Why research on proof-oriented mathematical behavior should attend to the role of particular mathematical content
Tài liệu tham khảo
Alcock, 2008, Doctoral students’ use of examples in evaluating and proving conjectures, Educational Studies in Mathematics, 69, 111, 10.1007/s10649-008-9149-x
Alcock, 2002, Definitions: Dealing with categories mathematically, For the Learning of Mathematics, 22, 28
Alcock, 2004, Convergence of sequences and series: Interactions between visual reasoning and learner’s beliefs about their own role, Educational Studies in Mathematics, 57, 1, 10.1023/B:EDUC.0000047051.07646.92
Antonini, 2003, Non-examples and proof by contradiction, vol. 2, 49
Dawkins, 2015, Guiding reinvention of conventional tools of mathematical logic: Students’ reasoning about mathematical disjunctions
Dawkins, 2012, Extensions of the semantic/syntactic reasoning framework, For the Learning of Mathematics, 32, 39
Dawkins, P. C., 2014. Disambiguating research on logic as it pertains to advanced mathematical practice. In:T. Fukawa-Connelly, G., Karakok, K. Keene, M. Zandieh (Eds.), Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education, Denver, Colorado
Dawkins, 2015, Explication as a lens for the formalization of mathematical theory through guided reinvention, The Journal of Mathematical Behavior, 37, 63, 10.1016/j.jmathb.2014.11.002
Epp, 2003, The role of logic in teaching proof, The American Mathematical Monthly, 110, 886, 10.2307/3647960
Firestone, 1993, Alternative arguments for generalizing from data as applied to qualitative research, Educational Researcher, 22, 16, 10.3102/0013189X022004016
Hanna, 2000, Proof, explanation and exploration: An overview, Educational Studies in Mathematics, 44, 5, 10.1023/A:1012737223465
Inglis, 2007, Modeling mathematical argumentation: The importance of qualification, Educational Studies in Mathematics, 66, 3, 10.1007/s10649-006-9059-8
Karunakaran, 2014
Mariotti, 1997, Approaching geometry theorems in contexts: From history and epistemology to cognition, vol. 1, 180
Mejia-Ramos, 2015, Factors influencing students’ propensity for semantic and syntactic reasoning in proof writing: A case study, International Journal for Research in Undergraduate Mathematics Education, 1, 187, 10.1007/s40753-015-0014-x
National Council of Teacher of Mathematics, Principles and standards for school mathematics, 2000, Author, Reston, VA.
Oaksford, 2002, Commonsense reasoning, logic, and human rationality, 174
Ouvrier-Buffet, 2011, A mathematical experience involving defining processes: In-action definitions and zero-definitions, Educational Studies in Mathematics, 76, 165, 10.1007/s10649-010-9272-3
Piaget, 1950
Raman, 2009, Is that a proof? Using video to teach and learn how to prove at the university level, vol. 2, 154
Reid, 2010, Proof in mathematics education
Reid, 2011, Understanding proof and transforming teaching, 15
Sandefur, 2013, Generating and using examples in the proving process, Educational Studies in Mathematics, 83, 323, 10.1007/s10649-012-9459-x
Selden, 1995, Unpacking the logic of mathematical statements, Educational Studies in Mathematics, 29, 123, 10.1007/BF01274210
Sowder, 2003, Case studies of mathematics majors’ proof understanding, production, and appreciation, Canadian Journal of Math, Science & Technology Education, 3, 251, 10.1080/14926150309556563
Stylianides, 2009, Proof constructions and evaluations, Educational Studies in Mathematics, 72, 237, 10.1007/s10649-009-9191-3
Stylianides, 2016, Research on the teaching and learning of proof: Taking stock and moving forward
Stylianou, 2014, 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, 10.1007/s40753-015-0003-0
Thompson, 2013, In the absence of meaning
Toulmin, 1958
Yin, 2014
Zandieh, 2006, Exploring the role of metonymy in mathematical understanding and reasoning: The concept of derivative as an example, The Journal of Mathematical Behavior, 25, 1, 10.1016/j.jmathb.2005.11.002
Zandieh, 2014, Conceptual blending: Student reasoning when proving conditional implies conditional statements, Journal of Mathematical Behavior, 33, 209, 10.1016/j.jmathb.2013.11.007