Students' beliefs on empirical arguments and mathematical proof in an introduction to proof class

References

• Bieda, K. N., & Lepak, J. (2014). Are you convinced? Middle-grade students’ evaluations of mathematical arguments. School Science and Mathematics, 114(4), 166–177. doi:10.1111/ssm.12066
   Google Scholar
• Brown, S. (2014). On skepticism and its role in the development of proof in the classroom. Educational Studies in Mathematics, 86(3), 311–335. doi:10.1007/s10649-014-9544-4
   Web of Science ®Google Scholar
• Chazan, D. (1993). High school geometry students’ justifications for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359–387. doi:10.1007/BF01273371
   Google Scholar
• Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. CBMS Research in Collegiate Mathematics Education. III, 7, 234–283.
   Google Scholar
• Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Second Handbook of Research on Mathematics Teaching and Learning, 2, 805–842.
   Google Scholar
• Healy, L., & Hoyles, C. (2000). A study of proof concepts in algebra. Journal for Research in Mathematics Education, 31(4), 396–428. doi:10.2307/749651
   Web of Science ®Google Scholar
• Iannone, P., & Inglis, M. (2010). Undergraduate students’ use of deductive arguments to solve “prove that … ” tasks. Proceedings of the 7th congress of the European society for Research in Mathematics education.
   Google Scholar
• Knuth, E., 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). Routledge.
   Google Scholar
• Knuth, E. J. (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
• 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), 591–608. doi:10.1007/s10763-006-9039-6
   Google Scholar
• Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41–51. doi:10.5951/jresematheduc.20.1.0041
   Web of Science ®Google Scholar
• Miller, D., & CadwalladerOlsker, T. (2020). Investigating undergraduate students’ view of and consistency in choosing empirical and deductive arguments. Research in Mathematics Education, 22(3), 249–264. doi:10.1080/14794802.2019.1677489
   Web of Science ®Google Scholar
• Moore, R. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266. doi:10/1007/BF01273731
   Google Scholar
• Raman, M. (2003). Key ideas: What are they and how can they help US understand how people view proof? Educational Studies in Mathematics, 52(3), 319–325. doi:10.1023/A:1024360204239
   Google Scholar
• Recio, A., & Godino, J. (2001). Institutional and personal meanings of mathematical proof. Educational Studies in Mathematics, 48(1), 83–99. doi:10/1023/A:1015553100103
   Google Scholar
• Rowland, T. (2002). Generic proofs in number theory. Learning and Teaching Number Theory: Research in Cognition and Instruction, 157–183.
   Google Scholar
• Samkoff, A., Lai, Y., & Weber, K. (2012). On the different ways that mathematicians use diagrams in proof construction. Research in Mathematics Education, 14(1), 49–67. doi:10/1080/14794802.2012.657438
   Google Scholar
• Sankey Diagram. (2022, March 14). In Wikipedia. https://en.wikipedia.org/wiki/Sankey_diagram.
   Google Scholar
• 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(1), 4–36. doi:10.2307/30034698
   Web of Science ®Google Scholar
• 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
   Google Scholar
• Sowder, L., & Harel, G. (2003). Case studies of mathematics majors’ proof understanding, production, and appreciation. Canadian Journal of Math, Science & Technology Education, 3(2), 251–267. doi:10/1080/14926150309556563
   Google Scholar
• Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40, 314–352. doi:10.5951/jresematheduc.40.3.0314
   Web of Science ®Google Scholar
• Stylianou, D., Blanton, M., & Rotou, O. (2015). Undergraduate students’ understanding of proof: Relationships between proof conceptions, beliefs, and classroom experiences with learning proof. International Journal of Research in Undergraduate Mathematics Education, 1, 91–134. doi:10.1007/s40753-015-0003-0
   Google Scholar
• Thurston, W. P. (1995). On proof and progress in mathematics. For the Learning of Mathematics, 15(1), 29–37.
   Google Scholar
• Weber, K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course. The Journal of Mathematical Behavior, 23(2), 115–133. doi:10/1016/j.mathb.2004.03.001
   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., & Czocher, J. (2019). On mathematicians’ disagreements on what constitutes a proof. Research in Mathematics Education, 21(3), 251–270. doi:10/1080/14794802.2019.1585936
   Web of Science ®Google Scholar
• Weber, K., Inglis, M., & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49(1), 36–58. doi:10/1080/00461520.2013.865527
   Web of Science ®Google Scholar
• Weber, K., Lew, K., & Mejia-Ramos, P. (2020). Using expectancy value theory to account for individuals’ mathematical justification. Cognition and Instruction, 38(1), 27–56. doi:10.1080/07370008.2019.1636796
   Web of Science ®Google Scholar
• Weber, K., & Mejia-Ramos, P. (2014). Mathematics major’s beliefs about proof reading. International Journal of Mathematical Education in Science and Technology, 45(1), 89–103. doi:10.1080/0020739X.2013.790514
   Google Scholar