We learn language by using language (Tomasello, 2003). 

The more children communicate their thinking through graphicacy, the more readily they come to understand the abstract written language of mathematics. Language is socially learned. Children will spontaneously communicate their mathematical thinking through their Mathematical Graphics and speech -  in their free pretend play - provided adults in their setting are interested and supportive.

The focal point of my PhD (Maulfry)

   - was the emergence and development of 3 and 4-year-olds' mathematical inscriptions (i.e., Children's Mathematical Graphics) and their development in the children's spontaneous and free pretend play (Worthington, 2021). My research is underpinned by Vygotskian socio-cultural and social semiotic theory. Four distinct chapters provided the main section (click on the following links):

• Pretend play and the cultural foundations of mathematics; 

• Children's social literacies: Meaning making and the emergence graphical signs and texts in pretence;

• The development of mathematical abstraction in the nursery; 
• Intertextuality and the advance of mathematisation in young

         children's inscriptions.

Among a number of findings, I identified the open and democratic culture of the early childhood setting as the most significant contribution that teachers can make to support young children’s mathematical understandings.

        Other important findings included the powerful context of spontaneous pretend play, in which children drew on their 'funds of knowledge'. Furthermore, children with the most extensive graphical lexicons were at an advantage in using graphical signs to communicate their thinking, and that those who had developed the most extensive lexicons of graphical signs, were also those who spontaneously wrote Arabic number symbols (SWANS). Importantly, intertextuality (i.e., learning from and with others' signs and texts) played a highly significant role in the children's developing thinking and understanding of mathematical sign use.

The results of this research -

      "... substantiate its socio-cultural hypothesis of the genesis of mathematical thinking as a social-semiotic process, describing the emergence and evolution of children's mathematical thinking, stimulated by communication with more knowledgeable others, rather than Piaget's view of cognitive structures and their interaction in the environment. It shows that within rich pretend play, young children's development of mathematical sign use can be much more thorough and far-reaching, than has been found in previous studies" (Worthington, Dobber & van Oers, emphasis added, 2023).

Pretend play and children's mathematical graphics

See also:  

    Moll, L. Amanti, C., Neff, D., & Gonzales, N. (1992). Funds of knowledge for teaching: Using a

qualitative approach to connect homes and classrooms. Theory into Practice, 31(2), 132-141.

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

     van Oers, B. (2024). The development of mathematical thinking in young children’s play: The role of communicative tools. In: Palmér, H., Björklund, C., Reikerås, E., Elofsson, J. (eds) Teaching Mathematics as to be Meaningful – Foregrounding Play and Children’s Perspectives. Springer, Cham.

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

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

    Worthington, M. (2021). The emergence and development of young children’s personal mathematical inscriptions: The evolution of graphical signs explored through children’s spontaneous pretend play. [Doctoral Dissertation]. Vrije Universiteit, Amsterdam.