Mathematics Majors' Perceptions of Conviction, Validity, and Proof

REFERENCES

• Alcock , L. 2010 . Mathematicians' perceptions on the teaching and learning and proof . Research in Collegiate Mathematics Education , 7 : 63 – 92 .
   Google Scholar
• Alcock , L. and Weber , K. 2005 . Proof validation in real analysis: Inferring and evaluating warrants . Journal of Mathematical Behavior , 24 ( 2 ) : 125 – 134 .
   Google Scholar
• Balacheff , N. 1987 . Processus de preuves et situations de validation . Educational Studies in Mathematics , 18 ( 2 ) : 147 – 176 .
   Google Scholar
• Bell , A. 1976 . A study of pupil's proof-explanations in mathematical situations . Educational Studies in Mathematics , 7 : 23 – 40 .
   Web of Science ®Google Scholar
• Brown , J. 1999 . Philosophy of mathematics: A contemporary introduction into the world of proof and pictures , New York, NY : Routledge .
   Google Scholar
• Chazan , D. 1993 . High school geometry students' justifications for their views of empirical evidence and mathematical proof . Educational Studies in Mathematics , 24 : 359 – 387 .
   Google Scholar
• Coe , R. and Ruthven , K. 1994 . Proof practices and constructs of advanced mathematics students . British Educational Research Journal , 20 : 41 – 53 .
   Google Scholar
• de Villiers , M. 1990 . The role and function of proof in mathematics . Pythagoras , 24 : 17 – 24 .
   Google Scholar
• Dreyfus , T. 1991 . “ Advanced mathematical thinking processes ” . In Advanced Mathematical Thinking , Edited by: Tall , D. 25 – 41 . Dordrecht, , The Netherlands : Kluwer .
   Google Scholar
• Dreyfus , T. 1999 . Why Johnny can't prove . Educational Studies in Mathematics , 38 : 85 – 109 .
   Google Scholar
• Eisenberg , T. and Dreyfus , T. 1991 . “ On the reluctance to visualize in mathematics ” . In Visualization in teaching and learning mathematics , Edited by: Zimmerman , W. and Cunningham , S. Washington, D.C : The Mathematical Association of America .
   Google Scholar
• Ericsson , K. A. and Simon , H. A. 1993 . Protocol analysis: Verbal reports as data , 2nd , Cambridge, MA : Bradford Books/MIT Press .
   Google Scholar
• Fischbein , E. 1982 . Intuition and proof . For the Learning of Mathematics , 3 ( 2 ) : 9 – 18 .
   Google Scholar
• Giaquinto , M. 2007 . Visual thinking in mathematics: An epistemological study , Oxford : Oxford University Press .
   Google Scholar
• Hanna , G. 1991 . “ Mathematical proof ” . In Advanced mathematical thinking , Edited by: Tall , D. Dordrecht, , The Netherlands : Kluwer .
   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 , Edited by: Campbell , S. and Zazkis , R. 185 – 212 . Mahwah, NJ : Erlbaum .
   Google Scholar
• Harel , G. and Sowder , L. 1998 . Students proof schemes . Research in Collegiate Mathematics Education , 3 : 234 – 282 .
   Google Scholar
• Harel , G. and Sowder , L. 2007 . “ Towards a comprehensive perspective on proof ” . In Second handbook of research on mathematical teaching and learning , Edited by: Lester , F. Washington, D.C : NCTM .
   Google Scholar
• Hazzan , O. and Zazkis , R. 2003 . Mimicry of proofs with computers: The case of linear algebra . International Journal of Mathematics Education in Science and Technology , 34 : 385 – 402 .
   Google Scholar
• Healy , L. and Hoyles , C. 2000 . A study of proof conceptions in algebra . Journal for Research in Mathematics Education , 31 : 396 – 428 .
   Web of Science ®Google Scholar
• Hemmi, K. (2006). Approaching proof in a community of mathematical practice. Doctoral dissertation. Stockholm University, Stockholm, Sweden. Retrieved from http://fou.skolporten.com/art.aspx?id=a0A20000000DOi7EAG& typ=art (http://fou.skolporten.com/art.aspx?id=a0A20000000DOi7EAG& typ=art)
   Google Scholar
• Herbst , P. 2004 . Interactions with diagrams and the making of reasoned conjectures in geometry . ZDM , 36 ( 5 ) : 129 – 139 .
   Google Scholar
• Hoyles , C. and Healy , L. 2007 . “ Curriculum change and geometric reasoning ” . In Theorems in School: From history, epistemology, and cognition to classroom practice , Edited by: Boero , P. 81 – 115 . Rotterdam, , The Netherlands : Sense .
   Google Scholar
• Inglis , M. and Mejia-Ramos , J. P. 2009a . The effect of authority on the persuasiveness of mathematical arguments . Cognition and Instruction , 27 : 25 – 50 .
   Web of Science ®Google Scholar
• Inglis , M. and Mejia-Ramos , J. P. 2009b . On the persuasiveness of visual arguments in mathematics . Foundations of Science , 14 : 97 – 110 .
   Web of Science ®Google Scholar
• Knuth , E. 2002 . Secondary school mathematics teachers' conceptions of proof . Journal for Research in Mathematics Education , 33 ( 5 ) : 379 – 405 .
   Web of Science ®Google Scholar
• Knuth , E. , Choppin , J. and Bieda , K. 2009 . “ Middle school students' productions of mathematical justification ” . In Teaching and learning proof across the grades: A K-16 perspective , Edited by: Blanton , M. , Stylianou , D. and Knuth , E. 153 – 212 . NY : Routledge .
   Google Scholar
• Kulpa , Z. 2009 . Main problems of diagrammatic reasoning: Part 1. The generalization problem . To appear Foundations of Science ,
   Google Scholar
• Mamona-Downs , J. and Downs , M. 2005 . The identity of problem solving . Journal of Mathematical Behavior , 24 ( 3/4 ) : 385 – 401 .
   Google Scholar
• Martin , W. G. and Harel , G. 1989 . Proof frames of pre-service elementary teachers . Journal for Research in Mathematics Education , 20 ( 1 ) : 41 – 51 .
   Web of Science ®Google Scholar
• Mason , J. , Burton , L. and Stacey , K. 1981 . Thinking mathematically , London, , UK : Addison Wesley .
   Google Scholar
• Mason , J. and Pimm , D. 1984 . Generic examples: Seeing the generic in the particular . Educational Studies in Mathematics , 15 : 277 – 289 .
   Google Scholar
• Moore , R. C. 1994 . Making the transition to formal proof . Educational Studies in Mathematics , 27 : 249 – 266 .
   Google Scholar
• National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics , Reston, VA : Author .
   Google Scholar
• Nelson , R. 1993 . Proofs without words: Exercises in visual thinking , Washington, DC : The Mathematical Association of America .
   Google Scholar
• Pedemonte , B. 2007 . How can the relationship between argumentation and proof be analysed? . Educational Studies in Mathematics , 66 : 23 – 41 .
   Google Scholar
• Raman , M. 2002 . Proof and justification in collegiate calculus , Berkeley : Unpublished doctoral dissertation. University of California .
   Google Scholar
• Rav , Y. 1999 . Why do we prove theorems? . Philosophia Mathematica , 7 : 5 – 41 .
   Google Scholar
• Recio , A. M. and Godino , J. D. 2001 . Institutional and personal meanings of proof . Educational Studies in Mathematics , 48 ( 1 ) : 83 – 99 .
   Google Scholar
• Rowland , T. 2001 . “ Generic proofs in number theory ” . In Learning and teaching number theory: Research in cognition and instructions , Edited by: Campell , S. and Zazkis , R. 157 – 184 . Westport, CT : Ablex .
   Google Scholar
• Segal , J. 2000 . Learning about mathematical proof: Conviction and validity . Journal of Mathematical Behavior , 18 : 191 – 210 .
   Google Scholar
• Selden , J. , Mason , A. and Selden , A. 1989 . Can average calculus students solve non-routine problems? . Journal of Mathematical Behavior , 8 : 45 – 50 .
   Google Scholar
• Selden , J. and Selden , A. 1995 . Unpacking the logic of mathematical statements . Educational Studies in Mathematics , 29 ( 2 ) : 123 – 151 .
   Google Scholar
• Selden , A. and 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 .
   Web of Science ®Google Scholar
• Senk , S. L. 1989 . van Hiele levels and achievement in writing geometry proofs . Journal for Research in Mathematics Education , 20 : 309 – 321 .
   Web of Science ®Google Scholar
• Simon , M. A. 1996 . Beyond inductive and deductive reasoning: The search for a sense of knowing . Educational Studies in Mathematics , 30 : 197 – 210 .
   Google Scholar
• Sowder , L. and Harel , G. 2003 . Case studies of mathematics majors' proof understanding, production, and appreciation . Canadian Journal for Science, Mathematics, and Technology Education , 3 : 251 – 267 .
   Google Scholar
• Strauss , A. and Corbin , J. 1990 . Basics of qualitative research: Grounded theory procedures and techniques , London, , UK : Sage .
   Google Scholar
• Stylianides , A. and Stylianides , G. 2009 . Proof construction and evaluation . Educational Studies in Mathematics , 72 : 237 – 253 .
   Web of Science ®Google Scholar
• Tall , D. 1989 . The nature of mathematical proof . Mathematics Teaching , 128 : 28 – 32 .
   Google Scholar
• Vinner , S. 1997 . The pseudo-conceptual and pseudo-analytic thought processes in mathematical learning . Educational Studies in Mathematics , 34 : 97 – 129 .
   Google Scholar
• Weber , K. 2001 . Student difficulty in constructing proofs: The need for strategic knowledge . Educational Studies in Mathematics , 48 ( 1 ) : 101 – 119 .
   Google Scholar
• Weber , K. 2004 . Traditional instruction in advanced mathematics: A case study of one professor's lectures and proofs in an introductory real analysis course . Journal of Mathematical Behavior , 23 : 115 – 133 .
   Google Scholar
• Weber , K. 2008 . How mathematicians determine if an argument is a valid proof . Journal for Research in Mathematics Education , 39 : 431 – 459 .
   Web of Science ®Google Scholar
• Weber, K. (2009). Mathematics majors evaluation of mathematical arguments and their conception of proof. In Proceedings of the 12 th Conference on Research in Undergraduate Mathematics Education. Raleigh, NC. Accessed on April 28, 2010 from http://sigmaa.maa.org/rume/crume2009/proceedings.html (http://sigmaa.maa.org/rume/crume2009/proceedings.html)
   Google Scholar
• Weber , K. and Alcock , L. 2004 . Semantic and syntactic proof productions . Educational Studies in Mathematics , 56 : 209 – 234 .
   Google Scholar
• Weber , K. and Alcock , L. 2005 . Using warranted implications to understand and validate proofs . For the Learning of Mathematics , 25 ( 1 ) : 34 – 38 .
   Google Scholar
• Weber , K. , Alcock , L. and Radu , I. Proceedings of the 27th Conference for the North American Chapter of the Psychology of Mathematics Education . Roanoke, VA. Undergraduates' use of examples in a transition to proof course , Edited by: Wilson , S. Electronic CD .
   Google Scholar