Making sense of mathematical graphics: The development of understanding abstract symbolism

REFERENCES

• Athey , C. 1990 . Extending Thought in Young Children: A Parent-Teacher Partnership , London : Paul Chapman Publishing .
   Google Scholar
• Berry , R. Alternative Assessment and Assessment for Learning . Paper presented at the 29th International Association for Educational Assessment (IAEA) Annual conference . http://www.aqa.org.uk/support/iaea/papers/berry.pdf
   Google Scholar
• Cambourne , B. 1988 . The Whole Story: Natural Learning and the Acquisition of Literacy in the Classroom , Auckland : Ashton Scholastic .
   Google Scholar
• Carpenter , T. and Moser , J. 1984 . The Acquisition of addition and subtraction concepts in grades one through three . Journal for Research in Mathematics Education , 15 ( 3 ) : 179 – 202 .
   Google Scholar
• Carruthers , E. 1997a . A number line in the nursery classroom: a vehicle for understanding children's number knowledge . Early Years , 18 ( 1 ) Autumn : 9 – 14 .
   Google Scholar
• Carruthers , E. 1997b . Number: a developmental theory. A case study of a child from twenty to forty-four months , University of Plymouth . Unpublished M. Ed dissertation
   Google Scholar
• Carruthers , E. 2004 . How e-graphics support the quality of discussions on-line, Mirandanet E-Journal (forthcoming) , Research jointly funded by the DfES & GTC .
   Google Scholar
• Carruthers , E. and Worthington , M. 2003 . MirandaNet Web Graphics Discussion: http://www.mirandanet.ac.uk/graphics
   Google Scholar
• Clay , M. 1975 . What Did I Write? , London : Heineman .
   Google Scholar
• Cook , V. 2001 . Second Language Learning and Language Teaching , London : Arnold, Hodder Headline Group .
   Google Scholar
• Engel , B. 1995 . Considering Children's Art Work: Why and How to Value their Works , Washington, DC : National Association for the Education of Young Children .
   Google Scholar
• Ewers-Rogers , J. and Cowan , R. 1996 . Children as apprentices to number . Early Childhood Development and Care , 125 : 15.15 – 15.17 .
   Google Scholar
• Fitz-Gibbon , T. and Lyons Morris , L. 1987 . How to Analyse Data , London : Sage Publications .
   Google Scholar
• Fuson , K. and Hall , J. 1983 . “ The acquisition of early number word meanings ” . In The Development of Children's Mathematical Thinking , Edited by: Ginsberg , H. New York : Academic Press . in
   Google Scholar
• Fein , S. 1997 . “ Baby Art: art is me ” . In Reflections on Early Education and Care, Early Education Papers , Edited by: Gura , P. 1 – 11 . London : British Association for Early Childhood Education . cited in D. Selleck
   Google Scholar
• Gardner , H. 1980 . Artful Scribbles: The Significance of Children's Drawings , New York : Basic Books .
   Google Scholar
• Gifford , S. 1990 . Young children's representations of number operations . Mathematics Teaching , 132 September : 64 – 71 .
   Google Scholar
• Gelman , R. and Gallistel , C.R. 1978 . The Child's Understanding of Number , Cambridge, MA : Harvard University Press .
   Google Scholar
• Glaser , B. and Strauss , A. 1967 . The Discovery of Grounded Theory , Chicago, IL : Aldine .
   Google Scholar
• Goodman , K. 1986 . What's Whole in Whole language? , London : Scholastic .
   Google Scholar
• Hughes , M. 1986 . Children and Number: Difficulties in Learning Mathematics , Oxford : Blackwell .
   Google Scholar
• Kellog , R. 1969 . Analysing Children's Art , Palo Alto, CA : National Press Books .
   Google Scholar
• Hall , N. 1987 . The Emergence of Literacy , London : Hodder and Stoughton .
   Google Scholar
• Hoshmand , L.T. 1989 . Alternate research paradigms: A review and teaching proposal . Counselling Psychologist , 17 : 3 – 79 .
   Web of Science ®Google Scholar
• Kress , G. 1997 . Before Writing: Re-thinking the Paths to Literacy , London : Routledge .
   Google Scholar
• Malchiodi , C. 1998 . Understanding Children's Drawings , London : Jessica Kingsley .
   Google Scholar
• Matthews , J. 1999 . The Art of Childhood and Adolescence: The Construction of Meaning , London : Falmer Press .
   Google Scholar
• Montague-Smith , A. 1997 . Mathematics in Nursery Education , London : David Fulton .
   Google Scholar
• Munn , P. 1997 . “ Children's beliefs about counting ” . In Teaching and Learning Early Number , Edited by: Thompson , I. Buckingham : Open University Press . in
   Google Scholar
• Oers , B. van . 1994 . Semiotic activity of young children in play: the construction and use of schematic representations . European Early Childhood Education Research Journal , 2 ( 1 ) : 19 – 33 .
   Google Scholar
• Oers , B. van . 1997 . The narrative nature of young children's iconic representations: some evidence and implications . International Journal of Early Years Education , 5 ( 3 ) : 237 – 245 .
   Google Scholar
• OFSTED . 2002 . The First Three Years of the National Numeracy Strategy , London : HMI .
   Google Scholar
• Pengelly , H. 1986 . Learning to write mathematics by writing mathematics unpublished article
   Google Scholar
• Figure 10: Joe: 3 years 11 monthsFIGURE 10: Joe: 3 years 11 monthsFIGURE 10: Joe: 3 years 11 months . 1989 . “ Phenomenological research methods ” . In Existential-Phenomenological Perspectives in Psychology , Edited by: Valle , R.S. and Halling , S. New York : Plenum . in
   Google Scholar
• Pound , L. 1999 . Supporting Mathematical Development in the Early Years , Buckingham : Open University Press .
   Google Scholar
• QCA . 1999 . Teaching Written Calculations , London : Qualifications and Curriculum Authority . National Numeracy Strategy
   Google Scholar
• QCA . 2000 . Curriculum Guidance for the Foundation Stage , London : Qualifications and Curriculum Authority .
   Google Scholar
• Selleck , D. 1997 . “ Baby art: art is me ” . In Reflections on Early Education and Care , Edited by: Gura , P. London : British Association for Early Childhood Education . in
   Google Scholar
• Stenhouse , L. 1980 . Curriculum research and the art of the teacher . Curriculum , 1 ( 1 ) : 40 – 44 . Spring 1980
   Google Scholar
• Sophian , C. 1995 . Children's Numbers , Madison, Wisconsin : Brown and Benchmark .
   Google Scholar
• Torrance , H. 2001 . Assessing for learning: developing formative assessment in the classroom . Education , 29 ( 30 ) October : 26 – 42 . 3–13
   Google Scholar
• Torrance , H. and Pryor , J. 1998 . Investigating Formative Assessment: Teaching, Learning and Assessment in the Classroom , UK : OU Press .
   Google Scholar
• Trevarthen , C. 1988 . The Art of Childhood and Adolescence: the Construction of Meaning , Edited by: Matthews , J. London : Falmer Press . 1990
   Google Scholar
• Vygotsky , L.S. 1983 . “ The prehistory of written language ” . In The Psychology of Written Language , Edited by: Martlew , M. Chichester : John Wiley . in
   Google Scholar
• Vandersteen , G. November 2002 . “ Children's own methods of recording number ” . In Mathematics in Schools November , 2002
   Google Scholar
• Williams , H. 1997 . “ Developing Numeracy in the Early Years ” . In Teaching Numeracy , Edited by: Merttens , R. Leamington Spa : Scholastic . in
   Google Scholar
• Worthington , M. and Carruthers , E. 2003a . Children's Mathematics: Making Marks Making Meaning , London : Paul Chapman Publishing .
   Google Scholar
• Worthington , M. and Carruthers , E. Becoming Bi-Numerate: a study of teachers' practices concerning children's early ‘written’ mathematics . Paper presented at the 2003 European Early Childhood Conference . Glasgow, , Scotland : University of Strathclyde .
   Google Scholar
• Worthington , M. 2004 . Issues of collaboration and co-construction within an online discussion forum: information ecologies for CPD . Mirandanet E-Journal , January Research jointly funded by the DfES & GTC. http://www.e-magine.org.uk/publications_ejournal.htm
   Google Scholar