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Topic: [ME] English words hinder math skills development
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
[ME] English words hinder math skills development
Posted: Apr 14, 1999 10:23 PM
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[Note: From a colleague on the west coast ... some more research from
David Geary, whose work is referenced in the 1999 CA Mathematics Framework.]

APA Monitor, Volume 30, No. 4, April, 1999

English words may hinder math skills development

The words and symbols used to represent numbers may interfere with
understanding of math concepts.

By Beth Azar, Monitor staff

Each time the government releases a new round of test scores, the United
States laments the dismal performance of its children compared with
children in other nations, particularly those from Asia.

And although differences in classroom instruction may be partly to blame,
psychologists are finding that cultural differences in computational
ability can begin before school and may have their roots in the words and
symbols different cultures use to represent numbers.

For example, Asian children may get a head start in understanding that our
number system is base 10 because their number words make that connection
explicit whereas English does not. And fractions may pose a particular
problem for all children in part because using the same numerals for
fractions as for whole numbers may interfere with learning and in part
because their brains are hard-wired to deal with whole numbers.

Classroom instruction may be able to address these inherent problems by
explicitly teaching the concepts that children struggle with, says
psychologist David Geary, PhD, of the University of Missouri, Columbia.

Words get in the way

For English-speaking children, number words may hamper learning before they
even enter school: Studies by researchers including Kevin Miller, PhD, of
the University of Illinois-Urbana- Champaign, consistently show that Asian
children learn to count earlier and higher than their American counterparts
and can do simple addition and subtraction sooner as well.

Researchers argue that differences in number words may be a major factor
behind these differences. The culprit is the way English--as well as some
other languages--treats numbers between 10 and 100. The teen numbers in
these languages are irregular and difficult for children to learn and the
rest of the count is separated into decades with words such as "twenty,"
"thirty" and "forty."

In most Asian languages the number words are far more consistent. In China,
for example, the teen words are presented as 10 plus some ones: Eleven is
simply "ten one," 12 is "ten two" and 13 is "ten three." This pattern
continues into the decade numbers where 20 is "two ten," 30 is "three ten"
and 45 is "four ten five." The language makes it obvious that the number,
system is base 10.

This difference in language may partly explain why most Asian children
learn by the mid-dle of first grade to subtract and add by thinking of
numbers in as a 10 and some ones--an extremely helpful and efficient method
of doing addition and subtraction, says Geary. In contrast, children in the
United States, where much of the cross-cultural work has been conducted,
rarely use such a method, even as they get older, Geary and other
researcher find.

In fact, Chinese children who are good at counting at age 5 are already
beginning to understand that teen words can be thought of as 10 plus some
ones, find psychologists Karen Fuson, PhD and Connie Suk-Han Ho, PhD, of
the Chinese University of Hong Kong. No children in the United States or
England, regardless of their counting proficiency, understood this concept
by age 5, they found in a series of studies published in the <I>Journal of
Educational Psychology<P> (Vol. 90, No. 3, p. 536-544).

Children in the United States eventually learn that the number system is
base 10 and that teens are tens plus ones, but only the most mathematically
adept children ever learn to add by adding up to 10 and then adding the
remaining ones (as with adding 7+8 by breaking 7 into 5 and 2, adding 2 to
8 to get 10 and then adding 5 for 15), says Fuson.

She has emphasized teaching about base 10 in a curriculum she's developed
and is finding in preliminary evaluations that when taught this way
children from poor inner-city schools districts quickly begin to outperform
children from wealthier school districts. Countries that have similar
language problems, but better math scores than the United States, may
already use this kind of instruction.

Friction with fractions

Teachers may also need to work on the way they instruct children in
fractions, which are notoriously difficult even for adults, say

Children may have trouble with fractions for several reasons, says Rochel
Gelman, PhD, of the University of California, Los Angeles, whose research
is geared toward understanding how children's notion of fractions develops.
For one, because they learn to use numerals as whole numbers, it might
confuse them to use the same symbols in a different way. It may also be
that children have hard-wired mental structures that are designed to handle
whole numbers and have trouble dealing with fractions.

A new study by University of Chicago psychologist Janellen Huttenlocher,
PhD, and her colleagues supports the latter theory. They find that when
numerals are removed from the equation and children are asked to calculate
with fractions using nonverbal tasks, they do quite well.

In the study of 3- to 7-year-olds, instead of asking children to add
numerical fractions, the researchers asked children to recreate fractional
sums using wedge-shaped pieces of sponges that, when put together, formed a
circle. As the children aged, they grew better at solving the nonverbal
fraction problems. In fact, their skills improved in parallel, though at a
slower rate, with their skills for manipulating whole numbers.

This finding indicates that children are able to manipulate fractions when
they can form a mental model of the problem using real-world objects. They
stumble only when they're asked to work with fractions represented as
numerals, says Huttenlocher.

"With fractions the villain is putting 3's over 4's," says Huttenlocher,
whose study is published in _Developmental Psychology_ (Vol. 35, No. 5, p.
164-174). "Children can mentally handle fractions, but the numbers get in
their way--so with 4/5 and 4/8, children think 4/8 must be more because
there's an 8 there."

Gelman agrees that interference is likely part of the problem. But she also
believes--based on research in animals and humans--that there is an innate
and hard-wired part of the brain that was designed through the course of
evolution to handle whole numbers. This predisposition makes it easier for
children to learn about whole numbers and hinders their learning of
fractions, she argues.

"It's hard to think that we have trouble learning fractions just because we
have no experience with numbers used this way," says Gelman. "That can't
explain why the fraction problem extends well into college for some

Regardless of why children, and adults, have trouble with fractions, most
researchers agree that teachers should introduce fractions in the context
of real-world examples, including slices of a pie, pieces of an apple and
portions of candy

Further reading

* Geary, D. Reflections of evolution and culture in children's cognition:
implications for mathematical development and instruction. American
Psychologist, Vol. 50, No. 1, p. 24-37.


Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)

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