CHILDREN INVENTING SIGNS FOR MENTAL NUMBER STRATEGIES

References

• Atkinson , S. 1992 , Mathematics with Reason . London : Hodder and Stoughton .
   Google Scholar
• Dehaene , S. 1997 . The Number Sense , London : The Penguin Press .
   Google Scholar
• Donaldson , M. 1978 . Children's Minds , Glasgow : Fontana .
   Google Scholar
• Ernest , P. 1991 . The Philosophy of Mathematics Education , Basingstoke : The Falmer Press .
   Google Scholar
• Fuson , K. 1988 . Children's Counting and Concepts of Number , New York : Springer Verlag .
   Google Scholar
• Gallistel , C. R. and Gelman , R. 1992 . Preverbal and verbal counting and computation . Cognition , 44 : 43 – 74 .
   PubMed Web of Science ®Google Scholar
• Gardner , H. and Wolf , D. 1983 , Waves and streams of symbolization: Notes on the development of symbolic capacities in young children . In: D. Rogers and J. A. Sloboda The Acquisition of Symbolic Skills ( Proceedings of a NATO Conference, 1982, Keele ). New York : Plenum Press .
   Google Scholar
• Ginsburg , H. P. 1977 . ‘Children's Arithmetic: The Learning Process’ , New York : Van Nostrand .
   Google Scholar
• Gravemeijer , K. 1993 . “ ‘Modelling two-digit addition and subtraction with an empty number line’ ” . In Teaching and Learning Mathematics in Context , Edited by: Breiteig , T. , Huntley , I. and Kaiser-Messmer , G. 55 – 61 . Chichester : Ellis Harwood .
   Google Scholar
• Gravemeijer , K. 1994 . ‘Educational development and developmental research in mathematics education’ . Journal for Research in Mathematics Education , 25 ( 5 ) : 443 – 471 .
   Web of Science ®Google Scholar
• Haylock , D. 1995 . Mathematics explained for primary teachers , London : Paul Chapman Publishers .
   Google Scholar
• Hughes , M. 1986 . Children and Number , Oxford : Blackwell Publishers .
   Google Scholar
• Klein , A. and Beishuizen , M. 1998 . ‘The empty number line in Dutch second grades: realistic versus gradual program design’ . Journal for Research in Mathematics Education , 29 ( 4 ) : 443 – 464 .
   Web of Science ®Google Scholar
• Klein , A. and Starkey , P. 1987 . “ ‘The origins and development of numerical cognition: a comparative analysis’ ” . In Cognitive Processes in Mathematics , Edited by: Rogers , D. and Sloboda , J. A. Oxford : Clarendon Press .
   Google Scholar
• Mulligan , J. T. and Mitchelmore , M. C. 1997 . ‘Young children's intuitive models of multiplication and division’ . Journal for Research in Mathematics Education , 28 ( 3 ) : 331 – 354 .
   Google Scholar
• Munn , P. 1997 . “ ‘Children's belief's about counting’ ” . In Teaching and Learning Early Number , Edited by: Thompson , I. 9 – 19 . Buckingham : Open University Press .
   Google Scholar
• Neuman , D. 1993 . “ ‘Exploring numbers through subtraction in primary mathematics’ ” . In Teaching and Learning Mathematics in Context , Edited by: Breiteig , T. , Huntley , I. and Kaiser-Messmer , G. 37 – 50 . Chichester : Ellis Harwood Ltd .
   Google Scholar
• Piaget , J. 1962 . Play, dreams and Imitation in Childhood , London : Routledge and Kegan Paul Ltd .
   Google Scholar
• Resnick , L. B. , Lesgold , S. and Bill , V. 1990 . “ ‘From protoquantities to number sense’ ” . In Proceedings of the 14th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Booker , G. , Cobb , P. and de Mendicuti , T. N. Vol. 3 , 305 – 312 . Oaxaca, Mexico. Program Committee of the 14th PME Conference .
   Google Scholar
• Rowland , T. 1982 . ‘Teaching directed numbers: an experiment'9 . Mathematics in School , 11 ( 1 ) : 24 – 27 .
   Google Scholar
• Sinclair , A. , Siegrist , F. and Sinclair , H. : 1983 , ‘ Young children's ideas about the written number system .’ In D. Rogers and J. A. Sloboda The Acquisition of Symbolic Skills ( Proceedings of a NATO Conference, 1982, Keele ) (pp. 535 – 542 ). New York : Plenum Press .
   Google Scholar
• Sinclair , H. and Sinclair , A. 1986 . “ ‘Children's mastery of written numerals and the construction of basic number concepts’ ” . In Conceptual and Procedural Knowledge , Edited by: Hiebert , J. 59 – 74 . Hillsdale : Lawrence Erlbaum Associates .
   Google Scholar
• Strauss , A. L. 1990 . Basics of Qualitative Research: Grounded theory procedures and techniques , London : Sage Publications .
   Google Scholar
• Vergnaud , G. 1982 . “ A classification of cognitive tasks and operations of thought involved in addition and subtraction problems ” . In Addition and Subtraction: A Cognitive Perspective. Hillsdale , Edited by: Carpenter , T. P. , Moser , J. M. and Romberg , T. A. 39 – 59 . New Jersey : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Vygotsky , L. S. 1962 . Thought and Language , Cambridge, Mass : M.I.T.Press .
   Google Scholar
• Womack , D. 1979 , ‘ Piaget's concept of the symbol together with proposals for a new framework of semiotic .’ Unpublished M.Sc. thesis . University of Manchester
   Google Scholar
• Womack , D. : 1995 , ‘ Arithmetic Images of Reality .’ In C. Keitel CIEAEM 47: The 47th Conference of the Commission Internationale pour l'Etude et l'Amélioration de l'Enseignement des Mathématiques . Berlin : Technischer Universitaet Berlin .
   Google Scholar
• Womack , D. 1998a . “ Teacher trainee students’ understanding of operation signs ” . In Proceedings of the BSRLM Day conference at the University of Birmingham , Edited by: Bills , E. 117 – 122 . Coventry : University of Warwick .
   Google Scholar
• Womack , D. 1998b . “ ‘Mental calculation strategies employed by teacher trainee students’ ” . In Proceedings of the BSRLM Day Conference at the University of Leeds , Edited by: Bills , E. 77 – 82 . Coventry : University of Warwick .
   Google Scholar
• Womack , D. : ( In preparation) Number intuitions in young children: Pedagogical implications and mathematical insights. Unpublished Ph.D. thesis , University of Manchester .
   Google Scholar
• Womack , D. and Williams , J. 1998 . “ ‘Intuitive counting strategies of 5- to 6-year-old children within a transformational arithmetic framework’ ” . In Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education , Edited by: Olivier , A. and Newstead , K. Vol. 4 , 185 – 192 . Stellenbosch SA : University of Stellenbosch .
   Google Scholar