References
- Ahmadpour Mobarakeh, F., & Fadaee, M. R. (2016). The status of reasoning and proof in Iranian seventh-grade mathematics textbook. Presented in TSG 18, 13th International Congress on mathematics Education. Hamburg, Germany, 24-31 July 2016.
- Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216–235). London, UK: Hodder and Stoughton.
- Blum, W., & Kirsch, A. (1991). Preformal proof: Examples and reflections. Educational Studies in Mathematics, 22(2), 183–203.
- Collis, K. F. (1974). Cognitive Development and Mathematics Learning. Paper prepared for the Psychology of Mathematics Education Workshop, published at the Shell Mathematics Unit Centre for Science Education, Chelsea College, University of London, UK.
- Dawson, J. W. (2006). Why do mathematicians re-prove theorems? Philosophia Mathematica, 14(3), 269–286.
- Hanna, G., & Jahnke, H. N. (2002). Another approach to proof: Arguments from physics. ZDM, 34(1), 1–8.
- Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education. III (pp. 234–283). Providence, RI: American Mathematical Society and Washington, DC: Mathematical Association of America.
- Harel, G., & Tall, D. O. (1991). The general, the abstract, and the generic in advanced mathematics. For the Learning of Mathematics, 11(1), 38–42.
- Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428.
- Herscovics, N., & Bergeron, J. C. (1988). An extended model of understanding. In M. J. Behr & C. B. Lacampagne, (Eds.), Proceedings of the tenth annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 15–22). De Kalb, IL: Northern Illinois University.
- Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59–78.
- Knuth, E. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal of Research in Mathematics Education, 33(5), 379–405.
- Martin, G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41–51.
- Mason, J. (1989). Mathematical abstraction as the result of a delicate shift of attention. For the Learning of Mathematics, 9(2), 2–8.
- Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277–289.
- Mejía-Ramos, J. P., & Inglis, M. (2009). Argumentative and proving activities in mathematics education research. In F.-L. Lin, F.-J. Hsieh, G. Hanna, & M. de Villiers (Eds.), Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education (Vol.2, pp. 88–93). Taipei, Taiwan: Department of Mathematics, National Taiwan Normal University.
- Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3–18.
- Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223–239.
- Piaget, J. (1970). Genetic epistemology. New York, NY: W. W. Norton.
- Pirie, S., & Kieren, T. (1989). A recursive theory of mathematical understanding. For the Learning of Mathematics, 9(3), 7–11.
- Reid, D, & Knipping, C. (2010). Proof in mathematics education: research, learning and teaching. Rotterdam, The Netherlands: Sense.
- Sémadéni, Z. (1984). Action proofs in primary mathematics teaching and in teacher training. For the Learning of Mathematics, 4(1), 32–34.
- Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.
- Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks, CA: Sage.
- Stylianides, A. J. (2007). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65, 1–20.
- Tall, D. (1995). Cognitive development, representations and proof. In L. Healy & C. Hoyles (Eds.), Justifying and proving in school mathematics. Proceedings of an International Conference (pp. 27–38). London: Institute of Education, University of London.
- Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209–234.