Early Math: How Children Learn About Numbers
How to help children explore numbers and quantity
- Grades: Early Childhood, Infant, PreK–K, 1–2
Children's Books to Share
Hippos Go Berserk! by Sandra Boynton (Simon & Schuster; 1996)
How Do Dinosaurs Count to Ten? by Jane Yolen (Scholastic; 2004)
Math Man by Teri Daniels (Scholastic; 2001)
One Fish, Two Fish, Red Fish, Blue Fish by Dr. Seuss (Random House; 1960)
Russell the Sheep by Rob Scotton (HarperCollins; 2005)
Two preschoolers are watching a parade. "Look! There's clowns!" yells Paul. "And three horses!" exclaims his friend, Nathan.
Both friends are having a great experience. But only Nathan is having a mathematical experience at the same time. Other children see, perhaps, a brown, a black, and a dappled horse. Nathan sees the same colors, but also sees a quantity-three horses. The difference is probably this: At school and at home, Nathan's teachers and family notice and talk about numbers.
When Does Number Learning Begin?
When do children first become able to notice numbers? And, how important is it to notice and talk about them? Let's first explore when children are sensitive to quantity. Picture a 6-month-old child looking at three drawings. They show two dots, one dot, and three dots. The infant hears three drumbeats, and her eyes move to the picture with three dots. Infants are sensitive to quantity! Does that mean they "know" numbers? Probably only at an intuitive level. This little girl doesn't know that the dots represent three in the way older children and adults do, and doesn't know that three is more than two. But the beginnings of understanding numbers are there.
Sensitize Children to Numbers
Building on those beginnings is important. Every time you name a number, such as noticing, "Oh! I dropped three of the crayons," you sensitize children to numbers and teach a number word and its connection to a specific quantity. However, if you do it consistently, you are doing much more. You are encouraging children to think of the world in terms of, and to spontaneously recognize, numbers. That is a gift that keeps on giving, because children can then create hundreds, or thousands, of mathematical experiences for themselves.
Teachers need to be alert to naming small groups of objects and people whenever it is appropriate. "There are two airplanes." "Do you three want to play with the blocks?" Be especially alert to situations when naming small groups is important to the child. "You drew four baby horses! Are you going to draw four mommy horses?" Of course, children cannot recognize numbers in large groups. Unless they are arranged in certain ways, such as on a dice, the limit is usually four to six.
So, is recognition of numbers an early skill that fades away when real learning of numbers starts? The answer is no, for the following reasons:
1. Recognition of numbers supports the development of other number skills, such as counting. For example, one of the most important ideas about counting that many children do not develop is this: The last counting word tells how many. Children will count three objects, but then, when asked how many, will re-count. But if they recognize groups of one, two, and three, then when they count out one, they see they have one, when they count out two, they see they have two, and when they finish and count three they see three. They relate it to what they already know, and so the counting is more meaningful.
2. Recognition of numbers develops into more sophisticated abilities. The most obvious one is subitizing, or instantly seeing how many. From a Latin word meaning suddenly, subitizing is the direct and immediate recognition of the number of a group. Simply stated, it's fast number recognition. If someone shows you four fingers for only an instant, you recognize how many fingers they are holding up without counting. And that fast recognition is important. For example, subitizing will later help children with adding. Many children add 4 + 3 by counting out four objects, then three objects, then counting all seven. The trouble is that their memory of the three and four on one hand, and the seven on the other, is too far away for the child to make a connection. But if a child subitizes the four, she is more likely to count on, starting with four, then five, six, and seven. Then, she learns a more sophisticated counting strategy and starts learning the fact that 4 + 3 = 7.
So, be sure to notice and name numbers. Talk about how many objects appear in small groups everywhere around you. It's a sure way to put children on the path to math literacy, because it not only teaches them about numbers, but also ignites a mathematical way of thinking that will allow them to continue to teach themselves.