Burgeoning research into students’ difficulties with mathematics is starting to tease out cognitive differences between students who sometimes struggle with math and those who have dyscalculia, a severe, persistent learning disability in math.
A new, decade-long longitudinal study by researchers at the Kennedy Krieger Institute in Baltimore, published last month in the journal Child Development, finds that 9th-graders considered dyscalculic—those who performed in the bottom 10 percent of math ability on multiple tests—had substantially lower ability to grasp and compare basic number quantities than average students or even other struggling math students.
“Formal math requires some effort, and it requires effort to different degrees for different children,” said Michèle M. M. Mazzocco, the director of the Math Skills Development Project at Kennedy Krieger. “Just because someone is having difficulty with math doesn’t necessarily mean they have a math learning disability. This study points to a core marker” of true dyscalculia.
The study, she said, may help researchers and educators understand the underlying causes of persistent math problems and identify students who need the most instructional support.
Math-learning disability affects about 5 percent to 8 percent of school-age children nationwide, about as many people as are affected by dyslexia. Yet experts say research on the reading problem has for decades dwarfed studies of math difficulties by 20 to one.
“We know that basic numeracy skills are a greater predictor of later success in life than basic literacy skills,” said Daniel Ansari, one of the pioneers in the neuroscience of dyscalculia, speaking at a research forum on the disability held in Chicago last month, who is unconnected to the Kennedy Krieger study.
Difficulty or Dyscalculia?
The Kennedy Krieger study is the latest in a series of experiments on math ability and difficulties among a group of students in Baltimore public schools.
As part of that research, Ms. Mazzocco, who is also a psychiatry and behavioral sciences and education professor at the Johns Hopkins School of Medicine, started tracking 249 kindergarteners in Baltimore public schools in 1997.
She followed the students’ math performance through 9th grade, including their progress on regular math achievement tests using the Test of Early Mathematics Ability and the Woodcock-Johnson Revised Calculation test. From grades 6 to 9, she also tested specific math-related abilities, including timed computation and decomposition, or the ability to tell which numbers in a group add up to a target number, and general cognitive skills.
When the students reached 9th grade, she, Lisa Feigenson, and Justin P. Halberda, both associate professors of psychological and brain sciences at Johns Hopkins University in Baltimore, conducted two experiments to gauge their mastery of a foundation of mathematical thinking known as the “approximate number system.” That refers to a person’s ability to understand a number’s magnitude, to see a group of books, or dots on a screen, and estimate how many are there, or tell that one group has more than another group. The brain uses the same system whether comparing the numbers “7” and “12” or groups of seven and 12 symbols.
“Right away, early in the school-age years, it was apparent anecdotally that some of the children had real difficulty with that [estimation] number sense—but not all of them,” Ms. Mazzocco said.
Yet it took until the students entered 9th grade for the research team to find tools sensitive enough to measure their individual differences in estimating numbers.
The new experiments use a representative selection of 76 students in the study, including average math students; high-performers in the top 10 percent; those with “math difficulty,” performing in the bottom 10 percent to 25 percent; and the bottom 10 percent, identified as having dyscalculia.
In the first test, students first saw pictures of groups of nine, 12, or 15 yellow dots, flashed too quickly to count, and were asked to estimate the number in the group. Next, students saw intermixed blue and yellow dots flashed, and were asked to judge which color had more dots. Combined, these experiments tested both how well students could judge and compare the magnitude of numbers, as well as how easily they could translate the quantity to a number name.
Ms. Mazzocco found students with dyscalculia were significantly worse at estimating than other students.
“For [9th grade] children with math learning disability, there is precision at the level we would expect to see in a toddler or preschooler,” she said.
By contrast, there was no significant difference between students who performed in the low 10 to 25 percent of math ability and average-performing students, suggesting a difference in underlying causes of math problems for the lowest-performing students.
This study, while including a relatively small sample of students, backs up findings from emerging cognitive science and neuroscience in the field.
In the last decade, brain-imaging studies of students performing similar number-magnitude tasks began to connect this estimation ability to specific pathways in the brain between the frontal lobe, which is associated with higher thought, and a sliver within the parietal lobe, at the top rear of the brain, that is associated with basic number processing.
Adults and children estimating the number of items in a set or comparing one number to another showed increased brain activity in that area of the parietal lobe.
Mr. Ansari, the principal investigator for the Numerical Cognition Laboratory at the University of Western Ontario in London, Canada, found that people identified with dyscalculia showed much lower brain activation in the parietal lobe when identifying number magnitude, suggesting a deficiency in this basic processing.
Mr. Ansari even found that those with high anxiety about math as adults also had problems estimating number magnitude, which he said could point to an underlying reason for their fear.
“It’s about building blocks; if you lack that foundation, over time you will not be able to build these numerical calculations,” Mr. Ansari said.
