586
Views
3
CrossRef citations to date
0
Altmetric
Articles

Proof schemes combined: mapping secondary students’ multi-faceted and evolving first encounters with mathematical proof

, &

References

  • Argyrakis, D., Vourganas, P., Mentis, K., Tsikopoulou, S., & Chryssovergis, M. (2010). Μαθηματικά Γ τάξης Γυμνασίου [Mathematics gymnasium class C]. Athens, Greece: OEDB.
  • Balacheff, N. (1987). Processus de preuve et situations de validation [Proving processes and situations for validation]. Educational Studies in Mathematics, 18(2), 147–176.
  • Biza, I., Nardi, E., & Zachariades, T. (2009). Teacher beliefs and the didactic contract on visualisation. For the Learning of Mathematics, 29(3), 31–36.
  • Csíkos, C. A. (1999). Measuring students’ proving ability by means of Harel and Sowder’s proof-categorization. In O. Zaslavsky (Ed.), Proceedings of the 23rd conference of the international group for the psychology of mathematics education (Vol. 2, pp. 233–240). Haifa, Israel: PME.
  • Hanna, G. (1991). Mathematical proof. In D. Tall (Ed.), Advanced mathematical thinking (pp. 54–61). Dordrecht, The Netherlands: Kluwer Academic Publishers.
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1–3), 5–23.
  • Hanna, G. (2007). The ongoing value of proof. In P. Boero (Ed.), Theorems in school: From history, epistemology, and cognition to classroom practice (pp. 3–16). Rotterdam, The Netherlands: Sense Publishers.
  • Hanna, G., & Barbeau, E. (2008). Proofs as bearers of mathematical knowledge. ZDM the International Journal on Mathematics Education, 40(3), 345–353.
  • Harel, G. (1999). Students’ understanding of proofs: A historical analysis and implications for the teaching of geometry and linear algebra. Linear Algebra and Its Applications, 302–303, 601–613.
  • Harel, G. (2007). Students’ proof schemes revisited. In P. Boero (Ed.), Theorems in school: From history, epistemology, and cognition to classroom practice (pp. 65–78). Rotterdam, The Netherlands: Sense Publishers.
  • Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234–283). Providence, RI: American Mathematical Society.
  • Harel, G., & Sowder, L. (2007). Toward a comprehensive perspective on proof. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805–842). Charlotte, NC: Information Age Publications.
  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428.
  • Heinze, A. (2004). Schülerprobleme beim Lösen von geometrischen Beweisaufgaben-eine Interviewstudie. ZDM the International Journal on Mathematics Education, 36(5), 150–161.
  • Housman, D., & Porter, M. (2003). Proof schemes and learning strategies of above-average mathematics students. Educational Studies in Mathematics, 53(2), 139–158.
  • Kanellos, I. (2014). Secondary students’ proof schemes during the first encounters with formal mathematical reasoning: Appreciation, fluency and readiness (Unpublished doctoral thesis). University of East Anglia, UK. Retrieved from https://ueaeprints.uea.ac.uk/49759/1/2014KanellosIEdD.pdf
  • Kanellos, I., Nardi, E., & Biza, I. (2013). The interplay between fluency and appreciation in secondary students’ first encounter with proof. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th conference of the international group for the psychology of mathematics education (Vol. 5, pp. 84). Kiel, Germany: PME.
  • Küchemann, D., & Hoyles, C. (2006). Influences on students’ mathematical reasoning and patterns in its development: Insights from a longitudinal study with particular reference to geometry. International Journal of Science and Mathematics Education, 4(4), 581–608.
  • Lee, K. (2016). Students’ proof schemes for mathematical proving and disproving of propositions. Journal of Mathematical Behavior, 41, 26–44.
  • Nardi, E., & Knuth, E. (2017). Changing classroom culture, curricula, and instruction for proof and proving: How amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions? Educational Studies in Mathematics, 96(2), 267–274.
  • Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
  • Stylianides, A. J. (2007). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65(1), 1–20.
  • Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2004). Undergraduate students’ understanding of the contraposition equivalence rule in symbolic and verbal contexts. Educational Studies in Mathematics, 55(1–3), 133–162.
  • Stylianides, G. J., & Stylianides, A. J. (2008). Proof in school mathematics: Insights from psychological research into students’ ability for deductive reasoning. Mathematical Thinking and Learning, 10(2), 103–133.
  • Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56(2), 209–234.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.