918
Views
49
CrossRef citations to date
0
Altmetric
Articles

Contingency in the Mathematics Classroom: Opportunities Taken and Opportunities Missed

&
Pages 137-153 | Published online: 31 May 2013

REFERENCES

  • Adler , J. and Ball , D. 2009 . Knowing and using mathematics in teaching . For the Learning of Mathematics , 29 ( 3 ) : 2 – 3 .
  • Ball , D. L. , Thames , M. H. and Phelps , G. 2008 . Content knowledge for teaching: What makes it special? . Journal of Teacher Education , 59 ( 5 ) : 389 – 407 .
  • Bishop , A. J. 1976 . Decision-making, the intervening variable . Educational Studies in Mathematics , 7 : 42 – 47 .
  • Bishop , A. J. 2001 . “ Educating student teachers about values in mathematics education ” . In Making sense of mathematics teacher education , Edited by: Lin , F. -L. and Cooney , T. J. 233 – 246 . Dordrecht , , The Netherlands : Kluwer Academic Publishers .
  • Bishop , A. J. , Clarkson , P. , Fitzsimons , G. and Seah , W. T. 2000 . “ Why study values in mathematics teaching: Contextualising the VAMP project? ” . In Proceedings of the HPM 2000 conference on history in mathematics education , Edited by: Horng , W. S. and Lin , F.-L. Vol. 2 , 147 – 154 . Taipei , , Taiwan : National Taiwan Normal University . Retrieved from http://www.education.monash.edu.au/research/groups/smte/projects/vamp/hpm2000a.pdf
  • Brown , S. and Walter , M. 1983 . The art of problem posing , Hillsdale , NJ : Lawrence Erlbaum .
  • Chick , H. and Stacey , K. 2013 . Teachers of mathematics as problem-solving applied mathematicians . Canadian Journal of Science, Mathematics and Technology Education , 13 ( 2 ) : 121 – 136 .
  • Davenport , H. 2008 . The higher arithmetic , Cambridge, England : Cambridge University Press . (8th ed.).
  • Glaisher , J. W. L. 1894 . The collected mathematical papers of Henry John Stephen Smith , Oxford, England : Clarendon Press .
  • Hill , H. , Ball , D. and Schilling , S. 2008 . Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students . Journal for Research in Mathematics Education , 39 ( 4 ) : 372 – 400 .
  • Hoyles , C. 1997 . The curricular shaping of students’ approach to proof . For the Learning of Mathematics , 17 ( 1 ) : 7 – 15 .
  • Kahneman , D. , Slovic , P. and Tversky , A. 1982 . Judgment under uncertainty: Heuristics and biases , Cambridge , , England : Cambridge University Press .
  • Klein , F. 1896 . Ausgewählte kapitel der zahlentheorie Göttingen , , Germany: [s.n.]
  • Koichu , B. 2008 . If not, what yes? . International Journal of Mathematical Education in Science and Technology , 39 ( 4 ) : 443 – 454 .
  • Lakatos , I. 1976 . Proofs and refutations , Cambridge, England : Cambridge University Press .
  • Lampert , M. and Ball , D. L. 1999 . “ Aligning teacher education with contemporary K–12 reform visions ” . In Teaching as the learning profession: Handbook of policy and practice , Edited by: Sykes , G. and Darling-Hammond , L. 33 – 53 . San Francisco , CA : Jossey Bass .
  • Lankford , F. G. 1972 . Some computational strategies of seventh grade pupils , Washington , DC : Government Printing Office .
  • Lave , J. and Wenger , E. 1991 . Situated learning: Legitimate peripheral participation , New York , NY : Cambridge University Press .
  • Leikin , R. and Zazkis , R. 2010 . Learning through teaching mathematics: Developing teachers’ knowledge and expertise in practice , Dordrecht , , The Netherlands : Springer .
  • Martin , L. C. and Towers , J. 2009 . Improvisational coactions and the growth of collective mathematical understanding . Research in Mathematics Education , 11 ( 1 ) : 1 – 19 .
  • Mason , J. and Davis , B. 2013 . The importance of teachers’ mathematical awareness for in-the-moment pedagogy . Canadian Journal of Science, Mathematics and Technology Education , 13 ( 2 ) : 182 – 197 .
  • Mason , J. and Johnston-Wilder , S. 2004 . Fundamental constructs in mathematics education , London , , England : Routledge Falmer .
  • Mason , J. and Spence , M. 1999 . Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment . Educational Studies in Mathematics , 38 : 135 – 161 .
  • McNair , K. 1978–1979 . Capturing inflight decisions: Thoughts while teaching . Educational Research Quarterly , 3 ( 4 ) : 26 – 42 .
  • Remillard , J. T. and Geist , P. K. 2002 . Supporting teachers’ professional learning by navigating openings in the curriculum . Journal of Mathematics Teacher Education , 5 ( 1 ) : 7 – 34 .
  • Rowland , T. , Huckstep , P. and Thwaites , A. 2005 . Elementary teachers’ mathematics subject knowledge: The Knowledge Quartet and the case of Naomi . Journal of Mathematics Teacher Education , 8 ( 3 ) : 255 – 281 .
  • Rowland , T. and Ruthven , K. 2011 . Mathematical knowledge in teaching , London , , England : Springer .
  • Rowland , T. , Thwaites , A. and Jared , L. 2011 . “ Triggers of contingency in mathematics teaching ” . In Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education , Edited by: Ubuz , B. Vol. 4 , 73 – 80 . Ankara , , Turkey : International Group for the Psychology of Mathematics Education .
  • Ruthven , K. 2011 . “ Conceptualising mathematical knowledge in teaching ” . In Mathematical knowledge in teaching , Edited by: Rowland , T. and Ruthven , K. 83 – 96 . London , , England : Springer .
  • Schoenfeld , A. H. 1998 . Toward a theory of teaching-in-context . Issues in Education , 4 ( 1 ) : 1 – 94 .
  • Schon , D. A. 1987 . Educating the reflective practitioner , San Francisco , CA : Jossey-Bass .
  • Schwab , J. J. 1978 . “ Education and the structure of the disciplines ” . In Science, curriculum and liberal education , Edited by: Westbury , I. and Wilkof , N. J. 229 – 272 . Chicago , IL : University of Chicago Press .
  • Shulman , L. S. 1986 . Those who understand: Knowledge growth in teaching . Educational Researcher , 15 ( 2 ) : 4 – 14 .
  • Sirotic , N. and Zazkis , R. 2007 . Irrational numbers: The gap between formal and intuitive knowledge . Educational Studies in Mathematics , 65 ( 1 ) : 49 – 76 .
  • Star , J. R. and Stylianides , G. J. 2013 . Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality . Canadian Journal of Science, Mathematics and Technology Education , 13 ( 2 ) : 169 – 181 .
  • Stark , H. 1970 . An introduction to number theory , Chicago , IL : Markham Publishing .
  • Stylianides , G. J. and Stylianides , A. J. 2010 . Mathematics for teaching: A form of applied mathematics . Teaching and Teacher Education , 26 : 161 – 172 .
  • Watson , A. 2008 . “ Developing and deepening mathematical knowledge in teaching: Being and knowing ” . In The Nuffield seminar series on Mathematical Knowledge in Teaching Retrieved from http://www.mkit.maths-ed.org.uk/seminar5.html
  • Watson , A. and Barton , B. 2011 . “ Teaching mathematics as the contextual application of modes of mathematical enquiry ” . In Mathematical knowledge in teaching , Edited by: Rowland , T. and Ruthven , K. 65 – 82 . London , , England : Springer .
  • Zazkis , R. and Leikin , R. 2010 . Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers . Mathematical Thinking and Learning , 12 ( 4 ) : 263 – 281 .
  • Zazkis , R. and Mamolo , A. 2011 . Reconceptualizing knowledge at the mathematical horizon . For the Learning of Mathematics , 31 ( 2 ) : 8 – 13 .

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.