The Numbers Game
ome languages have more complicated ways of naming numbers than
others, and some people even think that if your native language has a
simple, clear way of naming numbers then it will be easier for you to learn
math — but I’d say this is wrong.
What does it mean to have "complicated" numbers? Let’s say you're learning
to count to 100 in English. To get there, you would really just need to know
20 words and suffixes:
one twelve
The first 12 numbers follow no special pattern and must be memorized.
-teen
to construct the rest of the numbers until 20 you use “teen”, but note that
you'd also need to remember...
thirteen, fifteen
rather than "threeteen" or "fiveteen"
-ty
to make the multiples of ten you’d need “ty”, but note that you'd also need
to learn...
thirty, forty, fifty
and not "threety", "fourty" and "fivety"
hundred
and of course “hundred” to cap it off.
With these 20 words and knowledge of the pattern used to make the
numbers, you can count to 100, or really all the way to 999 before having
to learn any new words.
Chinese, Japanese and a number of other Asian languages have a much
simpler system. To count to 100 and beyond, you'd only need to learn 11
words: the words for 1 through 10 and the word for "hundred".
In both Chinese and Japanese, 10 is written
十
like a small cross. (In fact, in both languages the Red Cross Society is called
the "Red Ten Society".)
But 十 also acts as the "-ty" suffix in English. So numbers above 10 follow
this pattern:
11 is “ten-one” (十一)
12 is “ten-two” (十二)
20 is “two-ten” (二十)
21 is “two-ten-one” (二十一), and so on.
Now this difference has led to the prevalent belief that kids who grow up
speaking Chinese or Japanese will be better at math than those who grow
up speaking the more complicated English. (For example, see this Wall
Street Journal report making this argument.)
I find this hard to believe though. Consider India, which has a very
respectable reputation in math. After all, India invented the zero, and today
India is often seen as a powerhouse in engineering and other math-heavy
pursuits.
Because of this, you might think that Indian languages such as Hindi and
Bengali and others would also have simple number systems like Japanese
does, but in fact many northern Indian languages have very complicated
numbering.
Where in Chinese you need 11 words to count to 100, and in English you
need 20 words to count to 100, in Hindi you will need to memorize all 100
words. They are all irregular. A rough system does exist, but there are just
too many exceptions, and so all the numbers up to 100 are usually taught
individually instead of trying to teach a pattern. Consider these:
छह
(cheh) – six
सीलह
(solah) – sixteen
छब्बीस
(chab-bees) – twenty-six
साठ
(satt’h) – sixty
In English, all these numbers have “six” in them, but Hindi is all over the
place — the only thing these have in common is that two start with a “स” (S)
and two start with a “छ” (CH).
And then there is the matter of Hindi fractions. In English, we have the word
“half” for ½, and we have “quarter” for ¼, but all other fractions follow a
rigid pattern, with a cardinal number followed by an ordinal number: one-
fifth, three-sevenths, etc.
Hindi also has special words for “half” (आधा – ahd'ha) and “quarter” (चौथाई –
chawt'hai) — but it has many others too:
“pauna” (पौना) means “three quarters”
“sawah” (सवा) means “one and a quarter”
“daird” (डेढ़) means “one and a half”
“d’hai” (ढाई) means “two and a half”
These fractions come into play when telling time. Instead of saying it’s “half
past two o’clock,” Hindi speakers say it’s “d’hai o’clock” (2½ o’clock).
So if India can be strong in math despite the very involved vocabulary for
numbers, then maybe language doesn't really have such a bearing on
mathematical ability. Probably it has a lot more to do with how much
emphasis the various cultures place on math education.
That said, India’s greatest modern mathematician, Srinivasa Ramanujan
(whose story was the basis of the 1997 film “Good Will Hunting”) grew up
speaking Tamil, which like other southern Indian languages has a much
simpler number system, more in line with the East Asian languages. Still,
it’s anyone’s guess on whether he was helped by his linguistic
circumstance.
The Numbers Game
ome languages have more complicated
ways of naming numbers than others, and
some people even think that if your native
language has a simple, clear way of
naming numbers then it will be easier for
you to learn math — but I’d say this is
wrong.
What does it mean to have "complicated"
numbers? Let’s say you're learning to
count to 100 in English. To get there, you
would really just need to know 20 words
and suffixes:
one twelve
The first 12 numbers follow no special
pattern and must be memorized.
-teen
to construct the rest of the numbers until
20 you use “teen”, but note that you'd also
need to remember...
thirteen, fifteen
rather than "threeteen" or "fiveteen"
-ty
to make the multiples of ten you’d need
“ty”, but note that you'd also need to
learn...
thirty, forty,
fifty
and not "threety", "fourty" and "fivety"
hundred
and of course “hundred” to cap it off.
With these 20 words and knowledge of the
pattern used to make the numbers, you
can count to 100, or really all the way to
999 before having to learn any new
words.
Chinese, Japanese and a number of other
Asian languages have a much simpler
system. To count to 100 and beyond,
you'd only need to learn 11 words: the
words for 1 through 10 and the word for
"hundred".
In both Chinese and Japanese, 10 is
written
十
like a small cross. (In fact, in both
languages the Red Cross Society is called
the "Red Ten Society".)
But 十 also acts as the "-ty" suffix in
English. So numbers above 10 follow this
pattern:
11 is “ten-one” (十一)
12 is “ten-two” (十二)
20 is “two-ten” (二十)
21 is “two-ten-one” (二十一), and so
on.
Now this difference has led to the
prevalent belief that kids who grow up
speaking Chinese or Japanese will be
better at math than those who grow up
speaking the more complicated English.
(For example, see this Wall Street Journal
report making this argument.)
I find this hard to believe though.
Consider India, which has a very
respectable reputation in math. After all,
India invented the zero, and today India is
often seen as a powerhouse in
engineering and other math-heavy
pursuits.
Because of this, you might think that
Indian languages such as Hindi and
Bengali and others would also have simple
number systems like Japanese does, but in
fact many northern Indian languages have
very complicated numbering.
Where in Chinese you need 11 words to
count to 100, and in English you need 20
words to count to 100, in Hindi you will
need to memorize all 100 words. They are
all irregular. A rough system does exist,
but there are just too many exceptions,
and so all the numbers up to 100 are
usually taught individually instead of
trying to teach a pattern. Consider these:
छह
(cheh) – six
सीलह
(solah) – sixteen
छब्बीस
(chab-bees) – twenty-six
साठ
(satt’h) – sixty
In English, all these numbers have “six” in
them, but Hindi is all over the place — the
only thing these have in common is that
two start with a “स” (S) and two start with a
“छ” (CH).
And then there is the matter of Hindi
fractions. In English, we have the word
“half” for ½, and we have “quarter” for ¼,
but all other fractions follow a rigid
pattern, with a cardinal number followed
by an ordinal number: one-fifth, three-
sevenths, etc.
Hindi also has special words for “half”
(आधा – ahd'ha) and “quarter” (चौथाई –
chawt'hai) — but it has many others too:
“pauna” (पौना) means “three quarters”
“sawah” (सवा) means “one and a
quarter”
“daird” (डेढ़) means “one and a half”
“d’hai” (ढाई) means “two and a half”
These fractions come into play when
telling time. Instead of saying it’s “half
past two o’clock,” Hindi speakers say it’s
“d’hai o’clock” (2½ o’clock).
So if India can be strong in math despite
the very involved vocabulary for numbers,
then maybe language doesn't really have
such a bearing on mathematical ability.
Probably it has a lot more to do with how
much emphasis the various cultures place
on math education.
That said, India’s greatest modern
mathematician, Srinivasa Ramanujan
(whose story was the basis of the 1997
film “Good Will Hunting”) grew up
speaking Tamil, which like other southern
Indian languages has a much simpler
number system, more in line with the East
Asian languages. Still, it’s anyone’s guess
on whether he was helped by his linguistic
circumstance.