289
Views
13
CrossRef citations to date
0
Altmetric
Articles

Preservice Teachers’ Understanding of the Relation Between a Fraction or Integer and its Decimal Expansion: The Case of and 1

, &
Pages 232-258 | Published online: 20 Aug 2013

REFERENCES

  • Arnon , I. , Cottrill , J. , Dubinsky , E. , Oktac , A. , Roa Fuentes , S. , Trigueros , M. and Weller , K. 2013 . APOS theory: A framework for research and curriculum development in mathematics education . New York, NY: Springer
  • Asiala , M. , Brown , A. , DeVries , D. , Dubinsky , E. , Mathews , D. and Thomas , K. 1996 . “ A framework for research and curriculum development in undergraduate mathematics education ” . In Research in collegiate mathematics education II , Edited by: Kaput , J. , Schoenfeld , A. H. and Dubinsky , E. 1 – 32 . Providence , RI : American Mathematical Society .
  • Beth , E. W. and Piaget , J. 1966 . Mathematical epistemology and psychology , Edited by: Mays , W. Dordrecht , The Netherlands : D. Reidel Publishing Company . Original work published 1965
  • Breidenbach , D. , Dubinsky , E. , Hawks , J. and Nichols , D. 1992 . Development of the process conception of function . Educational Studies in Mathematics , 23 : 247 – 285 .
  • Brown , A. , McDonald , M. and Weller , K. 2010 . “ Step by step: Infinite iterative processes and actual infinity ” . In Research in collegiate mathematics VII , Edited by: Hitt , F. , Holton , D. and Thompson , P. 115 – 142 . Providence , RI : American Mathematical Society .
  • Burroughs , E. A. and Yopp , D. 2010 . Prospective elementary mathematics teachers’ conceptions of decimals with single repeating digits . Investigations in Mathematics Learning , 3 ( 1 ) : 23 – 42 .
  • Dubinsky , E. and Lewin , P. 1986 . Reflective abstraction and mathematics education . Journal of Mathematical Behavior , 5 ( 1 ) : 55 – 92 .
  • Dubinsky , E. , Weller , K. , McDonald , M. A. and Brown , A. 2005a . Some historical issues and paradoxes regarding the concept of infinity: An APOS analysis: Part 1 . Educational Studies in Mathematics , 58 : 335 – 359 .
  • Dubinsky , E. , Weller , K. , McDonald , M. A. and Brown , A. 2005b . Some historical issues and paradoxes regarding the concept of infinity: An APOS analysis: Part 2 . Educational Studies in Mathematics , 60 : 253 – 266 .
  • Dubinsky , E. , Weller , K. , Stenger , C. and Vidakovic , D. 2008 . Infinite iterative processes: The tennis ball problem . European Journal of Pure and Applied Mathematics , 1 ( 1 ) : 99 – 121 .
  • Edwards , B. An undergraduate student's understanding and use of mathematical definitions in real analysis . Proceedings of the 19th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , Edited by: Dossey , J. , Swafford , J. O. , Parmentier , M. and Dossey , A. E. pp. 17 – 25 . Columbus ERIC/CSMEE, The Ohio State University.
  • Edwards , B. and Ward , M. 2004 . Surprises from mathematics education research: Student (mis)use of mathematical definitions . American Mathematical Monthly , 111 ( 5 ) : 411 – 425 .
  • Fischbein , E. 1987 . Intuition in sciences and mathematics , Dordrecht , , The Netherlands : Kluwer .
  • Fischbein , E. 1989 . Tacit models and mathematics reasoning . For the Learning of Mathematics , 9 ( 2 ) : 9 – 14 .
  • Fischbein , E. 1999 . Intuitions and schemata in mathematical reasoning . Educational Studies in Mathematics , 38 : 11 – 50 .
  • Hewitt , S. 1984 . Naught point nine recurring . Mathematics Teaching , 99 : 48 – 53 .
  • Hirst , K. 1990 . Exploring number: Point nine recurring . Mathematics Teaching , 111 : 12 – 13 .
  • Khoury , H. A. and Zazkis , R. 1994 . On fractions and non-standard representations: Pre-service teachers’ concepts . Educational Studies in Mathematics , 27 : 191 – 204 .
  • Meel , D. 2003 . “ Models and theories of mathematical understanding: Comparing Pirie and Kieren's model of the growth of mathematical understanding and APOS theory ” . In Research in collegiate mathematics education V , Edited by: Selden , A. , Dubinsky , E. , Harel , G. and Hitt , F. 132 – 187 . Providence , RI : American Mathematical Society .
  • Piaget , J. 1975 . “ Piaget's theory ” . In The process of child development , Edited by: Cellerier , G. , Langer , J. and Neubauer , P. B. 164 – 212 . New York , NY : Jason Aronson .
  • Piaget , J. 1976 . The grasp of consciousness , Edited by: Wedgwood , S. Cambridge , MA : Harvard University Press . Original work published 1974
  • Pirie , S. E. B. and Kieren , T. E. 1989 . A recursive theory of mathematical understanding . For the Learning of Mathematics , 9 ( 3 ) : 7 – 11 .
  • Post , T. , Harel , G. , Behr , M. and Lesh , R. 1991 . “ Intermediate teachers’ knowledge of rational number concepts ” . In Integrating research on teaching and learning mathematics , Edited by: Fennema , E. , Carpenter , T. P. and Lamon , S. J. 177 – 198 . Albany , NY : SUNY Press .
  • Putt , I. 1995 . Preservice teachers ordering of decimal numbers: When more is smaller and less is larger . Focus on Learning Problems in Mathematics , 17 ( 3 ) : 1 – 15 .
  • Resnick , L. , Nesher , P. , Leonard , F. , Magone , M. , Omanson , S. and Peled , I. 1989 . Conceptual bases of arithmetic errors: The case of decimal fractions . Journal for Research in Mathematics Education , 20 ( 1 ) : 8 – 27 .
  • Richman , F. 1999 . Is 0.999 … = 1? . Mathematics Magazine , 72 ( 5 ) : 396 – 401 .
  • Sfard , A. 1991 . On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin . Educational Studies in Mathematics , 22 ( 1 ) : 1 – 36 .
  • Sierpinska , A. 1987 . Humanities students and epistemological obstacles related to limits . Educational Studies in Mathematics , 18 : 371 – 397 .
  • Sinclair , N. , Liljedahl , P. and Zazkis , R. 2006 . A coloured window on pre-service teachers’ conceptions of rational numbers . International Journal of Computers for Mathematical Learning , 11 : 177 – 203 .
  • Tall , D. 1977 . Conflicts and catastrophes in the learning of mathematics . Mathematical Education for Teaching , 2 ( 4 ) : 2 – 18 .
  • Tall , D. and Schwarzenberger , R. 1978 . Conflicts in the learning of real numbers and limits . Mathematics Teaching , 82 : 44 – 49 .
  • Thipkong , S. and Davis , E. J. 1991 . Preservice elementary teachers’ misconceptions in interpreting and applying decimals . School Science and Mathematics , 91 ( 3 ) : 93 – 99 .
  • Vinner , S. 1983 . Concept definition, concept image, and the notion of function . International Journal of Mathematical Education in Science and Technology , 14 ( 3 ) : 293 – 305 .
  • Weller , K. , Arnon , I. and Dubinsky , E. 2009 . Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion . Canadian Journal of Science, Mathematics and Technology Education , 9 ( 1 ) : 5 – 28 .
  • Weller , K. , Arnon , I. and Dubinsky , E. 2011 . Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion: Strength and stability of belief . Canadian Journal of Science, Mathematics and Technology Education , 11 ( 2 ) : 129 – 159 .
  • Weller , K. , Clark , J. , Dubinsky , E. , Loch , S. , McDonald , M. and Merkovsky , R. 2003 . “ Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle ” . In Research in collegiate mathematics education V , Edited by: Selden , A. , Dubinsky , E. , Harel , G. and Hitt , F. 97 – 131 . Providence , RI : American Mathematical Society .
  • Yopp , D. , Burroughs , E. A. and Lindaman , B. J. 2011 . Why it is important for in-service elementary mathematics teachers to understand the equality .999 … = 1 . Journal of Mathematical Behavior , 30 ( 2 ) : 115 – 130 .
  • 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 .

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.