In 1977, Ginsburg identified the abstract written symbols of mathematics as a problem for young children, and in 1984, Hiebert wrote ‘Many of the children’s observed difficulties [with mathematics] can be described as a failure to link the understandings they already have with the symbols and rules they are expected to learn’ (p. 498). Munn (1994, p. 13) ) argued that the functional use of signs used by children in mathematical contexts is “essentially a literate strategy”.

     In 1986, in his seminal work Martin Hughes identified abstraction in language as causing difficulties for children without meaningful contexts, explaining that children need to be able to represent their mathematical thinking in personally meaningful ways. Hughes recommended that teachers ‘build on children’s own strategies’ and ‘respect children’s invented symbolism’ (p. 176-177). Since 1990, this is what we have aimed to do - firstly in our teaching, and throughout our extensive and groundbreaking research into Children's Mathematical Graphics.

    The abstract written language of mathematics is relevant throughout education, and Children's Mathematical Graphics can support children's understanding, from 2 - 8 years of age, from their earliest signs and symbols to problem solving, calculations and all other areas of maths.

    But meanwhile, like the proverbial 'ostrich' there continues to be little recognition of this critical aspect of mathematics, and the significance of young children's understanding of the abstract symbolic language of mathematics remains largely unrecognised since this problem was first identified.

References

Ginsburg, H. P. (1977). Children's arithmetic. Van Nostrand.

Hiebert, J. (1984). Children’s mathematical learning: The struggle to link form to understanding.

Elementary School Journal, 84(5), 496-513. 

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

Munn, P. (1994). The early development of literacy and numeracy skills. European Early Childhood

Education Research Journal, 4(1), 5-18.