440
Views
2
CrossRef citations to date
0
Altmetric
Articles

High school mathematics teachers’ content knowledge of the logical structure of proof deriving from figural-concept interaction in geometry

ORCID Icon &
Pages 585-603 | Received 13 May 2019, Published online: 17 Apr 2020

References

  • Alcock, L., & Weber, K. (2005). Proof validation in real analysis: Inferring and checking warrants. The Journal of Mathematical Behavior, 24, 125–134. https://doi.org/10.1016/j.jmathb.2005.03.003
  • Baker, D., & Campbell, C. (2004). Fostering the development of mathematical thinking: Observations from a proofs course. Primus, 14(4), 345–353. https://doi.org/10.1080/10511970408984098
  • Ball, D., Hill, H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(3), 14–22. 43–46.
  • Bradis, V. M., Minkovskii, V. L., & Kharcheva, A. K. (1999). Lapses in mathematical reasoning. Dover.
  • Cohen, L., & Manion, L. (1994). Research method in education (4th ed.). Routledge.
  • Creswell, J. W. (2009). Research design: Qualitative, quantitative and mixed methods approaches. Sage Publications.
  • Dreyfus, T., & Hadas, N. (1987). Euclid may stay and even be taught. In M. M. Lindquist & A. P. Shulte (Eds.), Learning and teaching geometry, K-12 (pp. 47–58). National Council of Teachers of Mathematics.
  • Durand-Guerrier, V., Boero, P., Douek, N., Epp, S. S., & Tanguay, D. (2012). Examining the role of logic in teaching proof. In G. Hanna, & M. de Villiers (Eds.), Proof and proving in mathematics education: The ICMI study (pp. 369–389). Springer.
  • Duval, R. (2007). Cognitive functioning and the understanding of mathematical processes of proof. In P. Boero (Ed.), Theorems in school: From history, epistemology, and cognition to classroom practice (pp. 137–161). Sense Publishers.
  • Epp, S. S. (2003). The role of logic in teaching proof. The American Mathematical Monthly, 110(10), 886–899. https://doi.org/10.1080/00029890.2003.11920029
  • Fetisov, A. I. ([1954] (2012)). Proof in geometry. Bound with Y. S. Dubnov: [1955] Mistakes in Geometric Proofs. Mineola, NY: Dover.
  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139–162. https://doi.org/10.1007/BF01273689
  • Fischbein, E., & Kedem, I. (1982). Proof and certitude in the development of mathematics thinking. In A. Vermandel (Ed.), Proceedings of the sixth international conference for the psychology of mathematics education (pp. 128–131). Universitaire Installing Antwerpen.
  • Fischbein, E., & Nachlieli, T. (1998). Concepts and figures in geometrical reasoning. International Journal of Science Education, 20(10), 1193–1211. https://doi.org/10.1080/0950069980201003
  • Harel, G. (2002). The development of mathematical induction as a proof scheme: A model for DNR-based instruction. In S. Campbell & R. Zaskis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 185–212). Ablex.
  • 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). NCTM.
  • Jones, K. (1997). Student-teachers’ conceptions of mathematical proof. Mathematics Education Review, 9, 21–32.
  • Knuth, E. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379–405. https://doi.org/10.2307/4149959
  • Ma, L. (1999). Knowing and teaching elementary mathematics. Lawrence Erlbaum.
  • Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20, 41–51. https://doi.org/10.2307/749097
  • Martinez, M. V., & Pedemonte, B. (2014). Relationship between inductive arithmetic argumentation and deductive algebraic proof. Educational Studies in Mathematics, 86(1), 125–149. https://doi.org/10.1007/s10649-013-9530-2
  • McCrone, S. S., & Martin, T. S. (2004). Assessing high school students’ understanding of geometric proof. Canadian Journal of Science, Mathematics and Technology Education, 4(2), 223–242. https://doi.org/10.1080/14926150409556607
  • Ministry of National Education, Republic of Turkey (MoNE). (2013). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı [Republic of Turkey, Ministry of National Education secondary school mathematics curriculum (9, 10, 11 and 12. grades].
  • Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223–239. https://doi.org/10.1007/s10649-016-9720-9
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.
  • 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, 4–36. http://www.nctm.org/publications/jrme.aspx https://doi.org/10.2307/30034698
  • Selden, A., & Selden, J. (2008). Overcoming students’ difficulties in learning to understand and construct proofs. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp. 95–110). Mathematical Association of America.
  • Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15, 3–31. https://doi.org/10.1016/S0732-3123(96)90036-X
  • Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11, 307–332. https://doi.org/10.1007/s10857-008-9077-9 https://doi.org/10.1007/s10857-008-9077-9
  • 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. https://doi.org/10.1080/10986060701854425
  • 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, 133–162. https://doi.org/10.1023/B:EDUC.0000017671.47700.0b
  • Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10, 145–166. https://doi.org/10.1007/s10857-007-9034-z
  • Ubuz, B., & Yayan, B. (2010). Primary teachers’ subject matter knowledge: Decimals. International Journal of Mathematical Education in Science and Technology, 41(6), 787–804. https://doi.org/10.1080/00207391003777871
  • Weber, K. (2010). Mathematics majors’ perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12, 306–336. https://doi.org/10.1080/10986065.2010.495468
  • Yildirim, A., & Simsek, H. (2005). Qualitative research methods in the social sciences. Ankara: Seçkin Yayıncılık.

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.