Steph Zech graduated from high school this spring with an admirable academic record. She especially loved chemistry, writing and literature — though she has some reservations about Dante. A bright and diligent student, she took two Advanced Placement classes her senior year, sailing through both.
But when it comes to math, Steph has struggled mightily. At age 17, she still counts on her fingers to add 3 and 5. She doesn’t know her multiplication tables. She can’t understand fractions, process concepts of time such as “quarter after” or read dice without counting the dots. She did recently figure out that if something costs 75 cents, the change from a dollar should be 25 cents. But when asked what the change would be if the price were 70 cents, she considers at length before venturing, “15 cents?”
There are many reasons for a bright student to be bad at math, including poor learning environments, attention disorders and anxiety. But Steph’s struggles typify a specific math learning disability known as developmental dyscalculia. “A lot of people say, ‘I’m not good at math’ because they couldn’t handle pre-calculus or something,” says cognitive neuroscientist Edward Hubbard of the University of Wisconsin-Madison. “People with dyscalculia struggle to tell you whether seven is more than five.”
Although dyscalculia, which affects about 6 percent of people, is about as common as the analogous reading disorder dyslexia, it is far less well-understood. According to one analysis, studies on reading disabilities outnumber those that look at math deficits by a ratio of 14 to 1. One reason for that disparity may be the belief that literacy is more important than numeracy. “People freely admit at dinner parties that they are poor at math, while few would admit that they are a poor reader,” notes cognitive neuroscientist Daniel Ansari of the University of Western Ontario.
From calculating restaurant tips to navigating investment decisions to following medication instructions, the ability to understand numbers is essential to functional living. In one study conducted in the U.K., researchers found that at age 30, people with low numeracy tended to have less education and were more likely to be unemployed, in trouble with the law, and mentally and physically sicker than others the same age.
But now, thanks to advances in brain imaging techniques and improved understanding of numerical cognition in general, new insights into the disorder have begun to emerge. Researchers have tracked dyscalculia to a fold in the back of the brain known as the intraparietal sulcus, or IPS. This area, they’ve learned, is crucial for perceiving and approximately comparing quantities — say, a group of dots on a page, or spades on a playing card. This core mental capacity, known as approximate number sense, is important for arithmetic and much higher-level math.
New research “helps isolate the potential causes of dyscalculia and points to impairments in very basic number-processing abilities that can be measured before children enter formal schooling,” Ansari says. “This in turn can inform early diagnosis and intervention.”
Numbers Don’t Stick
Steph was in second grade when she decided she must be stupid. “We had those little one-minute math tests, and I would always be working till the last second, and everyone else would have [their papers] flipped over,” she says. “I felt extremely isolated.”
Teachers at her school in Wisconsin dismissed her troubles, concluding that because she did well in the rest of her schoolwork, she must have been lazy when it came to math. That assumption still hurts, because Steph knows better: For more than 10 years she and her mother, Susan, have spent countless hours hunched over math homework, trying to make the numbers stick in Steph’s brain. They’ve tried flashcards, computer games, videos, math songs, summer tutors … but “there’s nothing that has particularly helped” her truly understand, Steph says.
While Steph was learning to compensate for her disability, partly through clever memorization tactics and partly through sheer effort, scientists far removed from the school where she struggled were probing the disorder’s biological roots. Studies had shown for nearly a century that some brain injuries can cause impairments in quantity processing. Beginning in the late 1990s, neuroimaging studies showed that a specific area of the parietal lobe — the IPS — is important for very basic numerical magnitude processing, such as deciding which of two numbers is larger.
Only a few neuroimaging studies have examined numerical processing in children with developmental dyscalculia. In a 2007 study, Ansari and colleagues scanned the brains of dyscalculic children while they made judgments about quantities of squares presented on a screen. When asked to identify which clustering had more squares, the children made more errors and responded more slowly than those in a control group. In addition, unlike their peers, children with dyscalculia showed no difference in IPS activation when they were comparing pairs of numbers that were closer versus further apart in value, suggesting that their brains were less efficient at discerning the relative distance between numbers. Other studies since have found similar effects.
Recently, some researchers have proposed that in some cases, dyscalculia may arise not from a “core deficit” in the ability to compare quantities, but instead from an “access deficit” — a problem in how the brain links perceptions of quantity to number symbols such as Arabic numerals, or in how it maps numbers onto verbal or spatial processes. So far, the evidence for “core” versus “access” subtypes of dyscalculia has been mixed.
Rebooting Number Sense?
Over the years, Steph persevered through multiplication tables and ratios, fractions and decimals. It was never fun — and geometry in particular is an adventure she’d prefer to forget. Her junior year, she transferred to a different school where the teachers were more helpful and willing to make some accommodations, like letting her use a note card to remind her of basic math facts during tests. She stuck with math through high school, earning straight A’s in pre-calculus her senior year. Though her performance on some elementary parts of the ACT math test was abysmal, she did fairly well on some of the more advanced parts, which involve more reasoning than arithmetic. Her overall score was respectable — good enough, in fact, to land her a slot at a small private college in Iowa this fall, with academic scholarships.
Steph is more fortunate than many young people with dyscalculia, whose difficulties in math — and the anxiety their troubles tend to stir — can set them on a path of overall underachievement. Many children with dyscalculia, and especially highly intelligent ones, tend to go undiagnosed. By the time someone notices the discrepancy between their math ability and general performance, it may be too late to shore up shaky foundations.
But the advances in understanding how dyscalculia works suggest it might be possible to do better. Recently, researchers have focused their efforts on identifying faulty number sense earlier, in hopes of finding ways to blunt its effects. Ansari and others are designing behavioral tests that evaluate the processing of number symbols and the basic skills underlying math, such as comparison of quantities and numbers, dot counting and relationships between numbers. “These tools move beyond just testing children on calculation skills to assessing the underlying skills — the basic foundational or scaffolding abilities,” Ansari says.
Several recent studies have shown that rudimentary number sense — an ability to discriminate between varying quantities — emerges by the time infants are 6 months old. In a 2010 study, cognitive psychologists Melissa Libertus and Elizabeth Brannon, then both at Duke University, found that infants gazed longer at images of black circles when the number of circles changed, compared with when the quantity was always the same, as long as the ratio between the number of circles was always at least 2-to-1. And although all infants improved by age 9 months, those whose abilities were keenest at 6 months remained so a few months later.
The study is important, Hubbard says, because “it shows that we can reliably measure something about number sense and that the number sense is stable over time.” As such, he says, individual differences in number sense might predict later math abilities.
Several research groups are testing the prospects for rebooting dyscalculic children’s approximate number sense or their ability to map quantities onto symbols or a mental number line. One example is a computer game called The Number Race, developed by Stanislas Dehaene at INSERM (the French National Institute of Health and Medical Research) and his colleague Anna Wilson, now at the University of Canterbury in New Zealand.
In the game, which is designed to strengthen the brain circuits that support number sense, the child tries to beat a cartoon opponent to the end of a number line disguised as a colorful racetrack. Along the way, the child must practice several different foundational math skills, including comparing quantities of objects, counting and ordering numerals, and matching quantities with symbols. The game adapts in difficulty depending on the player’s success, so that it stays challenging without being frustrating.
Initial tests of The Number Race’s effectiveness with children who struggle in math have been encouraging, though “not a slam dunk,” Hubbard says. Young children who play the game do show improvements on basic numerical cognition, but it’s unclear how long these improvements last.
Clues from Dyslexia
Nonetheless, Hubbard is cautiously optimistic that early and intensive training can help children with dyscalculia. Part of that optimism, he says, stems from research on dyscalculia’s sister disorder, dyslexia. Reading research, he observes, has long shown that a key aspect of dyslexia is the child’s difficulty in understanding the sounds of language — a deficit that is similar to the faulty number sense seen in dyscalculia. But even though understanding the sounds of language is key to learning letter symbols, many studies have shown that learning letter symbols actually improves dyslexic children’s ability to hear the sounds of language.
Hubbard suggests it may be that the same is true with numbers: that learning the symbols of math changes how the brain actually perceives quantities. “Because number symbols are exact — a number is either a 3 or it isn’t — this may help ‘tune up’ the brain networks for non-symbolic numbers,” he says. “Once children are aware of the fact that numbers can be exact, they may then focus more on counting up the right number, which could in turn sharpen their ability to see even non-symbolic quantities more precisely.”
Whether that is true and, if so, exactly what kinds of training might jump-start the process are not yet clear. But what is key, Hubbard says, is that the brain a child is born with “may not be the brain the child is stuck with.”
Last winter, when Steph met with Hubbard to discuss her math problems, an online test (see “How Good Is Your Number Sense?”) confirmed that her number sense was truly impaired. The information provided no fix — just vindication, and the wish that dyscalculia could be more widely understood. “I want math teachers to be educated about it,” Steph says. “Think about all the other kids that don’t have as much motivation, or don’t have as caring parents as I do.”
Whether adults with dyscalculia, like Steph, can eventually tap into the tools that researchers are currently developing for children remains unknown. Hubbard says it may be possible, though harder, both because adults have missed opportunities to learn when they’re younger and because with age, the brain changes less in response to learning.
As for Steph, he says, “There are places in life where this will always cause her difficulty. But I get the feeling that she’s a very determined young girl and that she’s going to figure out how to have a very successful life no matter what happens.”
[This article originally appeared in print as "No Head for Numbers."]