Funds of Knowledge: Children’s Cultural Ways of Knowing Mathematics
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In the prevailing global climate, many teachers feel pressured to demonstrate children’s ‘basic skills’ that often result in direct teaching and a marginalization of play, and widespread orthodoxy means that direct teaching of mathematical notations continues, often causing children considerable problems. Yet research has shown that the beginnings of the abstract symbolic language of mathematics have their roots in young children’s home cultural experiences, extended in meaningful contexts of pretend-play and other child-initiated activities. This chapter draws on findings from recent doctoral research into the beginnings of young children’s mathematical semiosis in their homes and nursery school, revealing the power of their mathematical thinking and understandings expressed through their graphical communications. The chapter focuses on the social and cultural contexts of home and pretend-play, the children’s mathematical graphics underpinned by Vygotsky’s cultural–historical theory, and his dialectical view of relationships between play and symbolic tool-use. Understandings of the abstract symbolic language of mathematics are social and cultural, this chapter arguing that children’s personal mathematical communications evolve over time. Competency develops as a continuum, revealing how children’s early understandings contribute to subsequent mathematical notations. This study chapter uncovers the beginnings of abstraction in early childhood mathematics, focusing on the importance of children’s interests and their cultural knowledge in underpinning their subject knowledge. It argues that spontaneous, social pretend-play be better understood for supporting children’s interests and for its mathematical potential, and for children’s mathematics be prioritized in early childhood curricula so that their existing competencies and informal representations are valued and understood.
KeywordsCultural knowledge Children’s interests Pretend-play Preschool Informal mathematics
Sincere thanks go to the children, parents, staff and headteacher of Redcliffe maintained nursery school, Bristol, for sharing the children’s inspirational play and mathematical thinking.
- Aubrey, C. (1997). Mathematics teaching in the early years. London: Falmer Press.Google Scholar
- Bertram, T., & Pascal, C. (2002). What counts in early learning? In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on early childhood curriculum (pp. 241–259). Greenwich, CT: Information Age Publishing.Google Scholar
- Broadhead, P., & Burt, A. (2012). Understanding young children’s learning through play. Abingdon, Oxon: Routledge.Google Scholar
- Brooker, L. (2010). Learning to play, or playing to learn? In L. Brooker. & S. Edwards. (Eds.), Engaging play (pp. 39–52). Maidenhead: Open University Press.Google Scholar
- Carr, M. (2001). Assessment in early childhood settings: learning stories. London: Sage Publications.Google Scholar
- Carruthers, E. (1997). Number: a developmental theory: a case study of a child from 20 to 44 months. Unpublished Masters (M. Ed.) Dissertation. University of Plymouth.Google Scholar
- Carruthers, E. (2015). Listening to children’s mathematics in school. In B. Perry., A. Gervasoni., & A. MacDonald. (Eds.), Mathematics and transition to school—International perspectives (pp. 313–330). Sydney, Australia: Springer.Google Scholar
- Carruthers, E., & Worthington, M. (2006). Children’s mathematics: Making marks, making meaning. London: Sage Publications.Google Scholar
- Carruthers, E., & Worthington, M. (2008). Children’s mathematical graphics: calculating for meaning. In I. Thompson, (Ed.), (2008) Teaching and Learning Early Number. Maidenhead: Open University Press, (2nd ed.).Google Scholar
- Carruthers, E., & Worthington, M. (2011). Understanding children’s mathematical graphics: Beginnings in play. Maidenhead: Open University Press.Google Scholar
- Carruthers, E., & Worthington, M. (2013). Taxonomy charting children’s mathematical graphics. http://www.childrens-mathematics.org.uk/taxonomy.pdf.
- Christie, J., & Roskos, K. (2009). Play’s potential in early literacy development. Encyclopedia on Early Childhood Development. http://www.childencyclopedia.com/sites/default/files/dossiers-complets/en/play.pdf#page=31.
- Clayden, E., Desforges, C., Mills, C., & Rawson, W. (1994). Authentic activity and learning. Journal of Education Studies, 42(2), 163–173.Google Scholar
- Corsaro, W. (2005). The sociology of childhood. London: Sage.Google Scholar
- Curtis, A. (1998). A curriculum for the preschool child (2nd ed.). London: Routledge.Google Scholar
- David, M. M., & Watson, A. (2008). Participating In what? Using situated cognition theory to illuminate differences in classroom practices. In A. Watson, A., & P. Winbourne (Eds.), New directions for situated cognition in mathematics (pp. 31–56). London: Springer.Google Scholar
- DCSF. (2009). Children thinking mathematically: PSRN essential knowledge for early years practitioners. London: DCSF. http://childrensmathematics.net/childrenthinkingmathematically_psrn.pdf.
- DfE. (2013). Early years foundation stage profile: Handbook. London: Standards and Testing Agency, https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/301256/2014_EYFS_handbook.pdf.
- DfE. (2014). Statutory framework for the early years foundation stage. http://dera.ioe.ac.uk/19831/1/DFE-00337-2014.pdf. Accessed 5th July 2016.
- Drummond, M. J., & Jenkinson, S. (2009). Meeting the child. Approaches to observation and assessment in Steiner kindergartens. Plymouth: The University of Plymouth.Google Scholar
- Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children’s mathematics. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Vol. 2. Tools and processes in mathematics teacher education (pp. 257–281). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
- Garrick, R. (2012). Pretend play: the affordances of flexible spaces, places and things for an interest based curriculum. Draft paper presented at the British Educational Research Association Annual Conference, University of Manchester, 4–6 September 2012.Google Scholar
- Gifford, S. (2005). Teaching mathematics 3-5. Maidenhead: Open University Press.Google Scholar
- Gmitrova, V., & Gmitrov, J. (2003). The impact of teacher-directed and child-directed pretend play on cognitive competence in kindergarten children. Early Childhood Education Journal, 30(4), 241–246 (Summer).Google Scholar
- Göncü, A. (Ed.). (1999). Children’s engagement with the world. Cambridge: Cambridge University Press.Google Scholar
- Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Oxford: Basil Blackwell.Google Scholar
- Lakoff, G., & Nunez, R. (2001). Where mathematics come from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
- Machón, A. (2013). Children’s drawings: The genesis and nature of graphic representation. Madrid: Fibulas Publishers.Google Scholar
- Marcon, R. (2002). Moving up the grades: Relationships between preschool model and later school success. Early Childhood Research & Practice, 4(1). http://www.ecrp.uiuc.edu/v4n1/marcon.html.
- Ministry of Education. (1996). Te Whäriki. He whäriki mätauranga mō ngä mokopuna o Aotearoa: Early Childhood Curriculum. Wellington: Learning Media. http://www.education.govt.nz/early-childhood/teaching-and-learning/ece-curriculum/te-whariki/.
- Moyles, J., Adams, S., & Musgrove, A. (2002). SPEEL study of pedagogical effectiveness in early learning. http://www.dfes.gov.uk/research/data/uploadfiles/RR363.pdf.
- Moyles, J., & Worthington, M. (2011). The early years foundation stage through the daily experiences of children’ TACTYC Occasional Paper No. 1. http://tactyc.org.uk/occasional-paper/occasional-paper1.pdf.
- Munn, P., & Kleinberg, S. (2003). Describing good practice in the early years—A response to the ‘third way’. Education 3-13. International Journal of Primary, Elementary and Early Years Education, 31(2), 50–53.Google Scholar
- National Agency for Education. (2011). Curriculum for the Preschool Lpfö 98, Revised 2010. Stockholm: Frizes. http://skolverket.se/publikationer?id=2704.
- Nutbrown, C. (1999). Threads of thinking (2nd ed.). London: Paul Chapman.Google Scholar
- OECD. (2006). Starting strong II: Early child education and care. Paris, France: OECD Publishing. http://www.unicef.org/lac/spbarbados/Implementation/ECD/StartingStrongII_OECD_2006.pdf.
- Poland, M. (2007). The treasures of schematising. Doctoral dissertation. Amsterdam: VU University.Google Scholar
- Rogers, S. (2010). Powerful pedagogies and playful resistance. In L. Brooker & S. Edwards (Eds.), Engaging play (pp. 152–165). Maidenhead: Open University Press.Google Scholar
- Rogoff, B. (2003). The cultural nature of human development. Oxford: Oxford University Press.Google Scholar
- Rogoff, B. (2008). Observing sociocultural activity on three planes. In P. Murphy, K. Hall & J. Soler. (Eds.), Pedagogy and practice: Culture and identities (pp. 58–74). London: Sage Publications.Google Scholar
- Smith, P. (2010). Children and play. Chichester: Wiley-Blackwell.Google Scholar
- Street, B., Baker, D., & Tomlin, A. (2008). Navigating numeracies: Home/school numeracy practices. London: Springer.Google Scholar
- Tizard, B., & Hughes, M. (1984). Young children learning: Talking and thinking at home and at school. London: Fontana.Google Scholar
- van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 521–525). Dordrecht, Heidelberg: Springer.Google Scholar
- van Oers, B. (2012). How to promote young children’s mathematical thinking? Mediterranean Journal for Research in Mathematics Education, 11(1–2), 1–15.Google Scholar
- Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.Google Scholar
- Vygotsky, L. S. (1998). Child psychology. In L. S. Vygotsky. The collected works of L. S. Vygotsky. Vol. 5. New York: Kluwer Academic and Plenum Publishers.Google Scholar
- Wood, E. (2010). Reconceptualizing the play-pedagogy relationship. In L. Brooker & S. Edwards (Eds.), Engaging play (pp. 11–24). Maidenhead: Open University Press.Google Scholar
- Worthington, M. (2009). Fish in the water of culture: Signs and symbols in young children’s drawing. Psychology of Education Review, 33(1), 37–46.Google Scholar
- Worthington, M. (2010). Play is a complex landscape: Imagination and symbolic meanings. In P. Broadhead, L. Wood. & J. Howard. (Eds.), Play and learning in educational settings (pp. 127–144). London: Sage Publications.Google Scholar
- Worthington, M. (2012). Children becoming expert symbol users. In M. McAteer (Ed.), Improving primary mathematics teaching and learning (pp. 39–57). Maidenhead: Open University Press.Google Scholar
- Worthington, M. (2015a). Mathematics and the ecology of pretend play. In J. Moyles. (Ed.), The excellence of play (pp. 237–249). 4th Ed. Maidenhead: Open University Press.Google Scholar
- Worthington, M. (2015b). Young children’s informal mathematical signs and symbols: cultural learning and ‘intent participation’. Presentation at the European Early Childhood Education Research Association (EECERA) conference. Barcelona, 07–10 September.Google Scholar
- Worthington, M., & Carruthers, E. (2003). Children’s mathematics, making marks, making meaning. London: Paul Chapman Publishing.Google Scholar
- Worthington, M., & van Oers, B. (2015). Children’s social literacies: Meaning making and the emergence of graphical signs and texts in pretence. Journal of Early Childhood Literacy. Published online December 2015. http://ecl.sagepub.com/content/early/2015/12/09/1468798415618534.full.pdf+html.
- Worthington, M., & van Oers, B. (Forthcoming). The emergence of abstraction in the nursery. Educational Studies in Mathematics.Google Scholar