Maybe your child has heard the classic nursery rhyme, “One, two, buckle my shoe.” But does she know that one and two are numbers? Or what the next numbers would be? And that numbers stand for quantities of things?
Kids who nail these concepts early in life do much better in math all through school, research shows.
A big window of opportunity opens in the preschool years.
But, deep breath. We’re not talking pre-nap flash cards or introductory algebra in the sandbox. We’re talking really simple basics that can easily be taught at home.
“Our study suggests that kids should at least know what one, two, and three mean by the time they’re 4 years old,” says David C. Geary, a cognitive developmental and evolutionary psychologist with an interest in mathematical learning at the University of Missouri.
Sounds simple. But many kids miss out.
And this basic pre-math skill is critical, Geary says, because it forms a kind of future-math-ability dividing line. Children who enter kindergarten unable to understand number basics start out behind, showed his latest study in The Journal of Experimental Child Psychology. They tend to stay behind in math too.
The good news: Just knowing this and giving it a little attention can put your preschooler on the right track.
“A lot of parents focus on pre-literacy stuff like sounds and the alphabet,” Geary told me. “It’s not as commonplace—even among well-educated parents—to help kids with pre-numeracy.”
What kind of pre-numeracy exactly? And how?
That’s a useful question because kids often get one extreme of early math attention (none) or the other extreme (academic preschools that expose them to a wide range of math concepts that can bring more stress—or confusion—than benefits).
To figure out what our littlest mathematicians really need to know, Geary and his colleagues assessed more than 100 kids over two years, at the beginning and end of preschool. (Their exact ages at the start ranged from 3 years, 3 months to 4 years, 3 months.) They gave them a number of different tasks that measured things like their ability to recognize and compare numerals, knowledge of counting principles, and more. (They controlled for factors like IQ, parental education, and income.) The goal: To try to tease out which of the many components of pre-math make the most foundational difference at this early age.
Indeed, just a couple of key concepts prove to be more fundamental than others.
These are the basics preschoolers need, Geary says:
1. Learning the count list
This one’s easy. It’s being able to say the numbers in order: one, two, three, four….
Four-year-olds should be able to count at least to the teens and maybe a bit beyond.
Most of us expose preschoolers to counting. Unfortunately, Geary says, “Parents often do it in a rote way, focusing only on counting over and over. You have to go beyond just counting and focus attention on what the words actually mean.”
That’s the next—and most critical—skill, he says.
2. Learning the quantities associated with these words (cardinal values)
Three-fourths of kids in the study who had a poor understanding of number words two years before starting kindergarten were below the 15th percentile on number fluency in kindergarten.
Knowing the meaning of number words— that “three” equals three apples or three dogs, for example, is the first symbolic math concept kids learn. “That makes it foundational for learning other aspects of symbolic math,” Geary told me.
At first, around ages 2.5 to 3, kids are “one-knowers.” If you put a kid this age in front of a pile of toys and ask for “one,” he’ll give you one. But if you ask for “two,” you’ll get random amounts.
Within a few months, kids become “two knowers.” It can take a few months longer for them to become “three knowers”—giving you three toys when you ask for “three.” Once they understand the amounts represented by “three” and “four,” Geary says, they quickly catch on to the idea that each successive number in the counting string they’ve memorized is one more than the number before. (That’s when they become “CV-knowers,” for cardinal-value knowers, like older kids or adults.)
“It’s a pretty long and complicated process,” he adds, which can take about a year-and-a-half overall.
Four-year-olds should be at least three-knowers, the Missouri study shows.
3. Learning rudimentary adding and subtracting
Key word here: rudimentary. Preschoolers don’t need to know how to do actual arithmetic. But it’s helpful for them to understand how “less” and “more” work. That is, that adding things to a set creates “more” (increasing the set size) and subtracting one creates “less” (decreasing the set size).
If you show a child a row of three things, then cover them up and remove one, and ask the child to show you (with a different set of objects) how many there should be left, they should put out two objects. At first, they can only demonstrate this understanding with very small quantities—three or fewer, Geary says, which is age-appropriate.
This skill is somewhat less of a priority than getting the counting and number knowledge down, though, he adds.
The easy fix: everyday numbers
We parents only need to do two things to get our kids off to a smart start in math:
First, just be aware that pre-numeracy exists and is as important as pre-literacy.
And second, find ways to make counting come alive for them (the way we already do with ABCs and letter sounds).
“You don’t want to push young kids too hard, but there are simple ways you can incorporate counting, discussion of associated quantities, and number talk into daily activities,” Geary says.
Count the stairs as you walk up them. Repetition is a good way to master the counting list. (You can count anything, of course, not just stairs.)
Refer to quantities when you talk about things during the day. Point out that “two” refers to two shoes or two hands. Or that there are “three” people at the table or “four” white trucks in a row.
Ask “how many?” If you give your child two crackers, ask her how many she has. If she doesn’t know, Geary says, count them out for her: “One, two.”
Make comparisons. Give your child two slices of apple and give yourself three. Ask, “Which is more, two or three?”
Read counting books. They’re a good way to expose your child to the Arabic numerals 1 to 9. At ages 3 and 4, kids also need experience understanding the amounts that numerals represent. Just start with 1, 2, and 3, Geary says. Some classics:
Introduce basic shapes too. Name circles, squares, triangles, and rectangles as you hand out Cheerios or look at windows. It’s another kind of pre-math thinking that will pay off later.
Every kid can be a math whiz!
Even as early as 3 or 4, there seems to be a lot of variation in kids’ innate math abilities, Geary says. Some toddlers seem to focus spontaneously on quantity, counting by themselves or having a natural understanding of how many of something there are (at least in very small quantities). Researchers don’t yet understand where this ability comes from.
But they do know that almost any preschooler can, with exposure and practice, pick up the basic pre-math concepts that will help set the stage for understanding math in first grade and beyond.
“The message is pretty simple: Once you know, ‘Okay, this is what’s important,’ you can focus on those things,” Geary told me. “Nothing too complicated.”