Millions
of high school and college algebra students are united in a shared agony over
solving for

*x*and*y*, and for those to whom the answers don’t come easily, it gets worse: Most preschoolers and kindergarteners can do some algebra before even entering a math class.
In a recently
published study in the journal

*Developmental Science*, lead author and post-doctoral fellow Melissa Kibbe and Lisa Feigenson, associate professor of psychological and brain sciences at Johns Hopkins University’s Krieger School of Arts and Sciences, find that most preschoolers and kindergarteners, or children between 4 and 6, can do basic algebra naturally.
“These
very young children, some of whom are just learning to count, and few of whom
have even gone to school yet, are doing basic algebra and with little effort,”
Kibbe said. “They do it by using what we call their ‘Approximate Number
System:’ their gut-level, inborn sense of quantity and number.”

The
“Approximate Number System,” or ANS, is also called “number sense,” and
describes humans’ and animals’ ability to quickly size up the quantity of
objects in their everyday environments. Humans and a host of other animals are
born with this ability and it’s probably an evolutionary adaptation to help
human and animal ancestors survive in the wild, scientists say.

Previous
research has revealed some interesting facts about number sense, including that
adolescents with better math abilities also had superior number sense when they
were preschoolers, and that number sense peaks at age 35.

Kibbe,
working in Feigenson’s lab, wondered whether preschool-age children could
harness that intuitive mathematical ability to solve for a hidden variable, or
in other words, to do something akin to basic algebra before they ever received
formal classroom mathematics instruction. The answer was “yes,” at least when
the algebra problem was acted out by two furry stuffed animals — Gator and
Cheetah — using “magic cups” filled with objects like buttons, plastic doll
shoes and pennies.

In
the study, children sat down individually with an examiner who introduced them
to the two characters, each of whom had a cup filled with an unknown quantity
of items. Children were told that each character’s cup would “magically” add
more items to a pile of objects already sitting on a table. But children
were not allowed to see the number of objects in either cup: they only saw the
pile before it was added to, and after, so they had to infer approximately how
many objects Gator’s cup and Cheetah’s cup contained.

At
the end, the examiner pretended that she had mixed up the cups, and asked the
children — after showing them what was in one of the cups – to help her figure
out whose cup it was. The majority of the children knew whose cup it was, a
finding that revealed for the researchers that the pint-sized participants had
been solving for a missing quantity, which is the essence of doing basic
algebra.

“What
was in the cup was the

*x*and*y*variable, and children nailed it,” said Feigenson, director of Johns Hopkins Laboratory for Child Development. “Gator’s cup was the*x*variable and Cheetah’s cup was the*y*variable. We found out that young children are very, very good at this. It appears that they are harnessing their gut level number sense to solve this task.”
If
this kind of basic algebraic reasoning is so simple and natural for 4, 5 and
6-year-olds, the question remains why it is so difficult for teens and others.

“One
possibility is that formal algebra relies on memorized rules and symbols that
seem to trip many people up,” Feigenson said. “So one of the exciting future
directions for this research is to ask whether telling teachers that children
have this gut level ability – long before they master the symbols – might help
in encouraging students to harness these skills. Teachers may be able to help
children master these kind of computations earlier, and more easily, giving
them a wedge into the system.”

While
the ANS helps children in solving basic algebra, more sophisticated concepts
and reasoning are needed to master the complex algebra problems that are taught
later in the school age years.

Another
finding from the research was that an ANS aptitude does not follow gender
lines. Boys and girls answered questions correctly in equal proportions during
the experiments, the researchers said.

Although
other research shows that even young children can be influenced by gender
stereotypes about girls’ versus boys’ math prowess, “we see no evidence for
gender differences in our work on basic number sense,” Feigenson said.

Parents
with numerically challenged kids shouldn’t worry that not showing a strong
aptitude with numbers is a sign that Bobby or Becky will be bad at math. The
psychologists say it’s more important to nurture and support young children’s
use of the ANS in solving problems that will later be introduced more formally
in school.

“We find links at all ages between the precision of
people’s Approximate Number System and their formal math ability,” Feigenson
said. “But this does not necessarily mean that children with poorer precision
grow up to be bad at math. For example, children with poorer number sense may
need to rely on other strategies, besides their gut sense of number, to solve
math problems. But this is an area where much future research is needed.”

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