
Senk, S. (1985). How well do students write geometry proofs? The Mathematics Teacher, 78(6), 448-456.
DOI
|
55 |
Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56(3), 209-234.
DOI
|
56 |
Hoyles, C. (1997). The curricular shaping of students' approaches to proof. For the Learning of Mathematics, 17(1), 7-16.
|
57 |
Skilling, K., & Stylianides, G. J. (2020). Using vignettes in educational research: A framework for vignette construction. International Journal of Research & Method in Education, 43(5), 541-556.
DOI
|
58 |
Stylianides, G. J., Stylianides, A. J., & Weber, K. (2016). Research on the teaching and learning of proof: Taking stock and moving forward. In Cai, J. (Ed.). Compendium for research in mathematics education (pp. 237-266). Reston, VA: NCTM.
|
59 |
Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289-321.
|
60 |
Stylianides, G. J. (2008). Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics. International Journal of Science and Mathematics Education, 6(1), 191-215.
DOI
|
61 |
Thompson, D. R., Senk, S. L., & Johnson, G. J. (2012). Opportunities to learn reasoning and proof in high school mathematics textbooks. Journal for Research in Mathematics Education, 43(3), 253-295.
DOI
|
62 |
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.
DOI
|
63 |
Knuth, E., Kim, H., Zaslavsky, O., Vinsonhaler, R., Gaddis, D., & Fernandez, L. (2020). Teachers' views about the role of examples in proving-related activities. Journal of Educational Research in Mathematics, Special Issue, 115-134.
|
64 |
Ellis, A., Ozgur, Z., & Reiten, L. (2019). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, 31, 107-132.
DOI
|
65 |
Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press.
|
66 |
Fischbein, E., & Kedem, I. (1982). Proof and certitude in the development of mathematical thinking. In A. Vermandel (Ed.), Proceedings of the 6th International Conference for the Psychology of Mathematical Education (pp. 128-131). Antwerp, Belgium: PME.
|
67 |
Zack, V. (1999). Everyday and mathematical language in children's argumentation about proof. Educational Review, 51(2), 129-146.
DOI
|
68 |
Knuth, E. J., Choppin, J., & Bieda, K. (2009). Middle school students' production of mathematical justifications. In Stylianou, D. A., Blanton, M. L., & Knuth, E. J. (Eds.), Teaching and learning proof across the grades: A K-16 perspective (pp. 153-170). New York, NY: Routledge.
|
69 |
Lynch, A. G., & Lockwood, E. (2019). A comparison between mathematicians' and students' use of examples for conjecturing and proving. The Journal of Mathematical Behavior, 53, 323-338.
DOI
|
70 |
Ministry of Education. (2011). Revised Korean mathematics curriculum. Seoul, Korea: Ministry of Education.
|