In order to well understand and use the abstract symbolic 

language of mathematics, above all, young children need to

be free to communicate their mathematical thinking in their own ways.

The 'Goldilocks principle'

          This refers to babies and young children's "preference to attend to events that are neither too simple nor too complex, according to their current representation of the world" (Kidd et al., 2012).

      Children's Mathematical Graphics meets the criteria of the 'Goldilocks principle'. Rather than teachers planning what and how young children should write or represent their mathematics, children's own mathematical graphics provide opportunities to explore their thinking in ways of their own choosing, and to engage in learning that is 'just right'.

      In kindergarten or school (depending on the children's ages), teachers may ask the children to write or represent something mathematical. Rather than copying something the teacher has given them or completing worksheets, blank paper or  whiteboards at a low hight, provide the very best opportunities for children to explore their own thinking in their own ways, and make personal sense of mathematical signs, symbols and meaningful ways of representing, such as problem solving, calculations or data handling. 

Child-initiated pretend play offers potentially rich contexts for children to communicate their mathematical thinking through their mathematical graphics (Worthington & van Oers, 2016). It also allows children to connect with their existing cultural knowledge, or 'funds of knowledge' (Moll et al., 1992).

References

Kidd, C., Piantadosi, S. T., Aslin., & R. N. (23 May 2012). "The Goldilocks Effect: Human Infants Allocate Attention to Visual Sequences That Are Neither Too Simple Nor Too Complex". PLOS ONE. 7 (5).

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. 

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