# Problem Solving Math Linked to Relating Quantities to Numerals

Author: National Institutes of Health
Published: 2011/10/28 - Updated: 2022/06/14
Contents: Summary - Definition - Introduction - Main - Related

Synopsis: Children starting school with difficulty associating small exact quantities of items with printed numerals more likely to develop a math-related learning disability. The researchers' analysis was based on a battery of tests they gave one to three times each year to 177 students at 12 Columbia, Mo., public schools. The testing process took place from kindergarten through fifth grade. Our findings suggest that children who generally struggle with math - the low achievers - may have a poor sense of numbers. Still, they can narrow the achievement gap partly because most of them can memorize new math facts and, thus, learn some aspects of math as quickly as their typically achieving peers.

## Introduction

Math disability linked to a problem relating quantities to numerals - Children who start elementary school with difficulty associating small exact amounts of items with the printed digits that represent those quantities are more likely to develop a math-related learning disability than are their peers, according to a study supported by the National Institutes of Health.

### Main Digest

NIH-funded study also finds math-disabled students fail to catch up to classmates. The children in the study who appeared to have difficulty grasping the fundamental concept of exact numerical quantities - that the printed numeral 3, for example, represents three dots on a page - went on to be diagnosed with a math learning disability by fifth grade.

Other early factors correlated with a math learning disability were difficulty recalling answers to single-digit addition problems, distractibility in class, and difficulty understanding that more complex math problems can be broken down into smaller problems that can be solved individually.

Although the math learning disabled children did make limited progress in subsequent grades, by fifth grade, they had not caught up to their typically achieving peers in the ability to recall number facts or in their ease of adding sets of dots and numerals together. The authors note that the math-disabled students did catch up in other areas, such as using counting to solve problems.

The study was not designed to prove cause and effect, so the researchers do not know whether the identified factors caused the children's math learning disability or were linked to other, unidentified factors.

"The search for factors underlying difficulty learning mathematics is critical," said Kathy Mann Koepke, Ph.D. of NIH's Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), which funded the study. "Once we identify such factors, the hope is that we can modify them through appropriate teaching methods to help people who have difficulty learning and using math."

Dr. Mann Koepke directs the NICHD's Mathematics and Science Cognition and Learning Development and Disorders program.

"Math skills are important for higher education and for entry into many higher-paying technical fields," she said. "Math skills have many health implications. For example, many American adults lack the basic math skills to estimate the appropriate number of calories in their diets or calculate the time intervals to take their medications."

The study was conducted by Mary K. Hoard, Ph.D., Lara Nugent, Drew H. Bailey, and David C. Geary, Ph.D., all of the University of Missouri, Columbia.

Their findings appear in the Journal of Educational Psychology.

The researchers' analysis was based on a battery of tests they gave one to three times each year to 177 students at 12 Columbia, Mo., public schools. The testing process took place from kindergarten through fifth grade. The researchers measured several factors:

• Math achievement
• Paying attention in class
• Understanding of the number line
• Intelligence and general cognitive ability
• Aptitude for solving simple and complex addition problems
• An understanding of numbers and their relation to each other
• Working memory, the ability to hold one idea or concept in mind while switching between tasks

The researchers classified the students into three groups based on their early achievement and the subsequent progress in math from kindergarten to fifth grade.

One group - referred to as typically achieving students - had average scores in kindergarten and developed their skills at an average rate during their early school years (132 students).

Low-achieving students had an average score in kindergarten and made inconsistent and slow progress (29 students).

Students with a low initial score and consistently slow progress were described as learning disabled in math (16 students).

After their analysis, the researchers found that differences between groups in kindergarten scores correlated with the result of one test. For this test, students were asked to look at a series of rectangles resembling dominoes on a computer screen. Each domino was divided into two or three areas; some contained one to nine dots, and others a written numeral. Students were asked to quickly circle any dominoes in which the number of dots, together with the numeral, matched the target number and not to circle those that did not match.

The researchers found that the difference in scores from this test was linked to the overall gap in math scores between typically achieving and math learning disabled groups.

"Our findings suggest that children who generally struggle with math - the low achievers - may have a poor sense of numbers, but they can narrow the achievement gap in part because most of them can memorize new math facts and, thus, learn some aspects of math as quickly as their typically achieving peers," said Dr. Geary.

Dr. Geary added that, in contrast to the low achievers, students with a math learning disability not only have a poor concept of numbers but also have difficulty memorizing math facts.

Clarifying the factors contributing to a math learning disability may lead to the development of teaching methods that help students overcome difficulty with number concepts and skills, Dr. Mann-Koepke said. It is important to identify potential difficulties early when chances for successfully overcoming them are greatest.

Other NICHD-funded investigators have also identified basic risk factors for a math learning disability. These researchers have shown that math skills are linked to the approximate number system, a person's intuitive ability to estimate quantities or identify the approximate number in a set.

One study of grade school children showed that this ability is impaired in children with a math learning disability. A related study showed that difficulty estimating such quantities is apparent in children as young as three and is correlated with later poor math performance in school. Researchers do not yet know if the ability to distinguish between small, exact quantities is related to the approximate number system.

This quality-reviewed publication titled Problem Solving Math Linked to Relating Quantities to Numerals was selected for publishing by Disabled World's editors due to its relevance to the disability community. While the content may have been edited for style, clarity, or brevity, it was originally authored by National Institutes of Health and published 2011/10/28 (Edit Update: 2022/06/14). For further details or clarifications, you can contact National Institutes of Health directly at nih.gov Disabled World does not provide any warranties or endorsements related to this article.

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