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Articles

Using Expectancy Value Theory to Account for Individuals’ Mathematical Justifications

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References

  • Alcock, L., Hodds, M., Roy, S. & Inglis, M. (2015). Investigating and improving undergraduate proof comprehension. Notices of the American Mathematical Society, 62, 742–752. doi:10.1090/noti1263
  • Alcock, L., & Weber, K. (2005). Proof validation in real analysis: Inferring and checking warrants. The Journal of Mathematical Behavior, 24(2), 125–134. doi:10.1016/j.jmathb.2005.03.003
  • Balacheff, N. (1987). Processus de preuves et situations de validation. Educational Studies in Mathematics, 18(2), 147–176. doi:10.1007/BF00314724
  • Bandura, A. (1997). Self efficacy: The exercise of control. New York, NY: Freeman.
  • Bell, A. (1976). A study of pupil’s proof-explanations in mathematical situations. Educational Studies in Mathematics, 7, 23–40. doi:10.1007/BF00144356
  • Bell, E. (2000). The queen of mathematics. In J. Newman (Ed.), The world of mathematics (Vol. 3, pp. 498–520). Mineola, NY: Dover Publications.
  • Bieda, K. & Lepak, J. (2014). Are you convinced? Middle school students’ evaluation of mathematical arguments. School Science and Mathematics, 114, 166–177. doi:10.1111/ssm.12066
  • Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. doi:10.1191/1478088706qp063oa
  • Brown, S. (2014). On skepticism and its role in the development of proof in the classroom. Educational Studies in Mathematics, 86, 311–335. doi:10.1007/s10649-014-9544-4
  • Buchbinder, O., & Zaslavsky, O. (2007). How to decide? Students’ ways of determining the validity of mathematical statements. In D. Pita-Fantasy & G. Philippot (Eds.), Proceedings of the 5th congress of the European society for research in mathematics education (pp. 561–571). Larnaca, Cyprus: University of Cyprus.
  • Common Core Content Standards Initiative. (2012). Common Core State Standards initiative: Standards for mathematical practice. Downloaded from http://www.corestandards.org/Math/Practice.
  • Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24, 359–387. doi:10.1007/BF01273371
  • Cobb, P. (1990). A constructivist perspective on information-processing theories of mathematical activity. International Journal of Educational Research, 14(1), 67–92. doi:10.1016/0883-0355(90)90017-3
  • Coe, R. & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20, 41–53. doi:10.1080/0141192940200105
  • Conradie, J., & Frith, J. (2000). Comprehension tests in mathematics. Educational Studies in Mathematics, 42, 225–235. doi:10.1023/A:1017502919000
  • Davis, P. and Hersh, R. (1981). The mathematical experience. New York, NY: Viking Penguin Inc.
  • Department for Education. (2013). Mathematics: Programmes of study: Key Stages 1-2 (National Curriculum in England). Retrieved from https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239129/PRIMARY_national_curriculum_-_Mathematics.pdf.
  • Engle, R. A., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399–483. doi:10.1207/S1532690XCI2004_1
  • Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual review of psychology, 53(1), 109–132. doi:10.1146/annurev.psych.53.100901.135153
  • Fischbein, E. (1982). Intuition and proof. For the Learning of Mathematics, 3(2), 9–18.
  • Fischbein, E., & Kedem, I. (1982). Proof and certitude in the development of mathematical thinking. In A. Vermandel (Ed.), Proceedings of the 6th International Conference of the Psychology of Mathematics Education (pp. 128–131). Antwerp, Belgium: Universitaire Instelling Antwerpen.
  • Franklin, J. (2013). Non-deductive logic in mathematics: the probability of conjectures. In A. Aberdein and I. Dove (Eds.), The argument of mathematics (pp. 11–29). Dordrecht, Netherlands: Springer.
  • Harel, G. (1998). Two dual assertions: The first on learning and the second on teaching (or vice versa). The American Mathematical Monthly, 105, 497–507. doi:10.1080/00029890.1998.12004918
  • Harel, G. (2001). 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). Dordrecht, The Netherlands: Kluwer.
  • 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.
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805–842). Greenwich, CT: Information Age Publishing.
  • Healy, L., & Hoyles, C. (2000). Proof conceptions in algebra. Journal for Research in Mathematics Education, 31, 396–428. doi:10.2307/749651
  • Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389–399. doi:10.1007/BF01273372
  • Iannone, P., & Inglis, M. (2010). Self-efficacy and mathematical proof: Are undergraduates good at assessing their own proof production ability? Proceedings of the 13th conference for research in undergraduate mathematics education, Raleigh, NC.
  • Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66, 3–21. doi:10.1007/s10649-006-9059-8
  • Knuth, E. J., Choppin, J., & Bieda, K. (2009). Middle school students’ productions of mathematical justification. In M. Blanton, D. Stylianou, & E. Knuth (Eds.) Teaching and learning proof across the grades: A K-16 perspective (pp. 153–170). New York, NY: Routledge.
  • Knuth, E. J., Choppin, J., Slaughter, M., & Sutherland, J. (2002). Mapping the conceptual terrain of middle school students’ competencies in justifying and proving. In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Weigel, R. L. Bryant, & K. Nooney (Eds.), Proceedings of the 24th annual meeting of the North American chapter of the international group for the psychology of mathematics education (Vol. 4, pp. 1693–1670). Athens, GA: Clearinghouse for Science, Mathematics, and Environmental Education.
  • Ko, Y. Y., & Knuth, E. J. (2013). Validating proofs and counterexamples across content domains: Practices of importance for mathematics majors. The Journal of Mathematical Behavior, 32(1), 20–35. doi:10.1016/j.jmathb.2012.09.003
  • 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, 29–63. doi:10.3102/00028312027001029
  • Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41–51.
  • Mason, J., (with Burton, L., & Stacey, K.). (1982). Thinking mathematically. London, UK: Addison-Wesley.
  • Mejia-Ramos, J. P. & Weber, K. (2014). How and why mathematicians read proofs: Further evidence from a survey study. Educational Studies in Mathematics, 85, 161–173. doi:10.1007/s10649-013-9514-2
  • 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
  • Morris, A. K. (2007). Factors affecting pre-service teachers’ evaluations of the validity of students’ mathematical arguments in classroom contexts. Cognition and Instruction, 25(4), 479–522. doi:10.1080/07370000701632405
  • Müller-Hill, E. (2010). Die epistemische Rolle formalisierbarer mathematischer Beweise. Formalisierbarkeitsbasierte Konzeptionen mathemaischen Wissens und mathematischen Rechtfertigung innerhalb einer sozioempirisch informierten Erkenntnistheorie der Mathematik (Unpublished doctoral dissertation). Rheinische Friedrich-Wilhelms-Universitat Bonn, Bonn, Germany.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Nova (1997). The proof. Transcript downloaded from http://www.pbs.org/wgbh/nova/transcripts/2414proof.html.
  • Polya, G. (1957). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.
  • Recio, A. M., & Godino, J. D. (2001). Institutional and personal meanings of mathematical proof. Educational Studies in Mathematics, 48, 83–99. doi:10.1023/A:1015553100103
  • Rowland, T. (2001). Generic proofs in number theory. In S. Campbell & R. Zaskis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 157–183). New Jersey: Ablex Publishing Corporation.
  • Schoenfeld, A. H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55–80. doi:10.1016/0732-3123(94)90035-3
  • Segal, J. (1999). Learning about mathematical proof: Conviction and validity. The Journal of Mathematical Behavior, 18(2), 191–210. doi:10.1016/S0732-3123(99)00028-0
  • Selden, J., & Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29(2), 123–151.
  • Selden, A., & Selden, J. (2003). Validations of proofs written as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 36(1), 4–36. doi:10.2307/30034698
  • Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4–13. doi:10.3102/0013189X027002004
  • Sowder, L., & Harel, G. (2003). Case studies of mathematics majors’ proof understanding, construction, and appreciation. Canadian Journal of Science, Mathematics and Technology Education, 3, 251–267. doi:10.1080/14926150309556563
  • Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38, 289–321.
  • Stylianides, A. J., & Al-Murani, T. (2010). Can a proof and a counterexample coexist? Students’ conceptions about the relationship between proof and refutation. Research in Mathematics Education, 12(1), 21–36. doi:10.1080/14794800903569774
  • Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237–253.
  • Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40, 314–352.
  • Stylianides, G., Stylianides, A. & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (ed.) Compendium for Research in Mathematics Education (pp. 237–266). Reston, VA: National Council of Teachers of Mathematics.
  • Tapan, M. S., & Arslan, C. (2009). Preservice teachers’ use of spatio-visual elements and their level of justification dealing with a geometrical construction problem. US-China Education Review, 6(3), 54–60.
  • Thompson, P. W. (1982). Were lions to speak, we wouldn’t understand. Journal of Mathematical Behavior, 3, 147–165.
  • Volminik, J. (1990). The nature and role of proof in mathematics education. Pythagorus, 23, 7–10.
  • Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119. doi:10.1023/A:1015535614355
  • Weber, K. (2003). Students’ difficulty with proof. In A. Selden and J. Selden (eds.) Research sampler, 8. Available from the following MAA website on the teaching of learning of mathematics: http://www.maa.org/t_and_l/sampler/research_sampler.html
  • Weber, K. (2008a). The role of affect in learning real analysis: A case study. Research in Mathematics Education, 10, 71–85. doi:10.1080/14794800801916598
  • Weber, K. (2008b). How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education, 39, 431–459.
  • 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
  • Weber, K. (2018). The role of sourcing in mathematics. In J. Braasch, I. Bråten, M. McCrudden (Eds.), Handbook of multiple source use (pp. 238 –253). New York, NY: Routledge.
  • Weber, K., Inglis, M. & Mejia-Ramos, J.P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and epistemic cognition. Educational Psychologist, 49, 36–58. doi:10.1080/00461520.2013.865527
  • Weber, K. & Mejía-Ramos, J.P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76(3), 329–344. doi:10.1007/s10649-010-9292-z
  • Weber, K., & Mejia-Ramos, J. P. (2013). On the influence of sources in the reading of mathematical text. Journal of Literacy Research, 45, 87–96. doi:10.1177/1086296X12469968
  • Weber, K. & Mejia-Ramos, J.P. (2015). The contextual nature of conviction in mathematics. For the Learning of Mathematics, 35(2), 9–14.
  • Winicki-Landman, G. (2007). Making possible the discussion of "impossible in mathematics". In Theorems in school (pp. 183 –195). Sense Publishers: Rotterdam.
  • Wu, H. (1996). The mathematician and the mathematics education reform. Notices of the American Mathematical Society, 43(12), 1531–1537.

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