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Patterns of Counting Words

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Children can learn surprisingly sophisticated patterns related to the counting words. In this handout, Anna illustrates her understanding of the decades pattern in the English-language counting-word sequence.

by Herbert P. Ginsburg

In their everyday environments, children can see patterns in the arrangement of physical objects. But another context in which children can examine patterns is number itself, specifically the counting words, without regard to any concrete objects. You may find this surprising. After all, learning to count out loud (as opposed to counting things) is usually considered merely a matter of memorization with no meaning. It’s true that rote memory is involved when children learn the first ten or so counting words in English, but Anna, close to her fifth birthday, shows that she understand the crucial mathematical patterns involved in counting out loud. (You can see the full video at the bottom of Anna Counts in the Counting Module, which covers the topic of number words in depth.) 

Alba, an assistant teacher in Anna’s class at a childcare center, begins by asking her to count as high as possible. Anna gets up to 23 without much difficulty. Watch what happens as she continues.  

What’s most interesting is her inflection on both “twenty-nine” and “thirty-nine.” She stretches out both words and says them like a question before going on. Clearly she sees those words as special. And they are. Each is the last number in a sequence, after which, the next tens-number must be used. In other words, each counting number Anna was trying to say involves a tens-number, such as twenty, followed in turn by the numbers one through nine. When she elongated the “twenty-nine,” it is as if she were asking, “What’s the tens-number I have to say now?” When she got “thirty,” she tacked onto it the numbers from one to nine. That’s the rule involved in creating the counting pattern: take your tens-number and just append to it all the unit numbers.

After her question-like “thirty-niiiiiiiiiine,” she does something remarkable. 

Anna asks what comes after three and answers her own question: “Oh, I know. Four.” Although she does not actually say “forty,” she continues correctly from forty-one to fifty.

Why did she ask what comes after three and how did the answer help her? She seemed to understand that numbers are grouped in tens: the twenties, thirties, forties, and so on. She also seemed to know that the first number in each tens sequence (twenty, thirty, forty) is related to the unit numbers (two, three, four). In other words, it’s as if she thought of the tens-numbers as “two-ten,” “three-ten,” and “four-ten.” If you think of them this way, and you don’t know what comes after the three-ten numbers, you can easily figure out that next must come the “four-ten” numbers. And from there, it’s easy to see that “four-ten” is very similar to forty.  Bingo! 

Anna has uncovered the pattern that underlies counting. This knowledge served her well: she continued up to 99, performing her rhythmic chant all the way.

As you can see, Anna has discerned a secret to learning how to count... patterns!

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