Just as athletes stretch and jog before a
competition, practicing with quantities "could be seen as a warm-up
for your brain to do math," said Melissa Libertus, a cognition
researcher at the University of Pittsburgh in Pennsylvania, who
wasn't involved in the new study.
For years, psychologists have known that human infants are born with
an "approximate number sense," called ANS, or the ability to
estimate amounts without counting. But researchers have puzzled over
how this intuitive sense of number relates to and affects arithmetic
Results from the study published in the journal Cognition show "the
engagement of ANS leads to better math performance," said lead
author Daniel Hyde of the University of Illinois at
Nearly 100 first-graders from the Boston area, about half girls and
half boys, participated in a series of experiments for the study.
First, the researchers tested if the ability to estimate quantities
could be directly tied to math skills. The kids were divided equally
into four groups, and each group was assigned to make estimates and
comparisons of different non-numerical things.
One set of kids had to estimate the quantity of dots in two groups
of dots and say which had more. Another set of children had to "add"
groups of dots together to say if a final group was larger than the
previous groups. Other kids compared the lengths of lines or levels
Afterwards, boys and girls who worked with the black dots completed
easy addition problems roughly 25 percent faster than counterparts
who interacted with the lines or brightness exercises.
On harder math problems, the black dot groups scored an average of
15 points higher — about a letter grade and a half — than boys and
girls who didn't work with quantities of things.
"One of the most striking things was that they were able to find an
effect just after a few short training exercises," Ariel Starr told
Reuters Health. Starr, a doctoral student at Duke University in
Durham, North Carolina, has done similar research but was not
involved in the current work.
In a second exercise, which included only 48 of the original kids,
Hyde and his team wanted to rule out the possibility that the
training exercises had an overall positive effect on any sort of
test, not just math. So they added a language test to the quizzes
given to the kids afterwards.
In this second experiment, they also increased the difficulty of the
math problems. The researchers couldn't find any significant
differences between the groups on the verbal test. But once again,
children who worked with dots did better than those who compared
brightness levels when presented with a mathematical challenge.
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Hyde and his team say that the findings show direct causal evidence that
exercising the ANS, as the current study did, leads to better math performance.
Starr said the findings are suggestive of a relationship, but more research is
necessary to know exactly what caused the improvement in arithmetic.
"The key takeaway here is that getting children to think about
quantities or numbers can put them in a state of mind that might
enable them to do better on math problems," Starr said.
Without knowing more about the children in the experimental groups,
she added, "it's difficult to know how broadly to apply the
Both Starr and Libertus agreed that games are available on the
market now for parents to try with their children. French
researchers have been working since 2006 on a free downloadable
computer game called "The Number Race," which deals with choosing
different quantities. Both that game and one called "Rescue
Calcularis," are tailored for children with learning disabilities,
but, "it's very possible they could be beneficial for all kids,"
Board games like Chutes and Ladders, which require children to
count spaces along the board, help them to organize their mental
number line, Starr said.
"The effect they show here is based only on an improvement in timed
arithmetic done immediately after the training," Libertus said. She
said that future studies could see if this effect could be seen in
other types of math problems, for example, word problems, or
learning new math concepts.
Another area that needs to be investigated is the best age to do
this type of training, she said.
"Just like with sports, you can wonder if repeated training could
have long-lasting effect on mathematical ability," Libertus said.
Cognition, online Jan. 29, 2014.
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