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Articles

Proof schemes of pre-service middle and secondary mathematics teachers

References

  • Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L. I. Tatsien (Ed.), Proceedings of the International Congress of Mathematicians (Vol. III, pp. 907–920). Beijing, People’s Republic of China: Higher Education.
  • Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382.
  • Bleiler, S. K., Thompson, D. R., & Krajčevski, M. (2014). Providing written feedback on students’ mathematical arguments: Proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17(2), 105–127. ( published first online). doi:10.1007/s10857-013-9248-1)
  • CadwalladerOlsker, T. (2011). What do we mean by mathematical proof? Journal of Humanistic Mathematics, 1(1), 33–60. doi:10.5642/jhummath
  • De Villiers, M. D. (1999). The role and function of proof with sketchpad. In M. de Villiers (Ed.), Rethinking proof with the Geometer’s Sketchpad, (pp. 3–10). Key Curriculum Press.
  • Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38(1), 85–109. doi:10.1023/A:1003660018579
  • Easterday, K. E., & Galloway, L. L. (1995). A comparison of sentential logic skills: Are teachers sufficiently prepared to teach logic? School Science and Mathematics, 95, 431–436. doi:10.1111/ssm.1995.95.issue-8
  • Ellis, A. (2007). Connections between generalizing and justifying: Students’ reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194.
  • Ellis, A. E., Lockwood, E., Knuth, E., Dogan, M. F., & Williams, C. C. W. (2013). Choosing and using examples: How example activity can support proof insight. In Proceedings of the 37th Annual Meeting of the International Group of the Psychology of Mathematics Education, Kiel, Germany.
  • Harel, G., & Rabin, J. M. (2010a). Teaching practices associated with the authoritative proof scheme. Journal for Research in Mathematics Education, 41(1), 14–19.
  • Harel, G., & Rabin, J. M. (2010b). Teaching practices that can promote the authoritative proof scheme. Canadian Journal of Science, Mathematics and Technology Education, 10(2), 139–159. doi:10.1080/14926151003778282
  • Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. Research in Collegiate Mathematics Education, 3, 234–283.
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. Lester (Ed.), Second handbook of research on mathematics education (pp. 805–842). Charlotte, NC: Information Age Pub Inc.
  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428. doi:10.2307/749651
  • Housman, D., & Porter, M. (2003). Proof schemes and learning strategies of above-average mathematics students. Educational Studies in Mathematics, 53(2), 139–158. doi:10.1023/A:1025541416693
  • Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358–390. doi:10.5951/jresematheduc.43.4.0358
  • Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33, 379–405. doi:10.2307/4149959
  • Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 10(1), 41–51. doi:10.2307/749097
  • Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Thousand Oaks, CA: Sage Publications, Inc.
  • Recio, A. M., & Godino, J. D. (2001). Institutional and personal meanings of mathematical proof. Educational Studies in Mathematics, 48(1), 83–99. doi:10.1023/A:1015553100103
  • Sears, R., Mueller-Hill, E., & Karadeniz, I. (2013, November). Preservice teachers’ perception of their preparation program to cultivate their ability to teach proof. Proceedings of the First Congress on Mathematics Education for Central America and the Caribbean (I CEMACYC), Santo Domingo, Dominican Republic.
  • Sears, R., & Chávez, Ó. (2014). Opportunities to engage with proof: The nature of proof tasks in two geometry textbooks and its influence on enacted lessons. ZDM, 46(5), 767–780.
  • Sears, R., & Chavez, O. (2015, February). Students of two-curriculum types performance on a proof for congruent triangles. Proceedings of the Ninth Congress of European Research in Mathematics Education (CERME 9). Prague, Czech Republic.
  • Selden, J., & Selden, A. (2009). Teaching proving by coordinating aspects of proofs with students’ abilities. In M. Blanton, D. Stylianou, & E. Knuth (Eds.), The learning and teaching of proof across the grades (pp. 339–354). London, UK: Routledge/Taylor & Francis.
  • Senk, S. (1985). How well do students write geometry proofs? Mathematics Teacher, 78(6), 448–456.
  • Steele, M. D., & Rogers, K. C. (2012). Relationships between mathematical knowledge for teaching and teaching practice: The case of proof. Journal of Mathematics Teacher Education, 15(2), 159–180. doi:10.1007/s10857-012-9204-5
  • Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289–321.
  • Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237–253. doi:10.1007/s10649-009-9191-3
  • Usiskin, Z. (1987). Resolving the continuing dilemmas in school geometry (Learning and Teaching Geometry, K-12: 1987 Yearbook, 17-31).
  • Weber, K. (2010). Mathematics majors’ perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12(4), 306–336. doi:10.1080/10986065.2010.495468
  • Zaslavsky, O., Nickerson, S. D., Stylianides, A. J., Kidron, I., & Winicki-Landman, G. (2012). The need for proof and proving: mathematical and pedagogical perspectives. In G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education: The 19th ICMI Study (New ICMI Study Series, vol. 15, pp. 215–229). New York, NY: Springer.

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