Alice Park,
TIME
Give a
three-year old a smartphone and she’ll likely figure out how to turn it on and
operate a few simple functions. But confront her with an algebra problem and
ask her to solve for x? Not likely.
For decades,
child developmental psychologist Jean Piaget convinced us that young,
undeveloped minds couldn’t handle complex concepts because they simply weren’t
experienced or mature enough yet. Piaget, in fact, believed that toddlers could
not understand cause and effect, that they couldn’t think logically, and that
they also couldn’t handle abstract ideas.
That’s because,
he argued, children learn to develop these higher skills through trial and
error. But child development specialists are finding out that preschoolers
without any formal education may have the capacity to understand more complex
concepts than we give them credit for, such as complicated rules for operating
a toy or even solving for an unknown in algebra. Some of this is due to their
ability to be more open and flexible about their world than adults. But beyond
that, toddlers may have the innate ability to understand abstract concepts like
quantities and causality, and that’s fueling an exciting stream of experiments
that reveal just how sophisticated preschoolers’ brains might be.
Alison Gopnik,
professor of psychology at University of California Berkeley and her team
devised a way to test how well young kids understand the abstract concept of
multiple causality—the idea that there may be more than one cause for a single
effect. They pitted 32 preschoolers around 4 years old against 143 undergrads.
The study centered around a toy that could be turned on by placing a single
blue-colored block on the toy’s tray, but could also be activated if two blocks
of different colors—orange and purple—were placed on the tray. Both the kids
and the undergraduates were shown how the toy worked and then asked which
blocks activated the toy.
The
preschoolers were adept at figuring out that the blue blocks turned on the toy,
as did the purple and orange ones, but that the purple and orange ones needed
to be paired together. The Berkeley undergraduates, however, had a harder time
accepting the scenario. Their previous experience in the world, which tends to
work in a single-cause-equals-single-effect way, hampered their ability to
accept the unusual rules that activated they toy; they wanted to believe that
it was activated either by a single color or by a combination of colors, but
not both. “The training didn’t seem to give them a hint that the world might
work in different ways,” says Gopnik, who published her work in the journal
Cognition.
The
preschoolers’ lack of bias about causality likely contributed to their ability
to learn the multiple ways to activate the toy, but the results also suggest
that preschoolers really can think logically and in more complicated ways. Just
because they can’t express themselves or aren’t as adept at demonstrating such
knowledge, doesn’t mean they don’t have it.
Researchers
from Johns Hopkins University, for example, found a similar effect among
preschoolers when it came to math. Previous studies showed that if you present
infants with eight objects over and over until they got bored, and then showed
them 16, they suddenly regained interest and sensed that things changed. Even
before they are taught about numbers or amounts, then, infants seem to have a
grasp on quantity. “All the evidence so far leads us to believe that this is something
that babies come into the world with,” says Melissa Kibbe, co-author of that
study.
She and her
colleague Lisa Feigenson wondered if that innate sense of quantity might
translate into an understanding of numbers and higher math functions, including
solving for unknowns—one of the foundations of algebra—which often isn’t taught
until seventh or eighth grades. So they conducted a series of experiments using
a cup with a fixed amount of objects that substituted for x in the equation 5 +
x = 17.
To divert the
four- and six-year olds’ attention away from Arabic numerals to quantities
instead, the researchers used a puppet and a “magic” cup that contained 12
buttons. In one of the experiments, the children saw five buttons on the table.
After watching the researchers add the 12 buttons from the cup, they were told
there were 17 buttons on the table. In another test, the youngsters saw three
piles of objects—buttons, coins or small toys—in varying amounts, and observed
the researchers adding the fixed number of contents of the puppet’s cup to
each.
After training
the kids on how the cup worked, the researchers tried to confuse them with
another cup containing fewer (such as four) or more (such as 24) objects.
However, the kids understood intuitively that the decoy cup contained the wrong
amount of items and that a specific amount—x, the “magic” cup amount—had to be
added to reach the sum.
When the
children were presented with the straight algebraic equation on a card, 5 + _ =
17, and asked to fill in the blank, their answers were no better than chance;
that’s because they were simply guessing. In the puppet and cup scenarios,
however, which did not involve numerals, they were able to accurately identify
the correct amount, increasing their accuracy dramatically, to between 59% to
79%.
That suggested
that the preschoolers had some concept of quantity, and the appropriate amount
that they needed to get from a small quantity (five) to a larger one (17). What
surprised Kibbe was not just that preschoolers understood the concept of adding
“more,” but that they could also calibrate how much more was needed to fill in
the unknown quantity.
“These kids had
very little formal schooling so far, but what we are finding is that when we
tap into their gut sense, something we call the Approximate Number Sense (ANS),
kids are able to do much more complex calculations than if we gave them numbers
and letters,” says Kibbe of her results, which were reported in the journal
Developmental Science. And there doesn’t seem to be any gender differences in
this innate ability, at least not among the girls and boys Kibbe studied.
Though it may
be too early to translate such findings to the classroom, the results lay the
groundwork for studying similar innate skills and how they might be better
understood. ANS, for example, is one of many so-called cognitive primitives, or
constructs that young children may have that could enhance their learning but
that current curricula aren’t exploiting. Developmental experts are still
trying to figure out how malleable these constructs are, and how much of an
impact they can have on future learning. For instance, do kids who hone their
ANS skills become better at algebra and calculus in high school? “We still need
to figure out which constructs matter most, and which are most amenable to
interventions to help children improve their learning,” says Star.
“The hard part
is, educationally, how do you build up and upon this intuitive knowledge in a
way that allows a child to capture the complexity but not hold them back,” says
Tina Grotzer, associate professor of education at Harvard. Tapping into a
child’s still developing sense of numbers and quantities is one thing, but
overloading it with too many new constructs about algebra, unknowns, and
problem solving may just gum up the working memory and end up adversely
affecting his learning and academic performance. “As soon as concepts get big
and complex, there are all sorts of perceptual, attentional, and cognitive
costs and challenges involved,” she says.
No comments:
Post a Comment