On the sophistication of naïve empirical reasoning: factors influencing mathematicians' persuasion ratings of empirical arguments

References

• Aberdein , A. 2007 . Fallacies in mathematics . Proceedings of the British Society for Research into Learning Mathematics 27 , no. 3 : 1 – 6 .
   Google Scholar
• Balacheff , N. 1987 . Processus de preuves et situations de validation . Educational Studies in Mathematics 18 : 147 – 76 doi: 10.1007/BF00314724
   Google Scholar
• Ball , J. , and M. Sanz-Sole . 2007 . Are pure and applied mathematics drifting apart? In Proceedings of the International Congress of Mathematicians, Spain 2006 , 757 – 76 . Madrid , , Spain : European Society of Mathematics .
   Google Scholar
• Borwein , J. 2008 . Implications of experimental mathematics for the philosophy of mathematics . Proofs and other dilemmas: Mathematics and philosophy , B. Gold and R. Simons , 33 – 60 . Washington , DC : MAA .
   Google Scholar
• Buldt , B. , B. Loewe , and T. Muller . 2008 . Towards a new epistemology of mathematics . Erkenntis , 68 , 309 – 29 doi: 10.1007/s10670-008-9101-6
   Web of Science ®Google Scholar
• de Villiers , M. 2004 . The role and function of quasi-empirical methods in mathematics . Canadian Journal of Science, Mathematics, and Technology Education 4 : 397 – 418 doi: 10.1080/14926150409556621
   Google Scholar
• Echeverria , J. 1996 . Empirical methods in mathematics. A case study: Goldbach's Conjecture . Spanish studies in the philosophy of science , G. Munevar , 19 – 56 . Dordrecht : Kluwer .
   Google Scholar
• Good , I.J. 1960 . The paradox of confirmation . The British Journal for the Philosophy of Science 42 : 145 – 9 .
   Google Scholar
• Harel , G. 2001 . The development of mathematical induction as a proof scheme: A model for DNR-based instruction . In Learning and teaching number theory , S. Campbell and R. Zazkis , 185 – 212 . New Jersey : Ablex Publishing Company .
   Google Scholar
• Harel , G. , and L. Sowder . 1998 . Students proof schemes . Research in Collegiate Mathematics Education 3 : 234 – 82 .
   Google Scholar
• Hempel , C.G. 1945a . Studies in the logic of confirmation (I) . Mind 54 : 1 – 26 doi: 10.1093/mind/LIV.213.1
   Google Scholar
• Hempel , C.G. 1945b . Studies in the logic of confirmation (II) . Mind 54 : 97 – 121 doi: 10.1093/mind/LIV.214.97
   Google Scholar
• Hersh , R. 1993 . Proving is convincing and explaining . Educational Studies in Mathematics 24 : 389 – 99 doi: 10.1007/BF01273372
   Google Scholar
• Inglis , M. , and L. Alcock . 2012 . Expert and novice approaches to reading mathematical proofs . Journal for Research in Mathematics Education 43 : 358 – 90 doi: 10.5951/jresematheduc.43.4.0358
   Web of Science ®Google Scholar
• Inglis , M. , and J.P. Mejia-Ramos . 2009 . The effect of authority on the persuasiveness of mathematical arguments . Cognition and Instruction 27 : 25 – 50 doi: 10.1080/07370000802584513
   Web of Science ®Google Scholar
• Inglis , M. , J.P. Mejia-Ramos , K. Weber , and L. Alcock . 2013 . On mathematicians' different standards when evaluating elementary proofs . Topics in Cognitive Science 5 : 270 – 282 .
   PubMed Web of Science ®Google Scholar
• National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics . Reston , VA : NCTM .
   Google Scholar
• Oaksford , M. , and N. Chater . 1994 . A rational analysis of the selection task as optimal data selection . Psychological Review 101 : 608 – 31 doi: 10.1037/0033-295X.101.4.608
   Web of Science ®Google Scholar
• Paseau , A. 2011 . Mathematical instrumentalism, Godel's theorem, and inductive evidence . Studies in History and Philosophy of Science 42 : 140 – 9 doi: 10.1016/j.shpsa.2010.11.030
   Web of Science ®Google Scholar
• Recio , A.M. , and J.D. Godino . 2001 . Institutional and personal meanings of proof . Educational Studies in Mathematics 48 : 83 – 99 doi: 10.1023/A:1015553100103
   Google Scholar
• Rota , G.-C. 1991 . The concept of mathematical truth . Review of Metaphysics 44 : 483 – 494 . Boston : Birkhauser .
   Google Scholar
• Rowland , E. 2008 . A natural prime-generating recurrence . Journal of Integer Sequences 11 : 1 – 11 .
   Google Scholar
• Segal , J. 2000 . Learning about mathematical proof: Conviction and validity . Journal of Mathematical Behavior 18 : 191 – 210 doi: 10.1016/S0732-3123(99)00028-0
   Google Scholar
• Shallit , J. 2008 . Rutgers graduate student finds new prime-generating function . http://recursed.blogspot.com/2008/07/rutgers-graduate-student-finds-new.html .
   Google Scholar
• Weber , K. 2001 . Student difficulties in constructing proofs: The need for strategic knowledge . Educational Studies in Mathematics 48 : 101 – 19 doi: 10.1023/A:1015535614355
   Google Scholar
• Weber , K. 2008 . How mathematicians determine if an argument is a valid proof . Journal for Research in Mathematics Education 39 : 431 – 59 .
   Web of Science ®Google Scholar
• Weber , K. 2010 . Mathematics majors’ perceptions of conviction, validity, and proof . Mathematical Thinking and Learning 12 : 306 – 36 doi: 10.1080/10986065.2010.495468
   Web of Science ®Google Scholar
• Weber , K. , and L. Alcock . 2004 . Semantic and syntactic proof productions . Educational Studies in Mathematics 56 : 209 – 34 doi: 10.1023/B:EDUC.0000040410.57253.a1
   Google Scholar
• Weber , K. , and J.P. Mejia-Ramos . 2011 . How and why mathematicians read proofs: An exploratory study . Educational Studies in Mathematics 76 : 329 – 44 doi: 10.1007/s10649-010-9292-z
   Web of Science ®Google Scholar