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NPR Ed
We're All Born With
Mathematical Abilities (And Why That's Important)
Julie Dependbrock
August 1, 2017
As an undergraduate at the University of Arizona, Kristy vanMarle knew
she wanted to go to grad school for psychology, but wasn't sure what
lab to join. Then, she saw a flyer: Did you know that babies can count?
"I thought, No way. Babies probably can't count, and they certainly
don't count the way that we do," she says. But the seed was planted,
and vanMarle started down her path of study. The person who made that
flyer, Karen Wynn, became her mentor and they have since co-published
several studies together.
I spoke with vanMarle, an associate professor at the University of
Missouri whose research focuses on children's early cognitive
development, to find out what she's been up to lately. The interview
that follows has been edited and condensed.
So, what's all this about being born mathematicians?
In my lab, we are particularly interested in numerical development and
understanding of objects — how the early number skills of young
infants, possibly even newborns, get built upon to develop a uniquely
human capacity for symbolic math.
The roots of those abilities and those skills seem to come from an
endowment that is evolutionarily ancient and that we share with most
other species.
In other words, we've evolved to know math — along with almost every
other animal. How did you become interested in this?
I've always been fascinated with the idea that you can have this
sophisticated knowledge — at least the foundations of it — in place,
very early on. And we know now that it's very broadly available across
animal species. Species as different from humans as fish: Guppies are
sensitive to numbers in the environment. Of course, primates are.
Salamanders. Various insects. It's this basic ability that helps
animals navigate their environment. I mean, literally, navigate the
environment by calculating angles and distances and so forth. It helps
them choose the greater amount of food if they're choosing between two
quantities. It shows up in foraging contexts all the time.
So I've gotten interested in how these early abilities might provide a
foundation for these much more sophisticated abilities that humans
grasp pretty ubiquitously. If you're exposed to math and counting, all
humans will get it to a degree. Some more easily than others, of
course, we all experience that. But the capacity is certainly available.
What's been the focus of your most recent research?
Being literate with numbers and math is becoming increasingly important
in modern society — perhaps even more important than literacy, which
was the focus of a lot of educational initiatives for so many years.
We know now that numeracy at the end of high school is a really strong
and important predictor of an individual's economic and occupational
success. We also know from many, many different studies — including
those conducted by my MU colleague, David Geary — that kids who start
school behind their peers in math tend to stay behind. And the gap
widens over the course of their schooling.
Our project is trying to get at what early predictors we can uncover
that will tell us who might be at risk for being behind their peers
when they enter kindergarten. We're taking what we know and going back
a couple steps to see if we can identify kids at risk in the hopes of
creating some interventions that can catch them up before school entry
and put them on a much more positive path.
How exactly do you study something like that?
We followed kids through two years of preschool and assessed a really
broad range of quantitative skills. Because when you talk about math
achievement and number knowledge, it's not a single solitary construct.
Over the two years of preschool, we gave them 12 different tasks —
twice a year. Some were symbolic: being able to recite the Arabic
numerals or the verbal count list. Others were tapping these earlier,
emerging non-symbolic skills: being able to estimate which of two sets
of dots is bigger, being able to keep track of additions and
subtractions that happen in the environment. Skills like that are
building on these evolutionarily ancient core capacities.
So which of those actually predict math achievement?
Out of those 12 different skills, there's really one or two that matter
most. When we followed up with these kids in kindergarten and first
grade, their ability to estimate quantities — this ancient ability —
seems to be really important. And also their ability to engage in
cardinal reasoning i.e. knowing that the number three — when you see it
on a page or hear someone say "three" — that it means exactly three,
which is really at the root of our ability to count.
This cardinality, in particular, seems to be the most important skill
that we can measure at a very young age and then predict whether kids
are going to be succeeding in a much broader assessment of math
achievement when they enter kindergarten.
Will this have an effect on what kids learn in preschool?
Well, we hope so. If you look at preschool curricula — kids who are
getting structured instruction in math early on — it's really trying to
tap these different skills. But when you have a lot of different things
you're trying to teach, you don't go into depth with them, right?
You're just trying to touch on all of them at once.
Our research points to the possibility that it might be more effective
for early education if you focus on these core skills that seem to
matter the most for developing symbolic knowledge. We're currently
running a pilot study — an intervention that targets this ability.
What does that intervention look like?
Children count and create sets. We use ice cube trays to count some
number of objects. We say, 'Can you put six items into this tray?' And
then we point out very interactively where they make mistakes and try
to reinforce rules.
Has it been effective?
It's too early to say. We are currently inputting the data and
analyzing it so I don't have the punchline for you, unfortunately. But
we're hopeful it will be effective.
It's the kind of thing that parents and early educators can engage in
with children. It's possible to even create an app that would allow
kids to make sets on an iPad. Of course, that's way down the road for
us. But that's kind of where we're headed — getting an intervention
that works. We know how to identify which kids are likely to be at risk
so the logical next step is to figure out a way to help them.
Your research points out that parents aren't engaging their kids in
number-learning nearly enough at home. What should parents be doing?
There are any number of opportunities (no pun intended) to point out
numbers to your toddler. When you hand them two crackers, you can place
them on the table, count them ("one, two!" "two cookies!") as they
watch. That simple interaction reinforces two of the most important
rules of counting — one-to-one correspondence (labeling each item
exactly once, maybe pointing as you do) and cardinality (in this case,
repeating the last number to signify it stands for the total number in
the set). Parents can also engage children by asking them to judge the
ordinality of numbers: "I have two crackers and you have three! Who has
more, you or me?"
Cooking is another common activity where children can get exposed to
amounts and the relationships between amounts.
I think everyday situations present parents with lots of opportunities
to help children learn the meanings of numbers and the relationships
between the numbers.
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