Gunter Kress (2010) emphasises,'Representation is focused on myself

                                                       and my interest; communication is focused on my interest in its relation to others [...] Both representation and communication are social processes, but differently so.' How often is children's 'written' (or recorded) mathematics in early childhood settings seen as social?

     In England the use of the words recording (or written maths) are used extensively to refer to individuals copying symbols and written strategies provided by the teacher, or writing something they have already done following a practical activity with objects. Such activities involve lower levels of thinking. Children do not need to record mathematics if they can do it mentally; neither do they need to record something they have worked out in a practical context.    

      We found that recording places the emphasis on signs and representations as products to be formally assessed, and requires a lower level of cognitive demand (thinking) in mathematics. The difference between representing mathematical thinking and recording is one of quality and depth of thinking. Most significantly, recording fails to enable the child to build deep understandings of semiotic representations for mathematics.

     In children’s own Mathematical Graphics, the emphasis is on the children's emerging understandings and on the processes of mathematical thinking (creative thinking, reasoning, meanings, understanding, problem-solving, flexible thinking, negotiation and co-construction of understanding). Authentic, meaningful social contexts for mathematics allow children to connect their existing cultural knowledge and make greater sense of their mathematics when they explore their thinking through their own representations.

     For children, one of the benefits of using paper (or another drawing/writing surface) to explore their thinking, is that their own marks, signs and symbols support understanding by allowing them to see some of their emerging understanding of ‘written’ mathematics, helping them to 'translate' between their early informal marks and the standard symbols and the formal, abstract written language of mathematics. Children need to be free to choose how they will represent their mathematical thinking that best fits their purpose, the particular mathematical context or calculation they are exploring, or the problem they wish to solve.

NRICH, Cambridge University: Children's mathematical graphics: understanding the key concept

Reference

Kress, G. (2010). Multimodality: A social semiotic approach to contemporary communication. Routledge.