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Early exposure to basic math concepts is vital to avoid innumeracy later on, Missouri study says

Published: Monday, Feb. 18 2013 12:30 p.m. MST

The long-term study followed 177 children from kindergarten through seventh grade. It found that children who don’t grasp the meaning and function of numerals before they enter first grade fall behind their peers in math achievement, and most of them don't catch up. Those who start first grade behind their peers in math achievement remain at heightened risk for low scores on math problems through seventh grade.

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One in five adults in the U.S. can’t do basic arithmetic problems such as adding fractions, working with measurements and doing whole number arithmetic problems, according to a new study about how math skills develop. More precisely, 22 percent of adult Americans are functionally innumerate — a word that sums up the inability to do math problems in the same way the word illiterate describes the inability to read or write. The millions of Americans who fit in this category don’t have the basic math skills for most modern jobs, the study says, including jobs open to people without college degrees.

The study, by researchers at the University of Missouri, showed it is important for children to comprehend that written numerals represent quantities by the time they enter first grade. They also need to be able to solve simple arithmetic problems by grouping numbers, not just counting.

The long-term study followed 177 children from kindergarten through seventh grade. It found that children who don’t grasp the meaning and function of numerals before they enter first grade fall behind their peers in math achievement, and most of them don't catch up. Those who start first grade behind their peers in math achievement remain at heightened risk for low scores on math problems through seventh grade.

It's the first study to link starting points of math knowledge to outcomes that will affect kids later in life, said psychologist David Geary, an author of the study.

Predicting innumeracy

"We know very little about the precursors of later innumeracy," Geary said. "A lot of focus has been on preparation for college math, and not as much focus on the bottom 25 percent of students who won't be going to college — and in addition to that, will have employment problems."

When Geary says young children must be taught to understand "number systems," he means they must thoroughly understand that numerals represent quantities that can be broken down in various ways. The numeral 9, for instance, can be expressed as several differing number sets: 1 and 8; 2 and 7; 4 and 5; or 3 and 3 and 3, for instance.

That understanding is the starting point for solving more complex problems, such as adding 7 to 18. A young child lacking understanding of "18" as a quantity might try to solve the problem by counting to 18, then counting seven more — probably losing track along the way. But a child who can break numbers in to sets, and who understands the numeral "18" as a quantity, can do the problem quickly: start with 18 and add two to make 20, then add five to make 25 — the right answer.

"A kid who understands that a numeral represents a quantity doesn't have to count," Geary said. "It's much easier, and has many fewer steps. But you can't do it in this more sophisticated way unless you understand numbers and quantities.

For the study, statistical adjustments were used to even out the subjects' differences in IQ, classroom behavior, gender, race and other factors, Geary said. These controls made up for the fact that some students might start school ahead of peers in math, and stay ahead, because they have more native intelligence or enjoy more life advantages.

It's whether children have been taught about numbers — and when — that matters, not how smart or advantaged they are, according to the study. And that means there is hope for changing the crippling effects of poor math achievement, which include heightened chances for dropping out of school — a connection identified in a 2007 report published by the National High School Center and funded by the U.S. Department of Education.

"If we catch (math comprehension problems) early enough, it's something we can probably do something about," Geary said.

Early intervention

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