ooppeerraattoorr This is a sign to show which operation is to be used, i.e. +, –,
×, .
ppiiccttooggrraapphhiicc A drawing giving something of the appearance of what was in
front of the child; actually representing something the child was
looking at (Hughes, 1986).
rreeccoorrddiinngg When children use practical equipment and then record what
they have done.
rreepprreesseennttaattiioonn This refers to children’s own mathematical thinking on paper. It
may also be used to refer to children’s interest in representing their
ideas through, for example, using blocks, paper cut-outs, play or
construction.
sscchheemmaass Patterns of children’s own repeated behaviour that give us a
window on their thinking (cognition) (Athey, 1990).
ssoocciioo--ccuullttuurraalliissmm Children learn about the world and construct mathematical
understanding through the sociocultural practices in which chil-
dren and adults are involved (see Barratt-Pugh and Rohl, 2000).
ssyymmbboolliicc This stage arises out of all previous stages. ‘Standard symbolic’
refers to the use of standard forms of numerals and some stan-
dard signs such as + and = (Hughes, 1986).
ssyymmbboolliicc ‘Written’ languages represent ideas and meanings in ways that
llaanngguuaaggeess are culturally and contextually specific, such as English, Man-
darin or Tamil; written mathematics; musical notation; chemical
formulae, maps or scientific equations.
ssyymmbboollss Mathematical symbols such as = and +. Children may also use
their own intuitive or invented symbols as they move towards
understanding the standard forms.
ttrraannssiittiioonnaall ffoorrmmssWhen children move between one graphical form and another,
for example, from pictographic to iconic.
wwrriitttteenn ((ffoorrmm)) Using words or letter-like marks in a calculation, which are read
as words and sentences.
wwrriitttteenn mmeetthhooddss These are forms of mathematics that children write down to
answer a problem, i.e. their own written calculations.
vviissuuaall ‘Visual representation’ (Matthews, 1999): not as a recordof actions
rreepprreesseennttaattiioonn or things seen, but a representation of thinking and of emergent
understanding. We use the term to encompass all aspects of
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