Mathematicians’ perspectives on their pedagogical practice with respect to proof

References

• Davis , PJ and Hersh , R . 1981 . The Mathematical Experience , New York , NY : Viking Penguin Inc. .
   Google Scholar
• Dreyfus , T . 1991 . “ Advanced mathematical thinking processes ” . In Advanced Mathematical Thinking , Edited by: Tall , D . 25 – 41 . Dordrecht : Kluwer .
   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 . J. Math. Behav. , 23 : 115 – 133 .
   Google Scholar
• Fukawa-Connelly , T . A tale of two courses: Teaching and learning abstract algebra, Unpublished doctoral dissertation, The University of Maryland, 2007
   Google Scholar
• Schoenfeld , A . 1992 . “ Learning to think mathematically: Problem solving, sense making, and metacognition in mathematics ” . In Handbook of Research on Mathematics Teaching and Learning , Edited by: Grouws , D . 334 – 370 . New York : Macmillan .
   Google Scholar
• Rasmussen , C , Zandieh , M , King , K and Teppo , A . 2005 . Advancing mathematical activity: A practice-oriented view of advanced mathematical thinking . Math. Think. Learn. , 7 : 51 – 73 .
   Google Scholar
• Stylianou , DA . 2002 . Interaction of visualization and analysis – the negotiation of a visual representation in problem solving . J. Math. Behav. , 21 : 303 – 317 .
   Google Scholar
• Alcock , L . 2009 . “ Mathematicians’ perspectives on the teaching and learning of proof ” . In Research in Collegiate Mathematics Education , Edited by: Hitt , F , Holton , DA and Thompson , P . Vol. 7 , 73 – 100 . Providence , RI : American Mathematical Society .
   Google Scholar
• Burton , L . 2004 . Mathematicians as enquirers: Learning about learning mathematics , Dordrecht : Kluwer .
   Google Scholar
• Nardi , E . 2007 . Amongst mathematicians: Teaching and learning mathematics at university level , New York : Springer .
   Google Scholar
• Fukawa-Connelly , T . 2005 . Thoughts on learning advanced mathematics . Learn. Math. , 25 ( 2 ) : 33 – 35 .
   Google Scholar
• Harel , G and Sowder , L . 2009 . “ College instructors views of students vis-a-vis proof ” . In Teaching and Learning Proof Across the Grades: A K-16 Perspective , Edited by: Blanton , M , Stylianou , D and Knuth , E . 275 – 289 . New York : Routledge/Taylor and Francis .
   Google Scholar
• Steiner , M . 1978 . Mathematical explanation . Philos. Stud. , 34 : 135 – 151 .
   Web of Science ®Google Scholar
• Hanna , G . 1990 . Some pedagogical aspects of proof . Interchange , 21 ( 1 ) : 6 – 13 .
   Google Scholar
• Alibert , D and Thomas , M . 1991 . “ Research on mathematical proof ” . In Advanced Mathematical Thinking , Edited by: Tall , DO . 215 – 230 . Dordrecht , , The Netherlands : Kluwer Academic Publishers .
   Google Scholar
• Hersh , R . 1993 . Proving is convincing and explaining . Educ. Stud. Math. , 24 : 389 – 399 .
   Google Scholar
• de Villiers , MD . 1990 . The role and function of proof in mathematics . Pythagoras , 24 : 17 – 24 .
   Google Scholar
• Hanna , G and Barbreau , E . 2008 . Proofs as bearers of mathematical knowledge . ZDM , 40 : 345 – 353 .
   Google Scholar
• Weber , K . 2010a . How proofs develop insight . Learn. Math. , 30 ( 1 ) : 32 – 36 .
   Google Scholar
• Harel , G and Sowder , L . 1998 . “ Students proof schemes ” . In Research in Collegiate Mathematics Education , Edited by: Schoenfeld , A , Kaput , J and Dubinsky , E . Vol. 3 , 234 – 282 . Washington , DC : American Mathematical Society .
   Google Scholar
• Weber , K . 2002 . Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique . Learn. Math. , 22 ( 3 ) : 14 – 17 .
   Google Scholar
• Healy , L and Hoyles , C . 2000 . A study of proof conceptions in algebra . J. Res. Math. Educ. , 31 : 396 – 428 .
   Web of Science ®Google Scholar
• Knuth , E . 2002 . Secondary school mathematics teachers’ conceptions of proof . J. Res. Math. Educ. , 33 ( 5 ) : 379 – 405 .
   Web of Science ®Google Scholar
• Hazzan , O and Zazkis , R . 2003 . Mimicry of proofs with computers: The case of linear algebra . Int. J. Math. Educ. Sci. Technol. , 34 : 385 – 402 .
   Google Scholar
• Selden , A and Selden , J . 2003 . Validations of proofs written as texts: Can undergraduates tell whether an argument proves a theorem? . J. Res. Math. Educ. , 36 ( 1 ) : 4 – 36 .
   Web of Science ®Google Scholar
• Mamona-Downs , J and Downs , M . 2005 . The identity of problem solving . J. Math. Behav. , 24 ( 3–4 ) : 385 – 401 .
   Google Scholar
• Weber , K . 2008 . How mathematicians determine if an argument is a valid proof . J. Res. Math. Educ. , 39 : 431 – 459 .
   Web of Science ®Google Scholar
• J.P. Mejia-Ramos and M. Inglis, Argumentative and proving activities in mathematics education research, in Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, Vol. 2, F.-L. Lin, F.-J. Hsieh, G. Hanna, and M. de Villiers, eds., Taipei, Taiwan, 10–15 May 2009, pp. 88–93
   Google Scholar
• Martin , WG and Harel , G . 1989 . Proof frames of pre-service elementary teachers . J. Res. Math. Educ. , 20 ( 1 ) : 41 – 51 .
   Web of Science ®Google Scholar
• Segal , J . 2000 . Learning about mathematical proof: Conviction and validity . J. Math. Behav. , 18 : 191 – 210 .
   Google Scholar
• Alcock , L and Weber , K . 2005 . Proof validation in real analysis: Inferring and evaluating warrants . J. Math. Behav. , 24 ( 2 ) : 125 – 134 .
   Google Scholar
• Weber , K . 2010b . Mathematics majors’ perceptions of conviction, validity, and proof . Math. Think. Learn. , 12 : 306 – 336 .
   Web of Science ®Google Scholar
• Weber , K and Alcock , L . 2005 . Using warranted implications to understand and validate proofs . Learn. Math. , 25 ( 1 ) : 34 – 38 .
   Google Scholar
• Yang , KL and Lin , F . 2008 . A model of reading comprehension of geometry proofs . Educ. Stud. Math. , 67 : 59 – 76 .
   Google Scholar
• Leron , U . 1983 . Structuring mathematical proofs . Am. Math. Mon. , 90 ( 3 ) : 174 – 184 .
   Web of Science ®Google Scholar
• Rowland , T . 2001 . “ Generic proofs in number theory ” . In Learning and Teaching Number Theory: Research in Cognition and Instruction , Edited by: Campbell , S and Zazkis , R . 157 – 184 . Westport , CT : Ablex Publishing .
   Google Scholar
• Weber , K and Mejia-Ramos , JP . 2011 . How and why mathematicians read proofs: An exploratory study . Educ. Stud. Math. , 76 : 329 – 344 .
   Web of Science ®Google Scholar
• Abbott , S . 2001 . Understanding Analysis , New York : Springer .
   Google Scholar
• Strauss , A and Corbin , J . 1990 . Basics of Qualitative Research: Grounded Theory Procedures and Techniques , London : Sage .
   Google Scholar
• Herbst , PG . 2002 . Engaging students in proving: A double bind on the teacher . J. Res. Math. Educ. , 33 : 176 – 203 .
   Web of Science ®Google Scholar
• Dubinsky , E , Dautermann , J , Leron , U and Zazkis , R . 1994 . On learning the fundamental concepts of group theory . Educ. Stud. Math. , 27 : 267 – 305 .
   Google Scholar
• Selden , J and Selden , A . 2009 . “ Teaching proving by coordinating aspects of proof with students’ abilities ” . In Teaching and Learning Proof Across the Grades: A K-16 Perspective , Edited by: Blanton , M , Stylianou , D and Knuth , E . 339 – 354 . New York : Routledge .
   Google Scholar
• Asiala , M , Brown , A , DeVries , D , Dubinsky , E , Mathews , D and Thomas , K . A framework for research and curriculum development in undergraduate mathematics education research, Res. Colle. Math. Educ. 2, 1996, pp. 1–32
   Google Scholar
• Cobb , P , Confrey , J , deSessa , A , Lehrer , R and Schauble , L . 2003 . Design experiments in educational research . Educ. Res. , 32 ( 1 ) : 9 – 13 .
   Google Scholar
• Conradie , J and Frith , J . 2000 . Comprehension tests in Mathematics . Educ. Stud. Math. , 42(3) : 225 – 235 .
   Google Scholar
• Mejia-Ramos , JP , Fuller , E , Weber , K , Samkoff , A and Rhoads , K . A model for proof comprehension in undergraduate mathematics, Educ. Stud. Math. (in press)
   Google Scholar
• Begle , EG . 1979 . Critical variables in mathematics education: Findings from a survey of the empirical literature , Washington , DC : MAA and NCTM .
   Google Scholar
• Schoenfeld , A . 1985 . Mathematical Problem Solving , Orlando , FL : Academic Press .
   Google Scholar