References
- Askew , M. , Bibby , T. and Brown , M. 2001 . Raising attainment in primary number sense: From counting to strategy , London : BEAM Education .
- Baroody , A.J. 1987 . Children's mathematical thinking , New York : Teachers College Press .
- Canobi , K.H. , Reeve , R.A. and Pattison , P.E. 1998 . The role of conceptual understanding in children's addition problem solving . Developmental Psychology , 34 ( 5 ) : 882 – 91 .
- Canobi , K.H. , Reeve , R.A. and Pattison , P.E. 2003 . Patterns of knowledge in children's addition . Developmental Psychology , 39 ( 3 ) : 521 – 34 .
- Carpenter , T.P. and Moser , J.M. 1984 . The acquisition of addition and subtraction concepts in grades one through three . Journal for Research in Mathematics Education , 15 ( 3 ) : 179 – 202 .
- Cowan , R. 2003 . “ Does it all add up? Changes in children's knowledge of addition combinations, strategies and principles ” . In The development of arithmetic concepts and skills , Edited by: Baroody , A.J. and Dowker , A. 35 – 74 . Mahwah : Lawrence Erlbaum Associates .
- Department for Children, Schools and Families . 2008 . Mathematics performance in primary schools: Getting the best results , London : National Audit Office .
- Department for Education and Employment . 1999 . The National Curriculum , London : DfEE and QCA .
- Department for Education and Skill . 2006 . Primary Framework for Literacy and Mathematics , Norwich : DfES .
- Fuson , K.C. 1988 . Children's counting and concepts of number , New York : Springer-Verlag .
- Geary , D.C. 2003 . “ Learning disabilities in arithmetic: Problem-solving differences and cognitive deficits ” . In Handbook of learning disabilities , Edited by: Swanson , H.L. , Harris , K.R. and Graham , S. 199 – 212 . New York : The Guilford Press .
- Geary , D.C. and Brown , S.C. 1991 . Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children . Developmental Psychology , 27 ( 3 ) : 398 – 406 .
- Gray , E.M. 1991 . An analysis of diverging approaches to simple arithmetic: Preference and its consequences . Educational Studies in Mathematics , 22 : 551 – 74 .
- Gray , E.M. 2009 . “ Compressing the counting process: Strength from the flexible interpretation of symbols ” . In Teaching and learning early number , Edited by: Thompson , I. 82 – 93 . Maidenhead : Open University Press .
- Putnam , R.T. , deBettencourt , L.U. and Leinhardt , G. 1990 . Understanding of derived-fact strategies in addition and subtraction . Cognition and Instruction , 7 ( 3 ) : 245 – 85 .
- Resnick , L.B. 1983 . “ A developmental theory of number understanding ” . In The development of mathematical thinking , Edited by: Ginsburg , H.P. 109 – 51 . New York : Academic Press .
- Resnick , L.B. 1989 . Developing mathematical knowledge . American Psychologist , 44 ( 2 ) : 162 – 69 .
- Resnick , L.B. 1992 . “ From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge ” . In Analysis of arithmetic for mathematics teaching , Edited by: Leinhardt , G. , Putnam , R. and Hattrup , R.A. 275 – 323 . Hillsdale, NJ : Erlbaum .
- Siegler , R.S. 1987 . The perils of averaging data over strategies: An example from children's addition . Journal of Experimental Psychology: General , 116 : 250 – 64 .
- Siegler , R.S. 2003 . “ Implications of cognitive science research for mathematics education ” . In A research companion to principles and standards for school mathematics , Edited by: Kilpatrick , J. , Martin , W.B. and Schiffer , D.E. 219 – 33 . Reston, VA : National Council of Teachers of Mathematics .
- Siegler , R.S. and Campbell , J. 1989 . “ Individual differences in children's strategy choices ” . In Learning and individual differences: Advances in theory and research , Edited by: Ackerman , P.L. , Sternberg , R.J. and Glaser , R. 218 – 54 . New York : Freeman .
- Siegler , R.S. and Lemaire , P. 1997 . Older and younger adults’ strategy choices in multiplication: Testing predictions of ASCM using the choice/no-choice method . Journal of Experimental Psychology: General , 126 : 71 – 92 .
- Sophian , C. 1997 . Beyond competence: The significance of performance for conceptual development . Cognitive Development , 12 : 281 – 303 .
- Thompson , I. 1995 . The role of counting in the idiosyncratic mental calculation algorithms of young children . European Early Childhood Education Research Journal , 3 ( 1 ) : 5 – 16 .
- Thompson , I. 1999 . Mental calculation strategies for addition and subtraction . Mathematics in School , 28 ( 5 ) : 2 – 4 .
- Thompson , I. 2008 . “ From counting to deriving number facts ” . In Teaching and learning early number , 2nd. ed. , Edited by: Thompson , I. 97 – 109 . Maidenhead : Open University Press .
- Thompson , I. 2010 . “ Getting your head around mental calculation ” . In Issues in teaching numeracy in primary schools , Edited by: Thompson , I. 161 – 73 . Maidenhead : Open University Press .
- Torbeyns , J. , Verschaffel , L. and Ghesquiere , P. 2002 . Strategic competence: Applying Siegler's theoretical and methodological framework to the domain of simple addition . European Journal of Psychology of Education , 7 ( 3 ) : 275 – 91 .
- Vershaffel , L. , Torbeyns , J. and Van Dooren , W. 2009 . Conceptualising, investigating, and enhancing adaptive expertise in elementary mathematics education . European Journal of Psychology of Education , 24 ( 3 ) : 335 – 59 .
- Watson , A. 2005 . “ Low attaining students can think mathematically ” . In Supporting mathematical thinking , Edited by: Watson , A. , Houssart , J. and Roaf , C. 18 – 26 . London : David Fulton .