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Jack (4 years 11 months): adding
grapes We were using grapes
to explore addition (they would eat the grapes later). Jack chose
two separate amounts of grapes to add for each of his calculations
and decided to use paper and pen to help him explore the use of
symbols.
He left a gap between the two sets of
grapes in each calculation so that it can be read as
‘4 + 3’ (and below) ‘6 + 6’. We term this use of a space between two
sets to be added or subtracted implicit symbols, since whilst the
child has not at this stage represented the addition symbol, his
layout – and when he reads it out, |

shows he has implied the
symbol and recognized that an operant is needed. Finally Jack drew a
line in each calculation before writing the total: this line
functioned as an equals sign for Jack at this point in time, helping
him move towards a deep understanding of standard symbols (see the
Taxonomy and exploring
symbols)
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