Brought to You by the Number 九十二

November 23, 2019
Posted by Jay Livingston

We were at 79th and Broadway, and I wanted to tell the French couple that they had to go up to 98th St. I had overheard them looking at their phone and puzzling about directions. I don’t get much chance to speak French, so I asked, in French, if I could help them.

Il faut aller jusqu’au . . .” I started, but it took me an extra moment to remember how to say “98" in French. “Au quatre-vingt dix huitième.”

I remember that my brother, a statistician by trade, once commented that France has had a disproportionate number of noted mathematicians, and he wondered if the difference might have something to do with how kids learn to count. Compared with English, counting in French involves more sophisticated mathematical operations. Once you get past 69, you can no longer use the base-10 template that worked for numbers in the 20s, 30s, and so on. Seventy is soixante-dix (sixty-ten); seventy-nine is soixante-dix neuf (sixty ten nine).*

After that you have to throw in some multiplication. Eighty is quatre-vingt (four twenty), and ninety-eight is quatre-vingt dix huit (four twenty ten eight) — 4 x 20 +10 +8.

In a recent BBC article (here), Anand Jagatia discusses the idea that how we count affects our ability in math. English, French, Dutch, Welsh all have slightly different ways of naming numbers. The biggest contrast is between Western systems and those of East Asia. 
In Mandarin, 92 is written ji shí èr, which translates as “nine ten two”. Japanese and Korean also use similar conventions. . . . Psychologists call systems like these “transparent”, where there is an obvious and consistent link between numbers and their names. There’s growing evidence that the transparency of a counting system can affect the way we process numbers.

The point is clearer if you use numbers rather than words — not “nine ten two” but “9 10 2.” To translate the Western “92” into math, you have to know about the tens place and the ones place. The Asian “9 10 2” shows more simply how the larger number is constructed from the smaller ones.

Does it make a difference?

Children who count in East Asian languages may have a better understanding of the base-10 system.

In one study, first-grade children were asked to represent numbers like 42 using blocks of tens and units. Those from the US, France or Sweden were more likely to use 42 individual unit blocks, while those from Japan or Korea were more likely to use four blocks of ten and two single-unit blocks, which suggests that the children’s early mental representation of numbers may have been shaped by their language. [emphasis added]

I’m not sure what the evidence is on the stereotype notion that Asian students do better in math than do Western students. But if there is any factual basis, maybe the language of numbers accounts for some of the difference.

* Belgians speak French, but they have simplified the numbers. Seventy and ninety are, respectively, septante and novante --- yet another reason for the French to look down on les belges. For some reason, eighty remains quatre-vingt.

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