1 |
Alcock, L., & Inglis, M. (2008). Doctoral students' use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69(2), 111-129.
DOI
|
2 |
Australian Curriculum, Assessment and Reporting Authority. (2015). Australian Curriculum: Mathematics. Retrieved from https://australiancurriculum.edu.au/f10-curriculum/mathematics/
|
3 |
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, England: Hodder & Stoughton.
|
4 |
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.
|
5 |
Almeida, D. (2000). A survey of mathematics undergraduates' interaction with proof: some implications for mathematics education. International Journal of Mathematical Education in Science and Technology, 31(6), 869-890.
DOI
|
6 |
Balacheff, N. (2002). A researcher epistemology: A deadlock for educational research on proof. In Proceedings of the 2002 international conference on mathematics: Understanding proving and proving to understand (pp. 23-44). Department of Mathematics: National Taiwan Normal University.
|
7 |
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.
|
8 |
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, 30(3), 115-134.
DOI
|
9 |
Knuth, E., Zaslavsky, O., & Kim, H. (2022). Argumentation, justification, and proof in middle grades: A rose by any other name. In Bieda, K., Conner, A., Kosko, K., & Staples, M. (Eds.). Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof (pp. 129-136). Springer.
|
10 |
Kwon, O., Kim, A., & Cho, H. (2012). An analysis on the curriculum and teaching methods of Korean mathematics education departments. Mathematics Education, 51(3), 281-300.
DOI
|
11 |
Mason, J. & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15(3), 277-289.
DOI
|
12 |
Ministry of Education. (2015). Revised Korean mathematics curriculum. Seoul, Korea: Ministry of Education
|
13 |
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
|
14 |
Kim, H. (2020). Embracing proving into everyday lesson by problem posing. 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, Mexico.
|
15 |
Basturk, S. (2010). First-year secondary school mathematics students' conceptions of mathematical proofs and proving. Educational Studies, 36(3), 283-298.
DOI
|
16 |
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
|
17 |
Hoyles, C. (1997). The Curricular Shaping of Students' Approaches to Proof. For the Learning of Mathematics, 17(1), 7-16.
|
18 |
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 criteria-affordances-purposes-strategies framework. The Journal of Mathematical Behavior, 53, 263-283.
DOI
|
19 |
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
|
20 |
Hanna, G., & Jahnke, H. N. (1999). Using arguments from physics to promote understanding of mathematical proofs, In O. Zaslavsky (ed.), Proceedings of the twenty-third conference of the international group for the Psychology of Mathematics Education (Vol. 3, pp. 73-80). Haifa, Israel: PME.
|
21 |
Schoenfeld, A. (1986). On having and using geometric knowledge. In J. Hiebert (Ed.) Conceptual and procedural knowledge: The case of mathematics. (pp. 225-263). Hillsdale, NJ: Lawrence Erlbaum Associates.
|
22 |
Polya, G. (1954). Mathematics and plausible reasoning: Induction and analogy in mathematics (Vol. I). Princeton, NJ: Princeton University Press.
|
23 |
Reid, D. A., & Knipping, C. (2010). Proof in mathematics education: Research, learning, and teaching. The Netherlands: Sense Publishers.
|
24 |
Sandefur, J., Mason, J., Stylianides, G. J., & Watson, A. (2013). Generating and using examples in the proving process. Educational Studies in Mathematics, 83(3), 323-340.
DOI
|
25 |
Schoenfeld, A. H. (1994). What do we know about mathematics curricula? The Journal of Mathematical Behavior, 13(1), 55-80.
DOI
|
26 |
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
|
27 |
Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington DC: Council of Chief State School Officers.
|
28 |
Leron, U., & Zaslasvsky, O. (2013). Generic Proving: Reflections on scope and method. For the Learning of Mathematics, 33(3), 24-30.
|
29 |
Bell, A. (1976). A study of pupils' proof-explanations in mathematical situations, Educational Studies in Mathematics, 7, 23-40.
DOI
|
30 |
Blanton, M. L., & Stylianou, D. A. (2014). Understanding the role of transactive reasoning in classroom discourse as students learn to construct proofs. The Journal of Mathematical Behavior, 34, 76-98.
DOI
|
31 |
de Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17-24.
|
32 |
Ellis, A. B., Lockwood, E., Dogan, M., Williams, C., & Knuth, E. J. (2013). Choosing And Using Examples: How Example Activity Can Support Proof Insight. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th conference of the international 2-265 group for the psychology of mathematics education (Vol. 2, pp. 265-272). Kiel, Germany: PME.
|
33 |
Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15(1), 3-31.
DOI
|
34 |
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
|
35 |
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.
|
36 |
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428.
DOI
|
37 |
Knuth, E. J. (2002b). Secondary school mathematics teachers' conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405.
DOI
|
38 |
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
|
39 |
Stylianides, G. J. (2007). 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
|
40 |
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
|
41 |
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
|
42 |
Coe, R. & Ruthven, K. (1994). Proof practices and construct of advanced mathematics students. British Educational Research Journal, 20, 41-53.
DOI
|
43 |
Creswell, J. W., & Poth, C. N. (2016). Qualitative inquiry and research design: Choosing among five approaches. Thousand Oaks, CA: Sage publications.
|
44 |
Department for Education. (2014). Mathematics programmes of study: Key stage 4 (National curriculum in England). Retrieved from https://www.gov.uk/government/uploads
|
45 |
de Villiers, M. (1999). Rethinking proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press.
|
46 |
Dickerson, D. S., & Doerr, H. M. (2014). High school mathematics teachers' perspectives on the purposes of mathematical proof in school mathematics. Mathematics Education Research Journal, 26(4), 711-733.
DOI
|
47 |
Epstein, D., & Levy, S. (1995). Experimentation and proof in mathematics. Notices of the AMS, 42(6), 670-674.
|
48 |
Hanna, G. (2000). Proof, explanation and exploration: an overview. Educational Studies in Mathematics, 44(1/2), 5-23.
DOI
|
49 |
Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389-399.
DOI
|
50 |
Harel, G., & Sowder, L. (1998). Students' Proof Schemes: Results from Exploratory Studies. Research in Collegiate Mathematics Education III, 7, 234-282.
|
51 |
Zack, V. (1999). Everyday and mathematical language in children's argumentation about proof, Educational Review, 51(2), 129-146.
DOI
|
52 |
Tall, D. (1999). The cognitive development of proof: Is mathematical proof for all or some? Developments in School Mathematics Education around the World, 4, 117-136.
|
53 |
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
|
54 |
Walther, G. (2006). Illuminating examples - an aspect of simplification in the teaching of mathematics. International Journal of Mathematical Education in Science and Technology, 17(3), 263-273.
DOI
|
55 |
Zaslavsky, O. (2018). Genericity, conviction, and conventions: examples that prove and examples that don't prove. In A. Stylianides, & G. Harel (Eds.). Advances in mathematics education research on proof and proving (pp. 283-298). Cham, Switzerland: Springer International Publishing AG.
|
56 |
Porteous, K. (1990). What do children really believe? Educational Studies in Mathematics, 21, 589-598.
DOI
|
57 |
Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press.
|
58 |
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.
|
59 |
Ministry of Education. (2011). Revised Korean mathematics curriculum. Seoul, Korea: Ministry of Education.
|
60 |
Rowland, T. (2002). Generic Proofs in Number Theory. Learning and Teaching Number Theory: Research in Cognition and Instruction, 157-183.
|
61 |
Schoenfeld, A. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, 23(2), 145-166.
DOI
|
62 |
Senk, S. (1985). How well do students write geometry proofs? The Mathematics Teacher, 78(6), 448-456.
DOI
|
63 |
Sowder, L., & Harel, G. (1998). Types of students' justifications. Mathematics Teacher, 91, 670-675.
DOI
|
64 |
Sowder, L., & Harel, G. (2003). Case studies of mathematics majors' proof understanding, production, and appreciation. Canadian Journal of Math, Science & Technology Education, 3(2), 251-267.
DOI
|
65 |
Knuth, E. J. (2002a). Teachers' Conceptions of Proof in the Context of Secondary School Mathematics. Journal of Mathematics Teacher Education, 5, 61-88.
DOI
|
66 |
Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289-321.
|
67 |
Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237-253.
DOI
|
68 |
Kim, H. (2021). Problem posing in the instruction of proof: Bridging everyday lesson and proof. Research in Mathematical Education, 24(3), 255-278.
DOI
|
69 |
Knuth, E. J., Choppin, J., & Bieda, K. (2009). Middle school students' production of mathematical justifications. In D. A. Stylianou, M. L. Blanton, & E. J. Knuth (Eds.), Teaching and learning proof across the grades: A K-16 perspective (pp. 153-170). New York, NY: Routledge.
|