For a good part of the 20th century, most people believed that children needed to be brought to math slowly. Teachers were taught to look at child development through the lens of Swiss psychologist Jean Piaget, who believed, among many other things, that no “a priori or innate cognitive structures exist in man.”
Taking a page from the Piaget model of child development, most teachers learned that discussing math with a young child was like talking to a parrot: You might succeed in cueing up some rote response, but the parrot was not learning. A child, according to Piaget, could not really grasp the concept of numbers until he or she was around six or seven. They could grasp the idea of mass at age eight and weight at around ten.
Informed by these ideas, many people believed that children were simply too concrete in their thinking to comprehend much more. Back then, elementary school teachers put a couple of colored number lines up on the bulletin board, but pretty much ignored math in the early years.
Piaget was a genius and far ahead of his time in a lot of areas. But it turns out he was dead wrong about how children learn math. Since the early 1980s, and in research that has been gaining depth and detail in the last five years or so, scientists have been able to show that many kinds of animals—rats, pigeons and primates—and yes, very young children, can discriminate between numbers and (up to a point) count, estimate, and figure out proportions. In the mid-1980s, scientists found that children who were only a few days old could differentiate between the numbers two and three.
Children, it turns out, have a sense of numbers far beyond what most people once imagined.
The earliest math ability seems to be controlled by the one-inch fold in the brain called the intraparietal sulcus, which is located approximately where you’d back comb your hair if you wanted to create a beehive hairdo.
Babies and young children don’t have math ability, but they (along with pigeons and primates) do have this evolutionary numbers sense. Some have a strong one, and some have a weaker one. And there are good studies, especially the ones done by Justin Halberta at Johns Hopkins, that suggest this numbers sense correlates to later math ability. (If you want to test your own numbers sense, go to TestMyBrain.org or Panamath.org)
“I don’t want to call that numbers sense math ability, since it is the same thing rats have. It isn’t a formal system of mathematics, but it is related to our learning and our performance.” Halberta says.
So how does this impact early math lessons in school? People who study how kids learn math say that math ability builds on math experiences. And since we now know that kids are primed for math early—much earlier than anyone thought—you need to make sure that your child is getting plenty of math in the early grades.
So in preschool, that means plenty of counting of fingers, toes, Cheerios, and ducks in the pond. In kindergarten and first grade, teachers should be discussing and developing hands-on games that rely on understanding numbers and their sequence, volume, mass, proportion and measurement. By the middle of first grade, children should be able to work out simple algorithms (You know, 2 +2 = 4).
When you are on a school tour, look for teachers who have 1.) an appreciation for all that kids can learn about math early on—and are finding ways of integrating math concepts into the curriculum and 2.) a healthy respect for the role memorization has in math facts. (There is a big body of research that suggests that kids need automaticity when it comes to things like multiplication.) Ask them to describe the balance between "conceptual math" and "rote learning" in their classroom (hint: there needs to be both).
In the early years, your child's teacher should be a cheerleader for math.
Math is one subject where practice makes perfect. Kids should get regular math homework so they can practice the concepts they are taught in school. So you might want to ask: how often do children get math homework?
In the earliest years, one or two math problems a night is appropriate and something less than ten problems a night for the upper elementary school grades. One hundred math problems a night—ugh! Ask more questions!
Too much tedious and repetitive homework could be a sign that a teacher is getting kids to learn math facts (which is necessary) or an avalanche of rote learning (which tends not to be a good thing).
And one more thing: In the early years, your child’s teacher should be a cheerleader for math. If it is not your child’s teacher’s favorite subject, your child’s teacher needs to keep that information to him or herself. So ask her or him straight up—do you like teaching math? Then listen closely to the answer.
Our kids are uniquely sensitive to the messages parents, teachers, and any authority figure delivers on a subject. “I don’t like math as much as reading” may be an honest reflection of your child’s teacher’s true orientation, and that simple sentiment is probably meant to be a compassionate effort to connect with reluctant mathematicians.
But research on the stereotype threat tells us that what authority figures communicate to children about their expectations can actually shape performance. It’s better for your child’s teacher to say, “Math is important, and it takes a lot of practice to get it right!” That teacher will help your children achieve more.