Young children’s graphical sign lexicons and the emergence of mathematical symbols

MAULFRY WORTHINGTON

Abstract

Young children’s personal repertoires or lexicons of graphical signs comprise multiple and diverse signs. These signs support understanding and progress of the symbolic languages of the culturally established, alphanumerical systems, development evolving early in childhood. Investigating language and inscriptional systems - including drawn, written and mathematical - this evidence-based position paper explores the extent to which children’s graphical sign lexicons support their emergent understandings as they move from intuitive marks and informal signs to formal symbols. These inscriptions are indispensable in communicating ideas, and have significance for the study of young children’s understanding of the abstract symbolic language of mathematics.

Keywords

Early childhood, graphical sign lexicons, repertoires, children’s mathematical graphics, emergent learners

Full Text:

PDF

References

Athey, C. (2007). Extending thought in young children: A parent-teacher partnership. London, England: Sage.

Anning, A. (2003). Pathways to the graphicacy club: The crossroad of home and pre-school. Journal of Early Childhood Literacy, 3(1), 5-35.

Blinkoff, E., & Hirsh-Pasek, K. (2019). Supporting language in the home. International Journal of Birth and Parent Education, 6(4), 13-15.

Brandt, A., & Chernoff, E. J. (2014). The importance of ethnomathematics in the math class. Ohio Journal of School Mathematics, 71, 31-36.

Buchler, J. (Ed.). (1955). Philosophical writings of Peirce. London: Dover Publications.

Bybee, J. (1998). The emergent lexicon. Chicago Linguistic Society 34, 421-435.

Carruthers, E. (1997). Number: A developmental theory; a case study of a child from 20 to 44 months. Masters Thesis, University of Plymouth, England.

Carruthers, E. (2015). Listening to children’s mathematics in school. In R. Perry, A. MacDonald & A. Gervasoni (Eds.), Mathematics and transition to school: International perspectives (pp. 313-330). Sydney, Australia: Springer.

Carruthers, E. (in process). The pedagogy of children’s mathematical graphics. Doctoral dissertation, University of Bristol, Bristol, England.

Carruthers, E., & Worthington, M. (2005). Making sense of mathematical graphics: The development of understanding abstract symbolism. European Early Childhood Education Research Journal, 13(1), 57-79.

Carruthers, E., & Worthington, M. (2006). Children’s mathematics: Making marks, making meaning. London, England: Sage.

Carruthers, E., & Worthington, M. (2011). Understanding children’s mathematical graphics: Beginnings in play. Maidenhead, England: Open University Press/McGraw Hill Education.

Clay, M. (1975). What did I write? London, England: Heinemann.

Cohn, N. (2012). Explaining ‘I can’t draw’: Parallels between the structure and development of language and drawing. Human Development, 55(4), 167-192.

Cook, D. (2001). ‘You can't have a cake unless it's written down’: Semiotic activity and authentic learning in play as a potential tool for analysis, Early Child Development and Care, 168(1), 49-62.

Emfinger, K. (2009) Numerical conceptions reflected during mutilage child-initiated pretend play. Journal of Instructional Psychology, 36(4), 326-334.

Ernest, P. (2005). Activity and creativity in the semiotics of learning mathematics. In M. Hoffmann, J. Lenhard & F. Seeger (Eds.), Activity and sign: Grounding mathematics education (pp. 23-34). London, UK: Springer.

Ernest, P. (2018). The ethics of mathematics: Is mathematics harmful? In P. Ernest (Ed.), The philosophy of mathematics education today (pp. 187-216). Switzerland: Cham.

Ferreiro, E., & Teberosky, A. (1979). Literacy before schooling. London, England: Heinemann Educational.

Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155-177.

Ginsburg, H. (1977). Children's arithmetic: The learning process. Oxford, England: Van Nostrand.

Greeno, J. G., & Hall, R. P. (1997). Practicing representation: Learning with and about representational forms. The Phi Delta Kappan, 78(5), 361-367.

Hiebert, J. (1984). Children's mathematics learning: The struggle to link form and understanding. The Elementary School Journal, 8(5), 497-513.

Hoff, E., & Naigles, L. (2002). How children use input to acquire a lexicon. Child Development, 73(2), 418-433.

Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Buckingham, England: Open University Press.

Johnston, J. (2010). Factors that influence language development. In R. E. Tremblay, M. Boivin & R. De V. Peters. (Eds.), Encyclopedia on Early Childhood Development [online] (pp. 1-6). Montreal, Quebec: Centre of Excellence for Early Childhood Development and Strategic Knowledge.

Kale, M., Nur, I., & Aslan, D. (2018). Theoretical framework to examining mathematical experiences in early childhood: Sociomathematical niche. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 12(2), 1-30.

Kamii, C., & DeClark, G. (1985). Young children reinvent arithmetic: Implications of Piaget’s theory. New York: Teachers College.

Kress, G. (1997). Before writing: Rethinking the paths to literacy. London, England: Routledge.

Lancaster, L. (2003). Moving into literacy: How it all begins. In N. Hall, J. Larson & J. Marsh (Eds.), Handbook of early childhood Literacy (pp. 145-153). London, England: Sage.

Lancaster, L. (2007). Representing the ways of the world: How children under three start to use syntax in graphic signs. Journal of Early Childhood Literacy, 7(2), 123-154.

Lancaster, L. (2014). The emergence of symbolic principles: The distribution of mind in early sign making. Biosemiotics, 7(1), 29-47.

Langacker, R. (2008). Cognitive grammar: A basic introduction. Oxford, England: Oxford University Press.

Lehrer, R., & Lesh, R. (2003). Mathematical learning. In W. M. Reynolds & G. E. Miller (Ed.), Handbook of Psychology, Volume 7, Educational Psychology, (pp. 357-390). New Jersey: Wiley.

Levin, I., & Bus, A. G. (2003). How is emergent writing based on drawing? Analyses of children's products and their sorting by children and mothers. Developmental Psychology, 39(5), 891-905.

Machón, A. (2013). Children’s drawings: The genesis and nature of graphic representation. Madrid, Spain: Fibulas Publishers.

Matthews, J. (1999). The art of childhood and adolescence: The construction of meaning. London, England: Farmer.

Matthews, J. (2006). Foreword. In E. Carruthers & M. Worthington (Eds.), Children’s mathematics: Making marks, making meaning (pp. xiii-xiv). London, England: Sage.

Merkley, R., & Ansari, D. (2016). Why numerical symbols count in the development of mathematical skills: Evidence from brain and behaviour. Current Opinion in Behavioural Science, 10, 14-20.

Moll, C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory into Practice, 31(2), 132-141.

Munn, P., & Schaffer, H. R. (1993). Literacy and numeracy events in social interactive contexts. International Journal of Early Years Education, 1(3), 61-80.

Nation, K. (2014). Lexical learning and lexical processing in children with developmental language impairments. Philosophical Transactions of the Royal Society, B, 369, 20120387.

Papandreou, M. (2019). Young children’s representational practices in the context of self-initiated data investigations. Early Years: An International Journal of Research and Development. Retrieved from https://www.tandfonline.com/doi/full/10.1080

/09575146.2019. 1703101.

Papandreou, M., & Tsiouli, M. (2020). Noticing and understanding children’s everyday mathematics during play in early childhood classrooms. International Journal of Early Years Education. Retrieved from https://www.tandfonline.com/doi/full/10.1080/09669760.2020.

Pascal, C., Bertram, T., & Rouse, L. (2019). Getting it right in the foundation stage: A review of the evidence. St Albans, England: Early Education.

Price, S., Jewitt, C., & Crescenci, L. (2015). The role of iPads in pre-school children's mark making development. Computers in Education, 87, 131-141.

Rieber, R., & Robinson, D. (Eds.). (2004). The essential Vygotsky. New York: Kluwer Academic/Plenum.

Rogoff, B. (2003). The cultural nature of human development. New York: Oxford University Press.

Stipek, D. (2013). Mathematics in early childhood education: Revolution or evolution? Early Education & Development, 24(4), 431-435.

Thomas, N. D., Mulligan, J. T., & Goldin, G. A. (2002). Children’s representation and structural development of the counting sequence 1-100. Journal of Mathematical Behaviour, 21, 117-133.

Tolchinsky, L. (2003). The cradle of culture and what children know about writing and numbers before being taught. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Tomasello, M. (2003). Constructing a language: A usage-based theory of language acquisition. Cambridge, MA: Harvard University Press.

Van Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46(1-3), 59-85.

Van Oers, B. (2005). The potentials of imagination. Inquiry: Critical thinking across the disciplines, 24(4), 5-17.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, Mass: Harvard University Press.

Werner, H., & Kaplan, B. (1963). Symbol formation. An organismic-developmental approach to the psychology of language. London, UK: Lawrence Erlbaum Associates.

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.

Worthington, M. (2010). Play is a complex landscape: Imagination and symbolic meanings. In P. Broadhead, J. Howard & E. Wood (Eds.), Play and learning in the Early Years (pp. 127-144). London, England: Sage.

Worthington, M. (2018). Funds of knowledge: Children’s cultural ways of knowing mathematics. In M.-Y. Lai, T. Muir & V. Kinnear (Eds.), Forging connections in early mathematics teaching and learning (pp. 239-258). Singapore: Springer Nature.

Worthington, M. (in process). The emergence and development of young children’s mathematical inscriptions: A natural history of signs. Doctoral Thesis, VU University, Amsterdam.

Worthington, M., & Van Oers, B. (2016). Pretend play and the cultural foundations of mathematics. European Early Childhood Education Research Journal, 24(1), 51-66.

Worthington, M., & Van Oers, B. (2017). Children’s social literacies: Meaning making and the emergence of graphical signs and texts in pretence. Journal of Early Childhood Literacy, 17(2), 147-175.

Worthington, M., Dobber, M., & Van Oers, B. (2019). The development of mathematical abstraction in the nursery. Educational Studies in Mathematics, 102, 91-110.

Worthington, M., Dobber, M., & Van Oers, B. (submitted). Intertextuality in young children’s inscriptions and their transformations into mathematical symbols. Mathematical Thinking and Learning.


DOI: https://doi.org/10.26220/rev.3368

View Counter: Abstract | 212 | times, and PDF | 73 | times



Re S M ICT E | ISSN: 1792-3999 (electronic), 1791-261X (print) | Laboratory of Didactics of Sciences, Mathematics and ICT, Department of Educational Sciences and Early Childhood Education - University of Patras.

Pasithee | Library & Information Center | University of Patras