The written and oral justifications of mathematical claims of middle school pre-service teachers

References

• Čadež, T. H., & Kolar, V. M. (2015). Comparison of types of generalisations and problem-solving schemas used to solve a mathematical problem. Educational Studies in Mathematics, 89(2), 283–306. doi: 10.1007/s10649-015-9598-y
   Web of Science ®Google Scholar
• Ernest, P. (1997). The legacy of Lakatos: Reconceptualising the philosophy of mathematics. Philosophia Mathematica, 5, 116–134. doi: 10.1093/philmat/5.2.116
   Google Scholar
• Evens, H., & Houssart, J. (2004). Categorizing pupils’ written answers to a mathematics test question: ‘I know but I can’t explain’. Educational Research, 46(3), 269–282. doi: 10.1080/0013188042000277331
   Web of Science ®Google Scholar
• Forman, E. A., Larreamendy, J., Steins, M. K., & Brown, C. A. (1998). “You’re going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527–548. doi: 10.1016/S0959-4752(98)00033-4
   Web of Science ®Google Scholar
• Giannakoulias, E., Mastorides, E., Potari, D., & Zachariades, T. (2010). Studying teachers’ mathematical argumentation in the context of refuting students’ invalid claims. The Journal of Mathematical Behavior, 29, 160–168. doi: 10.1016/j.jmathb.2010.07.001
   Google Scholar
• González, G., & Herbst, P. (2013). An oral proof in a geometry class: How linguistic tools can help map the content of a proof. Cognition and Instruction, 31(3), 271–313. doi: 10.1080/07370008.2013.799166
   Web of Science ®Google Scholar
• Hanna, G. (1989). Proofs that prove and proofs that explain. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the thirteenth conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 45–51). The International Group for the Psychology of Mathematics Education.
   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
• 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
   Web of Science ®Google Scholar
• Hollebrands, K. F., Conner, A., & Smith, R. C. (2010). The nature of arguments provided by college geometry students with access to technology while solving problems. Journal for Research in Mathematics Education, 41(4), 324–350. doi: 10.5951/jresematheduc.41.4.0324
   Web of Science ®Google Scholar
• Inglis, M., Mejía-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3–21. doi: 10.1007/s10649-006-9059-8
   Google Scholar
• Knuth, E. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379–405. doi: 10.2307/4149959
   Web of Science ®Google Scholar
• Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63. doi: 10.3102/00028312027001029
   Web of Science ®Google Scholar
• Martin, G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41–51. doi: 10.2307/749097
   Web of Science ®Google Scholar
• Moore-Russo, D., Conner, A., & Rugg, K. I. (2011). Can slope be negative in 3-space? Studying concept image of slope through collective definition construction. Educational Studies in Mathematics, 76(1), 3–21. doi: 10.1007/s10649-010-9277-y
   Web of Science ®Google Scholar
• Morris, A. K. (2002). Mathematical reasoning: Adults’ ability to make the inductive-deductive distinction. Cognition and Instruction, 20(1), 79–118. doi: 10.1207/S1532690XCI2001_4
   Web of Science ®Google Scholar
• Mullis, I. V. S., & Martin, M. O. (eds.). (2017). TIMSS 2019: Assessment frameworks. Boston, MA: International Association for the Evaluation of Educational Achievement.
   Google Scholar
• Nardi, E., Biza, I., & Zachariades, T. (2012). ‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79(2), 157–173. doi: 10.1007/s10649-011-9345-y
   Web of Science ®Google Scholar
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
   Google Scholar
• National Governors Association Center for Best Practices, Council of Chief State School Officers [NGAC]. (2010). Common core state standards for mathematics. Washington, DC: Author.
   Google Scholar
• Nunokawa, K. (2010). Proof, mathematical problem-solving, and explanation in mathematics teaching. In G. Hanna, H. Jahnke, & H. Pulte (Eds.), Explanation and proof in mathematics: Philosophical and educational perspectives (pp. 223–236). New York, NY: Springer.
   Google Scholar
• O’Halloran, K. L. (2005). Mathematical discourse: Language, symbolism and visual images. London: Continuum.
   Google Scholar
• Pedemonte, B., & Balacheff, N. (2016). Establishing links between conceptions, argumentation and proof through the ck¢-enriched Toulmin model. The Journal of Mathematical Behavior, 41, 104–122. doi: 10.1016/j.jmathb.2015.10.008
   Web of Science ®Google Scholar
• Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15(1), 3–31. doi: 10.1016/S0732-3123(96)90036-X
   Google Scholar
• Simpson, A. (2015). The anatomy of a mathematical proof: Implications for analysis with Toulmin’s scheme. Educational Studies in Mathematics, 90(1), 1–17. doi: 10.1007/s10649-015-9616-0
   Web of Science ®Google Scholar
• Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40(3), 314–352.
   Web of Science ®Google Scholar
• Toulmin, S. E. (1958). The uses of argument. Cambridge: Cambridge University Press.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• Weber, K., & Alcock, L. (2005). Using warranted implications to understand and validate proofs. For the Learning of Mathematics, 25(1), 34–38.
   Google Scholar
• Whitenack, J. W., Cavey, L. O., & Ellington, A. J. (2014). The role of framing in productive classroom discussion: A case for teacher learning. The Journal of Mathematical Behavior, 33, 42–55. doi: 10.1016/j.jmathb.2013.09.003
   Google Scholar
• Whitenack, J. W., & Knipping, N. (2002). Argumentation, instructional design theory and students’ mathematical learning: A case for coordinating interpretive lenses. The Journal of Mathematical Behavior, 21, 441–457. doi: 10.1016/S0732-3123(02)00144-X
   Google Scholar
• Yackel, E. (2001). Explanation, justification and argumentation in mathematics classrooms. In M. van den Heuvel-Panhuizen (Ed.), Proceeding of the conference of the international group of for the psychology of mathematics education (Vol. 1, pp. 9–24). Utrecht: PME.
   Google Scholar