This article appeared in the Winter 2012–13 issue of Erikson on Children under the headline “Nixing 'naked numbers'.”
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McCormick Math Minute: Discover foundational mathematics for young children — in 60 seconds or less

When children are asked to rattle off the numbers from 1 to 10 without actually counting something, all kinds of confusion can result. These “naked numbers” don’t help children understand that “three” is an adjective that tells us “how many,” not a noun that stands by itself. No matter what is being counted or how the objects are arranged, “three” has the same meaning.

Melinda Chum helped her kindergarteners at Chicago’s Norman A. Bridge Elementary School develop a sense of what the number “three” means with black dots, 3″ x 5″ index cards, and inspiration from Ten Black Dots by Donald Crews.

With a small group of children surrounding her, Chum modeled how she could arrange three black dots on a card in different ways. She labeled one card as “1-1-1” and put down three equidistant dots, saying, “I put one here, one here, and one here.” After showing that the dots add up to three, she created cards with 1-2 and 2-1 patterns: two dots closer together and one further away.

Chum invited her students to create their own patterns of three black dots, place their card together with others with the same pattern, and explain why their card fit the pattern they chose.

“It was wonderful to see how they think and decide that their card could belong just about anywhere on the number pattern graph depending on how you turn the card and how you are looking at it,” says Chum. “They continued to think and rearrange their cards, commenting on things like ‘My card looks like one, two and if I turn it this way it looks like two, one. So it could go here or there.’”

That rich conversation showed Chum that her students were developing a sense of “three-ness” and the different ways “three” can be constructed. No matter how the dots are arranged, there are still one, two, three!

The Erikson Early Mathematics Education Project, launched with the support of the Robert R. McCormick Foundation, works with teachers to bring foundational mathematics to the early childhood classroom.