number, quantities and their own written methods
iiccoonniicc Marks based on one-to-one counting. These may include tallies or
other marks and symbols of the children’s own devising (Hughes,
1986).
iimmpplliicciitt ssyymmbboollss Symbols that are implied within the child’s marks or layout, but
are not represented: this is a significant stage in children’s devel-
oping understanding of the abstract symbols of mathematics.
jjoottttiinnggss Informal, quick marks that are made to aid memory when working
out mental calculations. In England the term ‘jottings’ is used to
refer to some taught methods (e.g. the empty number line).
mmaarrkkss In the context of this study, we use this term to refer generally to
children’s marks on paper: children also make graphical marks
on other surfaces such as sand, paths and windows.
mmaarrkk--mmaakkiinngg Children’s own, self-initiated marks which may be explored
through their actions or forms of symbolic languages such as
drawing, writing or mathematics.
mmaatthheemmaattiiccaall Children’s own choice of marks that may include scribbles,
ggrraapphhiiccss drawing, writing, tallies, invented and standard symbols.
mmooddeelllliinngg Teachers (or children) using chosen ways to represent some
mathematics, usually for a real need and which they show to
other children. Modelling is not followed by children copying
what has been shown, but over time provides a ‘tool box’ of ideas
and possible marks, symbols, ways of representing and layout.
mmuullttii--mmooddaall Simply – many modes or forms; many different ways of repre-
senting meaning through a variety of media including speech,
gestures, dens, piles of things, cut-outs, junk models, drawings,
languages, symbols and texts. Meaning is created out of ‘lots of
different stuff’ (Kress, 1997).
nnaarrrraattiivvee When children represent their calculations as narratives with a
sense of relating a story: e.g. ‘first I did this, then I added two
more, then I had 5 altogether’.
nnaarrrraattiivvee aaccttiioonn Children include some means of showing the action of (often)
addition or subtraction by, for example, drawing a hand remov-
ing some items or arrows pointing to some numerals – more
often found in representations of subtraction.
nnuummbbeerr Numbers are ways of expressing and recording quantities and
measurements.
nnuummeerraall A numeral is a digit, which is a single symbol: for example, 45
is a number but within that number there are two numerals, 4
and 5.
ooppeerraattiioonn An operation is a rule that is used to process one or more
numbers, e.g. subtraction, addition, multiplication or division.
Algebraic forms of mathematics use more complex operations.Glossary 2418657part 2.qxd 04/07/2006 17:41 Page 241