While I have an affinity for the belief that the way a language expresses numbers can make mathematics either easier or harder, the logical part of my brain cautions skepticism.
Examples: in English we say "twenty-one", the German number translates to "one and twenty", and Chinese translates to "two-ten-one". Sure, the concept of place value is most obvious in the Chinese expression, but absent strong evidence I have to believe that any benefit is short-lived.
Welsh numbers are presented in the same way as Chinese numbers, and a researcher found the following:
Dowker's findings were nuanced. She found, for instance, that six-year-olds who spoke Welsh at home and school made fewer errors when reading aloud pairs of two-digit numbers.
They were also better able to point out which was the bigger of the
two, compared to those who spoke English. "There was a significant
advantage," she says.
However, these benefits didn't seem to translate to advantages in
other measures of general mathematical ability. For this reason, Dowker
concludes that the effects of language on numerical ability are subtle
and specific rather than large and "pervasive". She certainly doesn't
believe that linguistic transparence, alone, could explain why East
Asian countries tend to be placed higher in educational league tables.
Cross-country comparisons within Europe support this position.
Consider German, which shares many of the irregularities seen in
English, including the inversion of certain numbers. Forty-five, for
example is fünfundvierzig in German (five-and-forty). Some studies suggest that inversion confuses German children as they learn to write numbers as digits. (Hearing fünfundvierzig they
might write 54, for example.) But that doesn't seem to hold them back
for long. "Germany does rather well in international comparisons," says
Dowker.
"Nuanced" seems to be an apt description for advantages that are short-lived.
Then there are fractions:
Even if the influence of language does not extend to the whole of
mathematics, emerging evidence suggests it might extend to a handful of
skills beyond counting. So far, there is some evidence that language may
affect how quickly children learn to use fractions.
"When thinking about fractions, we have to look at the big part first
and then see how much of that is in the numerator," explains Jimin Park
at the University of Minnesota, whose PhD thesis concerns the linguistic
representation of fractions. (Who says the bigger part is in the denominator?--Darren)
In Korean, this relationship is explicitly spelled out. The term for 1/3 is sam bun ui il, which translates as "of three parts, one", and 3/7 is chil bun-ul sam,
which translates as "of seven parts, three" – where the English terms
"one third" or "three sevenths" do not make this so immediately obvious.
And this seems to give young Korean children
a slight advantage in matching named fractions to diagrams illustrating
the quantity, before they have even been taught formal lessons in the
idea. "When they have to verbally understand fractions, the Korean
children definitely benefit," says Park. Intriguingly, when English
children are taught to describe fractions with the Korean style of
phrasing, it does seem to improve their intuitive understanding of the
quantities.
Does the Korean method help understand fractions like 5/4? I wonder.
I understand that teaching children to read Finnish is easier, and hence takes less time, than does teaching children to read English. It might take less time, but no one is suggesting we all switch to Finnish, and those of us adults who can read English are at no disadvantage relative to those who read Finnish. Thus, the Finns had a small, temporary advantage that disappears over time, which I assert is probably the same as math issues described above.
