Alcock, L., & Inglis, M. (2008). Doctoral students’ use of examples in evaluating and proving conjectures.
Educational Studies in Mathematics, 69, 111–129.
CrossRefBall, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In Proceedings of the International Congress of Mathematicians (Vol. 3, pp. 907–920).
Bell, A. W. (1976). A study of pupils’ proof-explanations in mathematical situations.
Educational Studies in Mathematics, 7(1), 23–40.
CrossRefBransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.
Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics?
Educational Studies in Mathematics, 37, 121–143.
CrossRefChi, M. (1997). Quantifying qualitative analyses of verbal data: A practical guide.
Journal of the Learning Sciences, 6(3), 271–315.
CrossRefClement, J. (2000). Analysis of clinical interviews: Foundations & model viability. In R. Lesh (Ed.), Handbook of research methodologies for science and mathematics education (pp. 341–385). Hillsdale, NJ: Lawrence Erlbaum.
Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula.
Journal of Mathematical Behavior, 15, 375–402.
CrossRefde Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras, 24(1), 17–24.
Duffin, J., & Simpson, A. (2000). A search for understanding.
The Journal of Mathematical Behavior, 18(4), 415–427.
CrossRefEricsson, K. A., & Simon, H. A. (1984). Protocol analysis: Verbal reports as data. Cambridge, MA: MIT Press.
Glaser, B. G., & Strauss, A. L. (1977). The discovery of grounded theory: Strategies for qualitative research. London: Aldine.
Gray, E., Pinto, M. M. F., Pitta, D., & Tall, D. (1999). Knowledge construction and diverging thinking in elementary & advanced mathematics.
Educational Studies in Mathematics, 38(1), 111–133.
CrossRefHanna, G., & Barbeau, E. (2008). Proofs as bearers of mathematical knowledge.
ZDM, 40(3), 345–353.
CrossRefHanna, G., & de Villiers, M. (2008). ICMI study 19: Proof and proving in mathematics education.
ZDM, 40, 329–336.
CrossRefHatano, G., & Inagaki, K. (1986). Two courses of expertise. In H. William Stevenson, & K. H. Hiroshi Azuma (Eds.), Child development and education in Japan (pp. 262–272). San Francisco, CA: W. H. Freeman.
Hersh, R. (1993). Proving is convincing and explaining.
Educational Studies in Mathematics, 24(4), 389–399.
CrossRefInglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification.
Educational Studies in Mathematics, 66, 3–21.
CrossRefLakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press.
Mejia-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 international commission on mathematical instruction study 19, proof and proving in mathematics education (Vol. 2, pp. 88–93). Taipei, Taiwan: The Department of Mathematics, National Taiwan Normal University.
Michener, E. R. (1978). Understanding understanding mathematics.
Cognitive Science, 2, 361–383.
CrossRefNCTM (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.
Papert, S. (1971). On making a theorem for a child. Paper presented at the ACM Annual Conference, Boston, MA.
Papert, S. (1993). The children’s machine: Rethinking school in the age of the computer. New York: Basic Books.
Patel, V. L., & Groen, G. (1991). The specific and general nature of medical expertise: A critical look. In K. A. Ericsson, & J. Smith (Eds.), Toward a general theory of expertise: Prospects and limits. Cambridge, UK: Cambridge University Press.
Rav, Y. (1999). Why do we prove theorems? Philosophia Mathematica, 7(1), 5–41.
Roth, W. M., & Bowen, G. M. (2003). When are graphs worth ten thousand words? An expert–expert study.
Cognition and Instruction, 21(4), 429–473.
CrossRefSchoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
Sierpinska, A. (1994). Understanding in mathematics. Bristol, PA: The Falmer Press, Taylor & Francis Inc.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Stanford, T. (1998).
Found observations of n-triviality and Brunnian links.
http://arxivorg/abs/math/9807161.
Stylianou, D. A., & Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expert-novice similarities and differences.
Mathematical Thinking and Learning, 6(4), 353–387.
CrossRefTall, D. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 65–72). Utrecht, The Netherlands: PME.
Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. Advanced Mathematical Thinking, 11, 65–81.
Watson, A., & Mason, J. (2002). Student-generated examples in the learning of mathematics.
Canadian Journal of Science, Mathematics and Technology Education, 2(2), 237–249.
CrossRefWeber, K., & Alcock, L. (2004). Semantic and syntactic proof productions.
Educational Studies in Mathematics, 56(2/3), 209–234.
CrossRefWilensky, U. (1991). Abstract meditations on the concrete and concrete implications for mathematics education. In I. Harel, & S. Papert (Eds.), Constructionism (pp. 193–203). Norwood, NJ: Ablex.
Wilensky, U. (1993). Connected mathematics: Building concrete relationships with mathematical knowledge. Ph.D. thesis, MIT.
Wineburg, S. (1997). Reading Abraham Lincoln: An expert/expert study in the interpretation of historical texts.
Cognitive Science, 22(3), 319–346.
CrossRef