Script writing in the mathematics classroom: imaginary conversations on the structure of numbers

References

• Chinn, C. A., & Brewer, W. F. (1993). The role of anomalous data in knowledge acquisition: A theoretical framework and implications for science instruction. Review of Educational Research, 63(1), 1–49. doi:10.3102/00346543063001001
   Web of Science ®Google Scholar
• Durkin, K., & Shire, B. (1991). Lexical ambiguity in mathematical contexts. In K. Durkin & B. Shire (Eds.), Language in mathematical education: Research and practice (pp. 71–84). Milton Keynes: Open University Press.
   Google Scholar
• Edwards, L. D. (1997). Exploring the territory before proof: Students' generalizations in a computer microworld for transformation geometry. International Journal of Computers for Mathematical Learning, 2, 187–215. doi:10.1023/A:1009711521492
   Google Scholar
• Edwards, L., & Zazkis, R. (2002). Pre-service teachers' generalizations on a number theory task. In S. R. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 139–156). Westport, CT: Ablex.
   Google Scholar
• Gholamazad, S. (2007). Pre-service elementary school teachers' experiences with the process of creating proofs. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 265–272). Seoul, Korea: PME.
   Google Scholar
• 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.
   Google Scholar
• Koichu, B., & Zazkis, R. (2013). Decoding a proof of Fermat's Little Theorem via script writing. Journal of Mathematical Behavior, 32, 364–376. doi:10.1016/j.jmathb.2013.04.001
   Google Scholar
• Lakatos, I. (1976). Proofs and refutations. Cambridge: Cambridge University Press.
   Google Scholar
• Lesh, R., Behr, M., & Post, M. (1987). Rational number relations and proportions. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 41–58). Hillsdale, NJ: Erlbaum.
   Google Scholar
• Mason, J. (2006). What makes an example exemplary: Pedagogical and didactical issues in appreciating multiplicative structures. In R. Zazkis & S. R. Campbell (Eds.), Number theory in mathematics education: Perspectives and prospects (pp. 41–68). Hillsdale, NJ: Lawrence Erlbaum Press.
   Google Scholar
• Stavy, R., & Tirosh, D. (1996). Intuitive rules in science and mathematics: The case of ‘more of A – More of B’. International Journal of Science Education, 18, 653–667. doi:10.1080/0950069960180602
   Web of Science ®Google Scholar
• Zazkis, D. (2013). Odd dialogues on odd and even functions. In S. Brown, G. Karakok, K. H. Roh, & M. Oehrtman (Eds.), Proceedingsof the 16th Annual Conference on Research in Undergraduate Mathematics Education (Vol. 2, pp. 314–320). http://sigmaa.maa.org/rume/crume2013/Conference%20Proceedings.html
   Google Scholar
• Zazkis, R. (1995). Fuzzy thinking on non-fuzzy situations: Understanding students' perspective. For the Learning of Mathematics, 15(3), 39–42.
   Google Scholar
• Zazkis, R. (1998). Divisors and quotients: Acknowledging polysemy. For the Learning of Mathematics, 18(3), 27–30.
   Google Scholar
• Zazkis, R. (1999). Intuitive rules in number theory: Example of “the more of A, the more of B” rule implementation. Educational Studies in Mathematics, 40, 197–209. doi:10.1023/A:1003711828805
   Google Scholar
• Zazkis, R., & Gadowsky, K. (2001). Attending to transparent features of opaque representations of natural numbers. In A. Cuoco (Ed.), NCTM 2001 yearbook: The roles of representation in school mathematics (pp. 41–52). Reston, VA: NCTM.
   Google Scholar
• Zazkis, R., Sinclair, N., & Liljedahl, P. (2013). Lesson play in mathematics education: A tool for research and professional development. Dordrecht, The Netherlands: Springer. doi:10.1007/978-1-4614-3549-5
   Google Scholar
• Zazkis, R., & Sirotic, N. (2010). Representing and defining irrational numbers: Exposing the missing link. Research in Collegiate Mathematics Education, 7, 1–27.
   Google Scholar