3,824
Views
105
CrossRef citations to date
0
Altmetric
Articles

Reasoning-and-Proving in School Mathematics Textbooks

Pages 258-288 | Published online: 14 Oct 2009

REFERENCES

  • Arzarello , F. , Andriano , V. , Olivero , F. and Robutti , O. 1998 . Abduction and conjecturing in mathematics . Philosophica , 61 ( 1 ) : 77 – 94 .
  • Balacheff , N. 1988 . “ A study of students' proving processes at the junior high school level ” . In Proceedings of the Second UCSMP International Conference on Mathematics Education , Edited by: Wirszup , I. and Streit , R. 284 – 297 . Reston, VA : National Council of Teachers of Mathematics .
  • Ball , D. L. and Bass , H. 2003 . “ Making mathematics reasonable in school ” . In A research companion to Principles and Standards for School Mathematics , Edited by: Kilpatrick , J. , Martin , W. G. and Schifter , D. 27 – 44 . Reston, VA : National Council of Teachers of Mathematics .
  • Bell , A. W. 1976 . A study of pupil's proof-explanations in mathematical situations . Educational Studies in Mathematics , 7 ( 1 ) : 23 – 40 .
  • Bills , L. and Rowland , T. 1999 . “ Examples, generalisation and proof ” . In Making meaning in mathematics: advances in mathematical education , Edited by: Brown , L. Vol. 1 , 103 – 116 . York, U.K : QED Publications .
  • Cañadas , M. C. and Castro , E. 2005 . “ A proposal of categorisation for analysing inductive reasoning ” . In Proceedings of the 4th Congress of the European Society for Research in Mathematics Education , Edited by: Bosch , M. 401 – 408 . Spain : Saint Feliu de Guixols .
  • Collins , W. , Dritsas , L. , Frey-Mason , P. , Howard , A. C. , McClain , K. Molina , D. D. 1993 . Mathematics Applications and Connections Glencoe/ McGraw-Hill
  • Davis , P. J. and Hersh , R. 1981 . The mathematical experience , Boston : Houghton-Mifflin .
  • de Villiers , M. 1998 . “ An alternative approach to proof in dynamic geometry ” . In Designing learning environments for developing understanding of geometry and space , Edited by: Lehrer , R. and Chazan , D. 369 – 393 . London : Lawrence Erlbaum Associates .
  • de Villiers , M. 1999 . “ The role and function of proof ” . In Rethinking proof with the Geometer's Sketchpad , Edited by: de Villiers , M. 3 – 10 . Key Curriculum Press .
  • Dewey , J. 1903 . The psychological and the logical in teaching geometry . Educational Review , XXV : 387 – 399 .
  • Donaldson , M. 1978 . Children's minds , New York : Norton .
  • Gattegno , C. 1987 . The science of education part I: Theoretical considerations , New York : Educational Solutions .
  • Glaser , B. G. and Strauss , A. L. 1967 . The discovery of grounded theory , Hawthorne, N.Y : Aldine de Gruyter .
  • Hanna , G. 1990 . Some pedagogical aspects of proof . Interchange , 21 ( 1 ) : 6 – 13 .
  • Harel , G. and Sowder , L. 1998 . “ students' proof schemes: Results from exploratory studies ” . In Research in collegiate mathematics education III , Edited by: Schoenfeld , A. H. , Kaput , J. and Dubinsky , E. 234 – 283 . Providence, R.I : American Mathematical Society .
  • Harel , G. and Sowder , L. 2007 . “ Toward comprehensive perspectives on the learning and teaching of proof ” . In Second handbook of research on mathematics teaching and learning , Edited by: Lester , F. K. 805 – 842 . Greenwich, CT : Information Age Publishing .
  • Hiebert , J. and Carpenter , T. P. 1992 . “ Learning and teaching with understanding ” . In Handbook of research on mathematics teaching and learning , Edited by: Grouws , D. A. 65 – 97 . New York : Mcmillan .
  • Hiebert , J. , Gallimore , R. , Garnier , H. , Givvin , K. B. , Hollingsworth , H. Jacobs , J. 2003 . Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study , NCES 2003-013 Washington, D.C. : U.S. Department of Education, Institute of Education Sciences .
  • Knuth , E. J. 2002 . Secondary school mathematics teachers' conceptions of proof . Journal for Research in Mathematics Education , 33 ( 5 ) : 379 – 405 .
  • Knuth , E. J. , Choppin , J. , Slaughter , M. and Sutherland , J. 2002 . “ Mapping the conceptual terrain of middle school students' competencies in justifying and proving ” . In Proceedings of the 24th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , Edited by: Mewborn , D. S. , Sztajn , P. , White , D. Y. , Weigel , H. G. , Bryant , R. L. and Nooney , K. Vol. 4 , 1693 – 1670 . Athens, GA : Clearinghouse for Science, Mathematics, and Environmental Education .
  • Knuth , E. J. and Sutherland , J. 2004 . “ Student understanding of generality ” . In Proceedings of the 26th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , Edited by: McDougall , D. E. and Ross , J. A. Vol. 2 , 561 – 567 . Toronto, Canada : OISE/UT .
  • Küchemann, D., & Hoyles, C. (2001–03). Longitudinal Proof Project (Technical Reports). London: Institute of Education, University of London http://www.mathsmed.co.uk/ioe-proof/techreps.html (Accessed: 3 May 2009 ).
  • Küchemann , D. and Hoyles , C. 2009 . “ From empirical to structural reasoning in mathematics: tracking changes over time ” . In Teaching and learning proofs across the grades: A K-16 perspective , Edited by: Stylianou , D. A. , Blanton , M. L. and Knuth E , E. J. New York, N.Y : Routledge .
  • Lakatos , I. 1976 . Proofs and refutations: The logic of mathematical discovery , Cambridge University Press .
  • Lampert , M. 1992 . “ Practices and problems in teaching authentic mathematics ” . In Effective and responsible teaching: The new synthesis , Edited by: Oser , F. K. , Dick , A. and Patry , J. 295 – 314 . San Francisco, CA : Jossey-Bass Publishers .
  • Lappan , G. , Fey , J. T. , Fitzgerald , W. M. , Friel , S. N. and Philips , E. D. 1998/2004 . Connected Mathematics Project , Menlo Park, CA : Dale Seymour Publications .
  • Manaster , A. B. 1998 . Some characteristics of eighth grade mathematics classes in the TIMSS videotape study . American Mathematical Monthly , 105 ( 9 ) : 793 – 805 .
  • Martin , W. G. and Harel , G. 1989 . Proof frames of preservice elementary teachers . Journal for Research in Mathematics Education , 20 : 41 – 51 .
  • Mason , J. , Burton , L. and Stacey , K. 1982 . Thinking mathematically , London : Addison-Wesley .
  • Mason , J. and Pimm , D. 1984 . Generic examples: Seeing the general in the particular . Educational Studies in Mathematics , 15 : 277 – 289 .
  • Movshovitz-Hadar , N. 1988 . Stimulating presentation of theorems followed by responsive proofs . For the Learning of Mathematics , 8 ( 2 ) : 12 – 19 . , 30.
  • National Council of Teachers of Mathematics . 1989 . Curriculum and evaluation standards for school mathematics , Reston, VA : National Council of Teachers of Mathematics .
  • National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics , Reston, VA : National Council of Teachers of Mathematics .
  • Polya , G. 1954 . Induction and analogy in mathematics , Princeton, N.J : Princeton University Press .
  • Porter , A. 2002 . Measuring the content of instruction: Uses in research and practice. Educational Researcher , 31 ( 7 ) : 3 – 14 .
  • Raman , M. 2004 . Epistemological messages conveyed by three high-school and college mathematics textbooks . Journal of Mathematical Behavior , 23 ( 4 ) : 389 – 404 .
  • Reid , D. 2002 . Conjectures and refutations in grade 5 mathematics . Journal for Research in Mathematics Education , 33 ( 1 ) : 5 – 29 .
  • Romberg , T. and Kaput , J. 1999 . “ Mathematics worth teaching, mathematics worth understanding ” . In Mathematics classrooms that promote understanding , Edited by: Fennema , E. and Romberg , T. 3 – 18 . Mahwah, N.J : Lawrence Erlbaum Associates .
  • Schoenfeld , A. H. 1994 . What do we know about mathematics curricula? . Journal of Mathematical Behavior , 13 : 55 – 80 .
  • Schwab , J. J. 1978 . “ Education and the structure of the disciplines ” . In Science, curriculum, and liberal education: Selected essays , Edited by: Westbury , J. and Wilkof , N. J. 229 – 272 . Chicago & London : The University of Chicago Press .
  • Siegel , S. and Castellan , N. J. Jr. 1988 . Nonparametric statistics for the behavioral sciences , 2nd , New York : McGraw-Hill .
  • Stein , M. K. , Smith , M. S. and Remillard , J. 2007 . “ How curriculum influences student learning ” . In Second handbook of research on mathematics teaching and learning , Edited by: Lester , F. K. 319 – 370 . Greenwich, CT : Information Age Publishing .
  • Stylianides , G. J. 2005 . Investigating students' opportunities to develop proficiency in reasoning and proving: A curricular perspective , Ann Arbor, , USA : Unpublished doctoral dissertation, University of Michigan .
  • Stylianides , A. J. 2007a . Proof and proving in school mathematics . Journal for Research in Mathematics Education , 38 ( 3 ) : 289 – 321 .
  • Stylianides , A. J. 2007b . The notion of proof in the context of elementary school mathematics . Educational Studies in Mathematics , 65 ( 1 ) : 1 – 20 .
  • Stylianides , G. J. 2007c . Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics . International Journal of Science and Mathematics Education , 6 : 191 – 215 .
  • Stylianides , G. J. 2008a . An analytic framework of reasoning-and-proving . For the Learning of Mathematics , 28 ( 1 ) : 9 – 16 .
  • Stylianides , G. J. 2008b . Proof in school mathematics curriculum: A historical perspective . Mediterranean Journal for Research in Mathematics Education , 7 ( 1 ) : 23 – 50 .
  • Stylianides , G. J. and Stylianides , A. J. 2008 . Proof in school mathematics: Insights from psychological research into students' ability for deductive reasoning . Mathematical Thinking and Learning , 10 ( 2 ) : 103 – 133 .
  • Stylianides , G. J. , Stylianides , A. J. and Philippou , G. N. 2007 . Preservice teachers' knowledge of proof by mathematical induction . Journal of Mathematics Teacher Education , 10 : 145 – 166 .
  • Tarr , J. E. , Chávez , Ó. , Reys , R. E. and Reys , B. J. 2006 . From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students' opportunity to learn . School Science and Mathematics , 106 ( 4 ) : 191 – 201 .
  • U.S. Department of Education . 2000 . Before it's too late. A report to the Nation from the National Commission of Mathematics and Science Teaching for the 21st century , Washington, D.C : U.S. Department of Education .
  • Weiss , I. , Pasley , J. , Smith , P. , Banilower , E. and Heck , H. 2003 . Looking inside the classroom: A study of K-12 mathematics and science education in the United States , Chapel Hill, N.C : Horizon Research .
  • Yackel , E. and Hanna , G. 2003 . “ Reasoning and proof ” . In A research companion to Principles and Standards for School Mathematics , Edited by: Kilpatrick , J. , Martin , W. G. and Schifter , D. 22 – 44 . Reston, VA : National Council of Teachers of Mathematics .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.