In the March 4 edition of The Chronicle of Higher Education an article on `Why Chinese Students Score High in Math' (p. A16) reports a claim by a University of Michigan psychologist that the greater transparency of numeral words for 11-19 in East Asian languages accounts in part for young Chinese, Japanese, and Korean students' superior learning of math by comparison to American students. Professor Kevin F. Miller comments:
"American children are confused by the fact that you name seventeen but you write it as ten-seven...Most first graders, at the end of the school year, if you ask them how many 10s there are in 17, they'll say 7."
The article (and presumably the scholar as well) acknowledges that other factors also contribute to Asian students' greater success in learning math, but the article emphasizes the argument that both the ordering of the numerals in the compound English 'teen words (3+10, 4+10, ...) and the semantic opacity of the words eleven and twelve make math learning harder for American first-graders.
The article is too short to raise, much less answer, some obvious questions: what about Asian-American students raised in traditional households but with English as their only first language? Is the same effect detectable in young students from other language backgrounds with numeral systems similar to the East Asian one reported here? How about students whose first languages have numeral systems that are more transparent or significantly less transparent than the English and East Asian patterns?
I was curious, so I conducted a quick and dirty survey of some of the grammars on my shelves. The Chinese-Japanese-Korean pattern is a bit more common in my nonscientific sample than the English pattern, with varying degrees of opacity in both types. Some examples: Hungarian, Swahili, Tagalog, Cherokee, Mundari, Turkish, Vietnamese, Dakota, and several Salishan languages all have the East Asian pattern, often with a particle or other connective separating the parts of the complex numerals. Most of these are fairly transparent systems, but the usual Dakota words for the 'teens seem to be composed of a particle meaning `again' + the unit (`again' + 1, `again' + 2, etc.). One grammar explains this as a shortening of the full form, which is (10 +) `again' + 1, etc.
On the other side, Russian, Finnish, Cherokee, Comanche, Colloquial Egyptian Arabic, Kurdish, and possibly Hindi and Urdu have systems similar to the English one, at least in that the words for 11-19 start with `1', `2', and so forth. But in this set of languages there are many very opaque 'teen forms. The Hindi and Urdu words don't appear to have `10' in them at all, and some of them don't even clearly have the numerals 1-9. Kurdish (which is not too distantly related to Hindi and Urdu) has more recognizably compound forms for the 'teens, but the phonetic distortion is sufficient to obscure the connection between the `10' element in these compounds and the word for ten. The Russian system also has some phonetic distortion in the `10' half of the compound, but overall it's more transparent than the English 'teen words. The second element in the Finnish 'teen words means `second', not `ten', and the second element in the Comanche words probably means `to go in/out'.
It would be nice if scholars would investigate a greater diversity of languages and systems before drawing conclusions about links between numeral structure and math learning. As reported in the Chronicle, the claim about the linkage strikes me as simplistic. In particular, the relative opacity of the English system could well mean that young children have learned the 'teen words as wholes, or as units plus an otherwise meaningless suffix, rather than as combinations of unit + ten; in that case, the compositional opacity might be the relevant factor, not the ordering unit + ten vs. the East Asian ten + unit pattern: as far as I can tell from the grammars (which, admittedly, usually give only the orthography for these numerals, not the pronunciation), the three East Asian languages mentioned in the article all have quite transparent compound numerals for the 'teen words.
Posted by Sally Thomason at March 3, 2005 11:38 AM