Below we provide definitions for some of the important terms which we use in this
book: these definitions refer to their use within the context of this study.
aallggoorriitthhmm A step-by-step procedure that produces an answer to a particular
problem (a standard algorithm is a set procedure for a problem
which has been generally recognised as the most efficient way to
solve an addition, subtraction, division or multiplication
problem). Standard algorithms are part of the established arith-
metic culture in many countries.
bbii--nnuummeerraattee Through using their own mathematical graphics children trans-
late between their own informal understanding and abstract
mathematical symbolism, in an infinite feedback loop. We origi-
nated the term ‘bi-numerate’ to describe the translation between
these two systems. This allows children to exploit their own
informal marks and use this knowledge to gradually construct
deep personal meaning of standard mathematical symbols and
subsequent standard written calculations.
ccooddee sswwiittcchhiinngg Switching from informal representation to include some standard
symbols within a piece of mathematical graphics or calculation.
ddiimmeennssiioonnss ooff These represent the development of children’s mathematical
mmaatthheemmaattiiccaall graphics (see Chapters 6 and 7).
ggrraapphhiiccss
ddyynnaammiicc Marks that are lively and suggestive of action – full of energy and
new ideas.
eexxaammppllee When a teacher provides a direct example and then children
follow the teacher’s example when representing their mathemat-
ics: this usually results in all children copying what the teacher
has done.
ffoorrmmss The five graphical formsidentified in our research refer to the
range of mathematical marks that children choose to make (see
pp. 87–90). However, the forms alone do not represent the devel-
opment of children’s mathematical understanding of written240Glossary
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