We began thinking deeply about young children’s mathematics when (in the early nineties) we were both experienced, practising teachers in the early years. One aspect of our growing understanding of children’s mathematics, was how children can use their own ways of representing their mathematical thinking, provided their own thinking and meaning-making are valued and understood. Within our own classrooms, we saw that children could better understand and communicate their mathematical thinking through their own inscriptions more readily, than when using worksheets or any standard calculations presented to them. 

Influences

     Our research has its roots in authentic classroom practice and was initially influenced by approaches that acknowledged the emergent nature of children’s learning, known as emergent writing (e.g., Clay, 1975), to explore the extent to which an emergent approach to mathematical signs and symbols might also be possible.

     Our second early and significant influence was the work of Martin Hughes (1986). We built on his research by going further than the ‘tins game’ and extending our analysis beyond quantities that are counted. We were also mindful that Hughes did not focus on the pedagogy of children’s mathematics which is so vital for teachers who want to understand and support children’s own mathematics. To support teachers, our book Children’s Mathematics: Making marks, making meanings (2003; 2nd edition, 2006) was published, followed by Understanding Children’s Mathematics: Beginnings in Play (2011).

      We published our first peer-referenced academic paper (Carruthers & Worthington, 2005 - followed by many more since), in which we tracked the development of children’s mathematical signs and symbols from their earliest graphical marks to children’s own methods for calculations, publishing our taxonomy of this (the first time that young children's mathematical notations had been charted) in the same paper, and in our 2003, 2006 and 2011 books. Since our early beginnings, we have been particularly influenced by Vygotsky’s work and his socio-cultural theory.

      In one of our many discussions, we were unsure about what to term children’s own mathematical signs and symbols, deciding on the term Children's Mathematical Graphics since it encompasses all the marks, signs and symbols that we had already identified, and emphasises that the graphics to which we refer are the children's own. 

Recent research

     For her doctorate, Maulfry focused in depth on the genesis of Children’s Mathematical Graphics in open social and cultural contexts, concentrating particularly on free and spontaneous pretend play (Worthington, 2021) and Elizabeth focused on the pedagogy of children’s mathematics in her doctoral thesis (Carruthers, 2022). 

     We are the originators of the term Children’s Mathematical Graphics (in 2003) and its associated development, research and pedagogy, developed over more than the past 30 years. 

Carruthers, E. (2022). The Pedagogy of Children's Mathematical Graphics: Teacher perspectives. [Doctoral Dissertation]. University of Bristol.

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.

Clay, M. M. (1975). What did I Write? Beginning writing behaviour.

Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Basil Blackwell.

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.