WHAT'S THE “SAY TEN” METHOD OF COUNTING?
Jeff Suzuki
Jeff Suzuki teaches mathematics at Brooklyn College, and is one of the founders of the Mid-Hudson Valley Math Teachers Circle, a group of teachers, professors, and mathematics aficionados working to promote mathematics education in the Hudson Valley.
Counting is the basis for all arithmetic, and research on children in China and in the U.S. reveal some disturbing facts. Chinese and American children learn to count to 10 at about the same rate. But after the age of 3, Chinese children begin to rapidly outpace their American counterparts. Thus while a typical American 4-year-old is still learning to count to 20, a typical Chinese 4-year-old is able to count to 100 without difficulty.
The difference in counting abilities has some profound effects. Thus, after just two months of school, Chinese kindergartners are able to solve three times as many arithmetic problems as their American counterparts (and this disparity grows to nearly four times as many by the end of kindergarten). Studies of Korean and Japanese children show similarly advanced capabilities in comparison to children who grow up speaking English, Swedish, or French.
Later differences in mathematical ability could be attributed to differing views on education. But most researchers attribute this very early difference between children who grow up speaking an Asian language and those who don't to the language itself. When learning to count, Chinese-speaking and English-speaking children must learn the names of numbers from 1 through 10. These names are ten arbitrary words that give no hint of their relationship: It's not as easy as one-two-three, but rather as difficult as yi-er-san. Both Chinese-speaking and English-speaking children complete their learning of the numbers from 1 to 10 between the ages of 2 and 3.
To count past 10, an English-speaking child must master a new set of number words (collectively referred to as the teen numbers): eleven, twelve, thirteen, and so on up to nineteen. After these come the decade numbers: twenty, thirty, forty, and so on. Thus, in order to count as high as 100, an English speaking child must remember 27 different words, to be used in a very specific sequence. As a result, mathematics standards in both common core states and non-common core states only expect counting to twenty of their kindergartners.
To be sure, some of these words are related: there is a clear parallel between “six-seven-eight,” “sixteen-seventeen-eighteen,” and “sixty-seventy-eighty.” But this relationship may be more confusing than helpful, because when children learn to write these numbers, the “six” of “sixteen” is the second digit of the number (16), while the “six” of “sixty” is the first digit (60). Children are like mathematicians: we're confused and frustrated by inconsistent rules.
In contrast, the teen numbers in Chinese are shi yi (literally “ten one”), shi er (“ten two”), shi san (“ten three”), and so on, and the decades are er shi (“two tens”), san shi (“three tens”), and so on. A similarly regular system exists in Korean and in Japanese.
While we can't change our language, there's a good chance that your child will, on their own, invent a number phrase like “ten and two.” Rather than correcting this informal language, it's worth encouraging it: this leads to the say ten way of expressing numbers (also known as keeping ten). In deference to the grammarians, we omit “and” when giving number words: thus the teen numbers are “ten one,” “ten two,” and so on up to “ten nine;” the decades are “two tens,” “three tens,” “four tens,” and so on.
There are several advantages to such a system. First, children make the transition from counting on their fingers (which necessarily limits how high they can count) to counting verbally only after they have mastered the number words. Chinese children make this transition during preschool; English-speaking children generally do so during first grade.
Second, it eases the transition to writing numbers: “four tens two” becomes “4 tens 2” and then “42,” while “forty-two” too easily becomes “40-2” and then “402.” Finally, mental addition is far easier: Compare “ten five plus ten is two tens five” to “fifteen plus ten is twenty-five.”
One last point worth making: You are your child's first teacher. Since children often learn to count at home, it's worth introducing them to this form of counting as soon as they begin to wonder about counting past ten. This lays a solid foundation for later success in mathematics.