References
- Anghileri , J. 2000 . Teaching Number Sense , London : Continuum .
- Boulton-Lewis , G. M. 1998 . Children's strategy use and interpretations of mathematical representations' . Journal of Mathematical Behaviour , 17 ( 2 ) : 219 – 237 .
- Carpenter , T. P. , Fennema , E. , Franke , M. L. , Levi , L. and Empson , S. B. 1999 . Children's mathematics: Cognitively Guided Instruction , Portsmouth, NH : Heinemann .
- Cobb , P. , Yackel , E. and Wood , T. 1992 . A constructivist alternative to the representational view of mind in mathematics education . Journal of Research in Mathematics Education , 23 ( 1 ) : 2 – 33 .
- Department for Education and Skills ( 2006 ) Primary Framework for literacy and mathematics: core position papers underpinning the renewal of guidance for teaching literacy and mathematics ( Norwich : DfES ).
- Fennell , F. and Rowan , T. 2001 . Representation: an important process for teaching and learning mathematics . Teaching Children Mathematics , 7 ( 4 ) : 288 – 292 .
- Goldin , G. A. and Shteingold , N. 2001 . “ Systems of representation and the development of mathematical concepts ” . In The roles of representation in school mathematics , Edited by: Cuoco , A. A. and Curcio , F. R. Reston, VA : National Council of Teachers of Mathematics .
- Gravemeijer , K. P. E. 1991 . “ An instruction-theoretical reflection on the use of manipulatives ” . In Realistic Mathematics Education in Primary School , Edited by: Streefland , L. Utrecht : Cd-Press .
- Gray , E. , Pitta , D. & Tall , D.O. ( 1997 ) The nature of the object as an integral component of numerical processes , in: Pehkonen E. Proceedings of the 21st International Conference for the Psychology of Mathematics Education ( Lahti , Finland ), Vol. 1 , 115 - 130 .
- Hall , N. 1998 . Concrete representations and the procedural analogy theory . Journal of Mathematical Behaviour , 17 ( 1 ) : 33 – 51 .
- Harries , T. & Suggate , J. ( 2006 ) Exploring links across representations of numbers with young children , International Journal for Technology in Mathematics Education , 13 ( 2 ) (online journal) .
- 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. New York : NCTM .
- Kaput , J. 1991 . “ Notations and representations as mediators of constructive processes ” . In Constructivism and mathematics education , Edited by: von Glasersfeld , E. Dordrecht, , Netherlands : Kluwer .
- Kaput , J. 1994 . “ Technology and Mathematics Education ” . In Handbook of Research on Mathematics Teaching and Learning , Edited by: Grouws , D. A. New York : NCTM .
- Krutetskii , V. 1976 . The psychology of mathematical abilities in school children , Chicago : University of Chicago Press .
- Mason , J. 2005 . “ Micro-structure of attention in the teaching and learning of mathematics ” . In Mathematics Teaching 2005 Conference Report , 36 – 41 . Edinburgh Centre for Mathematical Education .
- Nickerson , R. S. 1985 . Understanding understanding . American Journal of Education , 93 ( 2 ) : 201 – 239 .
- Nunes , T. and Bryant , P. 1996 . Children doing Mathematics , Oxford : Blackwell Publishers .
- Sierpinska , A. 1994 . Understanding in Mathematics , London : The Falmer Press .
- Skemp , R. 1976 . Relational understanding and instrumental understanding . Mathematics Teaching , 77 : 20 – 26 .
- Thompson , I. 1999 . Issues in Teaching Numeracy in Primary Schools , Oxford : Open University Press .
- Wittmann , E. Ch. 1998 . Standard number representations in teaching arithmetic . Journal fur Mathematik-Didaltik , 19 ( 2 ) : 149 – 178 .
- Wittmann , E. Ch. 2002 . Developing mathematics education in a systemic process . Educational Studies in Mathematics , 48 ( 1 ) : 1 – 20 .
- Wittmann , E. Ch. ( 2005 ) Mathematics as the science of patterns - a guideline for developing mathematics education from early childhood to adulthood , Plenary Lecture at International ColloquiumMathematical learning from Early Childhood to Adulthood ( Belgium : Mons ).