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.
"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.
Spotting and correcting math deficits in time can yield big benefits according to Geary's study, which was supported by a grant from the Eunice Kennedy Shriver National Institute of Child Health and Human Development. The findings underscore the importance of expertly taught preschool and kindergarten math curricula, especially for children who are at risk for poor school performance because of poverty and other social disadvantages.
But in recent decades, attention on education's "Three Rs" — reading, writing and arithmetic — has focused sharply on the first two Rs to the exclusion of 'rithmetic during early school grades.
"A lot has been done to focus on reading skills of at-risk kids," Geary said. "And, a lot has been focused on math and science, but that's been largely about getting people ready for college math. Kids who are not going to college still need to have jobs, but they've fallen through the cracks. They need literacy skills, but also need to have quantitative skills — and that need will only go up as society becomes more technology-dependent."
The findings of the new study mesh with, and expand upon, conclusions drawn in a 2012 report co-authored by Chris Cain, a mathematics consultant to the U.S. Department of Education. It said grouping larger numbers into smaller sets makes them easier for the human brain to manage — the reason that long telephone numbers are broken into smaller sets by dashes.
Mathematical concepts are built one upon another in a logical, step-wise progression, Cain said. If early foundations are shaky, students will make slow progress thereafter. So, kids who are pushed toward learning addition and multiplication before they understand the relationships between numerals and quantities will simply memorize math facts.
Memorizing multiplication tables isn't a bad thing, but children who don't comprehend the processes behind adding and multiplying are likely to have problems in math that show up later. When that happens, intervention is valuable — even if it isn't immediate, according to Cain's research.
"If a student doesn't have great (number understanding) early on, there are still things we can do to help that child catch up through intensive intervention that focuses on what's missing," he said.
Like Geary, Cain feels that the sustained emphasis in the United States on reading well in early grades should be matched by equal efforts to build childrens' numeracy skills as early as possible. Better teacher training is the place to start, he said, noting that teacher preparation programs in U.S. colleges focus on building teachers' math knowledge, but put too little emphasis on teaching them how to impart that knowledge to students.
"I've been in lots of classrooms where the teacher knew how to do the math, but should never have been turned loose with a whiteboard and marker," he said.
A 2008 report by the National Mathematics Advisory Panel included recommendations for ways parents can help young children succeed in math after they enter school. Those include:
- Introduce babies and toddlers to numbers, counting and shapes.
- Before kindergarten, help your child understand phrases related to math, such as “more than,” “less than” and “equal to.”
- Do activities in counting, and in joining (adding) and separating (subtracting) objects.
- Show your child that you value math achievement, even if you feel you are not good at math.
- Help your child understand that being good at math is about working hard, not about being born smart.