Children's Mathematical Graphics | Mathematics | Play | Multi-modality | Drawing and Visual Representations | Schemas | Other

Children's Mathematical Graphics (including various publications on children's mathematical representations; 'emergent maths' and children's own written methods)

Allardice, B. (1997) ‘The development of written representations for some mathematical concepts’, Journal of Children’s Mathematical Behaviour, 1 (4) 135-48

Anghileri, J. (2001) ‘A study of progression in written calculations and division’, Support for Learning, 16, (1) 17-22.

Anghileri, J. (2002) ‘From informal strategies to structured procedures: mind the gap!’ in Educational Studies in Mathematics, 49: 149-170.

Atkinson, S. (2002) Maths with Reason, London: Hodder and Stoughton.

Brizuela, B. (2004) Mathematical Development in Young Children: Exploring Notations, New York: Teachers’ College Press.

Carruthers, E. and Worthington, M. (2006) (2^nd ed.) Children’s Mathematics: Making Marks, Making Meaning. London: Sage Publications

Other publications on children’s mathematical graphics by Carruthers and Worthington

Gifford, S. (1990)’Young children’s representations of number operations’, Mathematics Teaching, 132, 64-71, September.

Gifford, S. (1997) ‘“When should they start doing sums?”  A critical consideration of the emergent mathematics approach’, in I. Thompson, (ed.) Teaching and Learning Early Number, Buckingham: Open University Press.

Hughes, M. (1986) Children and Number: Difficulties in Learning Mathematics. Oxford: Blackwell.

Jacoby, S. (2005) ‘Thoughts on Emergent Mathematics’, Mathematics Teaching, 193, December.

Mark-Zigdon, N. and Tirosh, D. (2008) 'Kindergarten and first graders' knowledge of the number symbols: production and recognition' (Report) in Focus on Learning Problems in Mathematics, (January)

McClellan, E. (2001) ‘Representing addition and subtraction: learning the formal conventions’ in European Early Childhood Education Research Journal, Vol. 9, No. 1, 73 – 84.

Poland, M. and Van Oers, B. (2007) 'Effects of schematising on mathematical development' in European Early Childhood Education Research Journal, Vol. 15, N0. 2, June 2007, 269-293

Pound, L. (2006) (2^nd ed.) Supporting Mathematical Development in the Early Years, Maidenhead: Open University Press / McGraw Hill.

van Oers B.  see http://home.planet.nl/~oers0054/English default.htm (publications)

Vandersteen, G. (2002) ‘Children’s own methods of recording number: “I will do two writings”’, Mathematics in school, November: 2 - 8

Whitebread, D. (1995) ‘’Emergent mathematics or how to help young children become confident mathematicians’, in J. Anghileri. (ed), (1995) Children’s Mathematical Thin king in the Early Years, London: Cassell.

Whitin, Mills and O’Keefe, (1990) Living and Learning Mathematics: Stories and Strategies for Supporting Mathematical Literacy. Portsmouth, NH: Heinemann.

Williams, H. (1997) ‘Developing numeracy in the Early Years’, in R. Merttens (ed.) Teaching Numeracy, Leamington Spa: Scholastic.

Wilkinson, M. and Stoessiger, R. (1991) ‘Emergent Mathematics’ Education 3 – 13. 19 (1) 3–11, (* this was the first article that referred to the Emergent Mathematics Teachers Group of which Elizabeth Carruthers and Maulfry Worthington were founder members).

Mathematics

Atkinson, S. (ed.) (1992) Mathematics with Reason, London: Hodder Arnold.

Anghileri, J. (ed.) (1995) Children's Mathematical Thinking in the Primary Years, London: Cassell.

Anghileri, J. (2000) Teaching Number Sense, London: Continuum.

Brizuela, B. (2004) Mathematical Development in Young Children: Exploring Notations, Columbia University: Teachers College Press.

Carruthers, E. and Worthington, M. (2006) Children’s Mathematics: Making Marks, Making Meaning. London: Sage Publications, (2nd. Ed)

Ernest, P. (1991) The Philosophy of Mathematics Education, London: Falmer Press.

Gelman, R. and Galistel, C. (1986) The Child's Understanding of Number, Cambridge, Mass : Harvard University Press.

Gifford, S. (2005) Teaching Mathematics 3 - 5: Developing Learning in the Foundation Stage, Maidenhead: OU Press.

Gulliver, G. (1994) Key speech at Emergent Mathematics conference, Exeter University

Hughes, M. (1986) Children and Number: Difficulties in Learning Mathematics. Oxford: Blackwell.

Nunes, T. and Bryant, P. (1996) Children doing Mathematics, Oxford, Blackwell.

Pound, L. (2006) Supporting Mathematical Development in the Early Years, (2nd Ed), Maidenhead: OU Press.

Sophian, C. (1996) Children's Numbers, Oxford: Westview.

Thompson, I. (ed.) (1997) Teaching and Learning Early Number, Buckingham, OU Press.

Tucker, K. (2005) Mathematics through Play in the Early Years: Activities and Ideas, London, Paul Chapman.

Van Oers, B. (2001) ‘Educational forms of initiation in mathematical culture’, in, Educational Studies in Mathematics, 46: 59-85.

Play

Broadhead, P. (2004) Early Years Play and Learning: Developing Social Skills and Cooperation, London: Routledge Falmer.

Bruce, T. (1991) Time to Play in Early Childhood. London: Hodder and Stoughton.

Bruce, T. (2001) Learning Through Play - Babies, Toddlers and the Foundation Years, London: Hodder and Stoughton.

Bruce, T. (2004) Developing Learning in Early Childhood, London: Paul Chapman.

Canning, N. (2007) 'Children's Empowerment in Play' in European Early Childhood Education Research Journal, Vol. 15, No. 2, June 2007

Goldschmied, E. and Jackson, S. (2004) People Under Three, London: Routledge; (2nd ed.)

Gura, P. (ed.) (1992) Exploring Learning: Young Children and Block Play, London: Paul Chapman.

Moyles, J. (1989) Just Playing? The Role and Status of Play in Early Childhood, Milton Keynes: OU Press.

Moyles, J. (ed.) (2005) The Excellence of Play, (2nd Ed), Maidenhead: OU Press.

Sylva, K., Roy, C. and Painter, M. (1986) Childwatching at Playgroup and Nursery School, Oxford: Blackwell.

Wood, E. and Atfield, J. (2005) Play, Learning and the Early Childhood Curriculum, London: Paul Chapman Publishing.

Worthington, M. (2009) 'Play is a complex landscape: imagination and symbolic meanings'; in P. Broadhead, L. Wood. and J. Howard. (Eds) Play and Learning in Educational Settings, London: Sage Publications, (in preparation)

Multi-modality

Berne, E., Ellis, S., Graham, L., Hulme, P., Merchant, G. & Mills, C. (2004) More than Words: Multi-modal Texts in the Classroom, QCA / UKLA.

Berne, E., Ellis, S., Graham, L., Hulme, P. Meiner, J. and Wolstencroft. H. (2005) More than Words 2: Creating Stories on Page and Screen, London: QCA / UKLA

Jewitt, C. and Kress, G. (2003) Multimodal Literacies (New Literacies and Digital Epistemologies, V. 4), New York: Peter Lang.

Kress, G. (1997) Before Writing: Rethinking the Paths to Literacy, London: Routledge.

Kress, G. (2003) Literacy in the New Media Age, London: Routledge.

Kress, G. and Van Leeuwen, T. (1996) Reading Images: The Grammar of Visual Design, London: Routledge.

Pahl, K. (1999) Transformations: Meaning Making in the Nursery, Stoke-on-Trent: Trentham Books.

Pahl, K. and Rowsell, J. (2005) Literacy and Education: Understanding the New Literacy Studies in the Classroom, London: Paul Chapman Publishing.

Van Leeuwen, T. and Jewitt, C. (2001) The Handbook of Visual Analysis, London: Sage Publications.

Worthington, M. (2007) '"It's my birthday bridge": multi-modal meanings through play', in: J. Moyles (Ed) Beginning Teaching, Beginning Learning, London: McGrawhill / Open University Press

Worthington, M. (2007) 'Multi-modality, play and children's mark-making in maths' in: J. Moyles, (Ed.) (2007) Early Years Foundations: Meeting the Challenge, Maidenhead: Open University Press / McGraw Hill

Drawing and Visual Representations

Anning, A. and Ring, K. (2004) Making Sense of Children's Drawings, Maidenhead: OU Press.

Atkinson, D. (2002) Art in Education: Identity and Practice, London: Kluwer Academic Publishers.

Bresler, L. and Thompson, C. (2003) The Art in Children’s Lives: Context, Culture and Curriculum, London: Kluwer Academic Publishers.

New! DCSF, (2008) 'Mark Making Matters' , London: DCSF

Efland, A. (2002) Art and Cognition: Integrating the Visual Arts in the Curriculum, New York: Teachers’ College Press.

Gardner, H. (1980) Artful Scribbles: the Significance of Children's Drawings, New York: Basic Books.

Gardner, H. (1990) Art Education and Human Development, Los Angeles: The J. Paul Getty Museum.

Kindler, A. (ed.) Child Development in Art, Reston, Virginia: National Art Education Association.

Malchiodi, C. (1998) Understanding Children’s Drawings, London: The Guilford Press.

Matthews, J. (1999) The Art of Childhood and Adolescence: The Construction of Meaning, London: Falmer Press.

Matthews, J. (2003) Drawing and Painting: Children and Visual Representation, (2nd Ed) London: Paul Chapman Publishing.

Schemas

Athey, C. (2007) (Second Edition) Extending Thought in Young Children: A Parent-Teacher Partnership. London: Paul Chapman.

Arnold, C. (1997) Observing Harry. Buckingham: OU Press.

Nutbrown, C. (2006) Threads of Thinking: Young Children Learning and the Role of Early Education, London: Sage Publications (3rd ed.).

Carruthers, E. and Worthington, M. (2006) 'Mathematical Schemas' (chapter 3) in: Children’s Mathematics: Making Marks, Making Meaning. London: Sage Publications, (2nd. Ed)

Other

Olson, D. (1994) The World on Paper: The Conceptual and Cognitive Implications of Writing and Reading, Cambridge: Cambridge University Press. *Also includes wider aspects of visual representation.

Vygotsky, L.S. (1978). Mind and Society: The Development of Higher Mental Processes. Cambridge, MA: Harvard University Press.

Vygotsky, L.S. (1986) Thought and Language, Cambridge, Mass: MIT Press. (Revised edition, edited by A. Kozulin)