and NumberHughes pointed out that for many learners mathematics is ‘more like an
unfamiliar foreign language’ (Hughes, 1986, p. 42), an idea that he extends, propos-
ing that the difficulty is that children have to learn to translatebetween mathemat-
ical language and their everyday language.
But there is another highly significant aspect of language that has been largely
ignored in the debate about the difficulties children experience in translating from
home to school mathematics – the question of how children learn to writein a
second language – and it is this perspective that we believe can make a huge contri-
bution to the debate.
Halliday (1975) describes learning a first language as ‘learning how to mean’, a
phrase that sits well with our emphasis on children making meaningthrough their
mathematical graphics. John-Steiner reminds us that ‘the Vygotskian perspective ...
places the issues of bi-lingualism into the broader framework of the psychology of
language and thought’. Thus learners draw on their ‘internal meaning system while
comprehending or producing language’; they ‘are increasingly able to comprehend,
condense and store information, they start the process of weaving two meaning
systems together’ (John-Steiner, 1985, pp. 357, 364–5).Multicompetencies
In a recent and thought-provoking study of second language learning or L2 learning,
Cook observes that the starting point for teachers of second languages is ‘the learn-
ers’ own language system’ (Cook, 2001, p. 16). The descriptions of second language
learners match accepted understanding of early writing development and the few
studies of children’s early (written) mathematical development; they also match our
own findings closely. Cook describes second language learners as inventing ‘a system
of their own ... curious rules and structures which they invent for themselves as they
go along’ (Cook, 2001, p. 16). These personal systems have been termed ‘interlan-
guage’ (Selinker, 1972). This interlanguage showed that learners were using their
‘temporary language systems’ (Cook, 2001, p. 15).
However, Cook has challenged this assumption – widely accepted now in the field
of second language learning – as not going far enough: ‘on the one hand we have
the user’s knowledge of their first language; on the other, their interlanguage in the
second language. But both these languages co-exist in the same mind; one person
knows both languages’ (Cook, 1992 p. 16). Cook proposes that learners’ first lan-
guage and their interlanguage be viewed together as ‘multicompetence’: this leads to
competence for learners in their second language.
It is not difficult to exchange the words ‘first language’ with the concept of chil-
dren’s early, informal mathematics and substitute the abstract symbolism of mathe-
matics for ‘second language’.
Sometimes children’s second language is written using an alphabetic or symbolic
system that contrasts to that of their first language (for example in the letters, char-
acters or orientation of writing) and in recent years research has illuminated young
children’s behaviours as they develop competency in writing their second language.
Evidence comes from research with children combining Chinese, Arabic or Spanish78 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:11 Page 78