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 standard written language of mathematics. Language is socially learned. Children will spontaneously communicate their mathematical thinking through their speech and Mathematical Graphics in their free pretend play and in 'open' groups (and later in mathematics lessons) - provided they have genuine opportunities to do so, and 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 were also those more likely to spontaneously write Arabic number symbols (SWANS).

     Significantly, those who most frequently engaged in free, pretend play, most often chose to use their Mathematical Graphics to communicate their mathematical thinking. Importantly, intertextuality, i.e., learning from and with others' (peers and adults') 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).

References

Clay, M. M. (1975). What did I write? Beginning writing behaviour. Portsmouth, NH, USA. Heinemann Educational.

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. (2023). 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.

Wood, E. (2019). Unbalanced and unbalancing acts in the Early Years Foundation Stage: a critical discourse analysis of policy-led evidence on teaching and play from the office for standards in education in England (Ofsted). Education 3-13, 47(7), 784–795.

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. 

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., Dobber, M., & van Oers, B. (2023). Intertextuality and the advance of mathematisation in young children’s inscriptions. Research Papers in Education.