Posts tagged numerical cognition

TAU researcher finds that adults still think about numbers like kids

Children understand numbers differently than adults. For kids, one and two seem much further apart then 101 and 102, because two is twice as big as one, and 102 is just a little bigger than 101. It’s only after years of schooling that we’re persuaded to see the numbers in both sets as only one integer apart on a number line.

Now Dror Dotan, a doctoral student at Tel Aviv University’s School of Education and Sagol School of Neuroscience and Prof. Stanislas Dehaene of the Collège de France, a leader in the field of numerical cognition, have found new evidence that educated adults retain traces of their childhood, or innate, number sense — and that it’s more powerful than many scientists think.

"We were surprised when we saw that people never completely stop thinking about numbers as they did when they were children," said Dotan. "The innate human number sense has an impact, even on thinking about double-digit numbers." The findings, a significant step forward in understanding how people process numbers, could contribute to the development of methods to more effectively educate or treat children with learning disabilities and people with brain injuries.

Digital proof of a primal sense

Educated adults understand numbers “linearly,” based on the familiar number line from 0 to infinity. But children and uneducated adults, like tribespeople in the Amazon, understand numbers “logarithmically” — in terms of what percentage one number is of another. To analyze how educated adults process numbers in real time, Dotan and Dehaene asked the participants in their study to place numbers on a number line displayed on an iPad using a finger.

Previous studies showed that people who understand numbers linearly perform the task differently than people who understand numbers logarithmically. For example, linear thinkers place the number 20 in the middle of a number line marked from 0 to 40. But logarithmic thinkers like children may place the number 6 in the middle of the number line, because 1 is about the same percentage of 6 as 6 is of 40.

On the iPad used in the study, the participants were shown a number line marked only with “0” on one end and “40” on the other. Numbers popped up one at a time at the top of the iPad screen, and the participants dragged a finger from the middle of the screen down to the place on the number line where they thought each number belonged. Software tracked the path the finger took.

Changing course

Statistical analysis of the results showed that the participants placed the numbers on the number line in a linear way, as expected. But surprisingly — for only a few hundred milliseconds — they appeared to be influenced by their innate number sense. In the case of 20, for example, the participants drifted slightly rightward with their finger — toward where 20 would belong in a ratio-based number line — and then quickly corrected course. The results provide some of the most direct evidence to date that the innate number sense remains active, even if largely dormant, in educated adults.

"It really looks like the two systems in the brain compete with each other," said Dotan.

Significantly, the drift effect was found with two-digit as well as one-digit numbers. Many researchers believe that people can only convert two-digit numbers into quantities using the learned linear numerical system, which processes the quantity of each digit separately — for example, 34 is processed as 3 tens plus 4 ones. But Dotan and Dehaene’s research showed that the innate number sense is, in fact, capable of handling the complexity of two-digit numbers as well.

(Source: aftau.org)

Innate ability to identify quantities previews future mathematics performance

Babies who are good at telling the difference between large and small groups of items even before learning how to count are more likely to do better with numbers in the future, according to new research from the Duke Institute for Brain Sciences. 

The use of Arabic numerals to represent different values is a characteristic unique to humans, not seen outside our species. But we aren’t born with this skill. Infants don’t have the words to count to 10. So, scientists have hypothesized that the rudimentary sense of numbers in infants is the foundation for higher-level math understanding. 

A new study, appearing online in the Oct. 21 Proceedings of the National Academy of Sciences, suggests that children do, in fact, tap into this innate numerical ability when learning symbolic mathematical systems. The Duke researchers found that the strength of an infant’s inborn number sense can be predictive of the child’s future mathematical abilities.  

"When children are acquiring the symbolic system for representing numbers and learning about math in school, they’re tapping into this primitive number sense," said Elizabeth Brannon, Ph.D., a professor of psychology and neuroscience, who led the study. "It’s the conceptual building block upon which mathematical ability is built."

Brannon explained that babies come into the world with a rudimentary understanding referred to as a primitive number sense. When looking at two collections of objects, primitive number sense allows them to identify which set is numerically larger even without verbal counting or using Arabic numerals. For example, a person instinctively knows a group of 15 strawberries is more than six oranges, just by glancing. 

Understanding how infants and young children conceptualize and understand number can lead to the development of new mathematics education strategies, said Brannon’s colleague, Duke psychology and neuroscience graduate student Ariel Starr. In particular, this knowledge can be used to design interventions for young children who have trouble learning mathematics symbols and basic methodologies.

To test for primitive number sense, Brannon and Starr analyzed 48 6-month-old infants to see whether they could recognize numerical changes, capitalizing on the interest most babies show in things that change. They placed each baby in front of two screens, one that always showed the same number of dots (e.g., eight), changing in size and position, and another that switched between two different numerical values (e.g., eight and 16 dots). All the arrays of dots changed frequently in size and position. In this task, babies that could tell the difference between the two numerical values (e.g., eight and 16) looked longer at the numerically changing screen.  

Brannon and Starr then tested the same children at 3.5 years of age with a non-symbolic number comparison game. The children were shown two different arrays and asked to choose which one had more dots without counting them. In addition, the children took a standardized math test scaled for pre-schoolers, as well as a standardized IQ test. Finally, the researchers gave the children a simple verbal task to identify the largest number word each child could concretely understand.

"We found that infants with higher preference scores for looking at the numerically changing screen had better primitive number sense three years later compared to those infants with lower scores," Starr said. "Likewise, children with higher scores in infancy performed better on standardized math tests."

Brannon said the findings point to a real connection between symbolic math and quantitative abilities that are present in infancy before education takes hold and shapes our mathematical abilities.

"Our study shows that infant number sense is a predictor of symbolic math," Brannon said. "We believe that when children learn the meaning of number words and symbols, they’re likely mapping those meanings onto pre-verbal representations of number that they already have in infancy," she said. 

"We can’t measure a baby’s number sense ability at 6 months and know how they’ll do on their SATs," Brannon added. "In fact our infant task only explains a small percentage of the variance in young children"s math performance. But our findings suggest that there is cognitive overlap between primitive number sense and symbolic math. These are fundamental building blocks."

(Source: today.duke.edu)

A brain region activated when people are asked to perform mathematical calculations in an experimental setting is similarly activated when they use numbers — or even imprecise quantitative terms, such as “more than”— in everyday conversation, according to a study by Stanford University School of Medicine scientists.

Using a novel method, the researchers collected the first solid evidence that the pattern of brain activity seen in someone performing a mathematical exercise under experimentally controlled conditions is very similar to that observed when the person engages in quantitative thought in the course of daily life.

“We’re now able to eavesdrop on the brain in real life,” said Josef Parvizi, MD, PhD, associate professor of neurology and neurological sciences and director of Stanford’s Human Intracranial Cognitive Electrophysiology Program. Parvizi is the senior author of the study, published Oct. 15 in Nature Communications. The study’s lead authors are postdoctoral scholar Mohammad Dastjerdi, MD, PhD, and graduate student Muge Ozker.

The finding could lead to “mind-reading” applications that, for example, would allow a patient who is rendered mute by a stroke to communicate via passive thinking. Conceivably, it could also lead to more dystopian outcomes: chip implants that spy on or even control people’s thoughts.

“This is exciting, and a little scary,” said Henry Greely, JD, the Deane F. and Kate Edelman Johnson Professor of Law and steering committee chair of the Stanford Center for Biomedical Ethics, who played no role in the study but is familiar with its contents and described himself as “very impressed” by the findings. “It demonstrates, first, that we can see when someone’s dealing with numbers and, second, that we may conceivably someday be able to manipulate the brain to affect how someone deals with numbers.”

The researchers monitored electrical activity in a region of the brain called the intraparietal sulcus, known to be important in attention and eye and hand motion. Previous studies have hinted that some nerve-cell clusters in this area are also involved in numerosity, the mathematical equivalent of literacy.

However, the techniques that previous studies have used, such as functional magnetic resonance imaging, are limited in their ability to study brain activity in real-life settings and to pinpoint the precise timing of nerve cells’ firing patterns. These studies have focused on testing just one specific function in one specific brain region, and have tried to eliminate or otherwise account for every possible confounding factor. In addition, the experimental subjects would have to lie more or less motionless inside a dark, tubular chamber whose silence would be punctuated by constant, loud, mechanical, banging noises while images flashed on a computer screen.

“This is not real life,” said Parvizi. “You’re not in your room, having a cup of tea and experiencing life’s events spontaneously.” A profoundly important question, he said, is: “How does a population of nerve cells that has been shown experimentally to be important in a particular function work in real life?”

His team’s method, called intracranial recording, provided exquisite anatomical and temporal precision and allowed the scientists to monitor brain activity when people were immersed in real-life situations. Parvizi and his associates tapped into the brains of three volunteers who were being evaluated for possible surgical treatment of their recurring, drug-resistant epileptic seizures.

The procedure involves temporarily removing a portion of a patient’s skull and positioning packets of electrodes against the exposed brain surface. For up to a week, patients remain hooked up to the monitoring apparatus while the electrodes pick up electrical activity within the brain. This monitoring continues uninterrupted for patients’ entire hospital stay, capturing their inevitable repeated seizures and enabling neurologists to determine the exact spot in each patient’s brain where the seizures are originating.

During this whole time, patients remain tethered to the monitoring apparatus and mostly confined to their beds. But otherwise, except for the typical intrusions of a hospital setting, they are comfortable, free of pain and free to eat, drink, think, talk to friends and family in person or on the phone, or watch videos.

The electrodes implanted in patients’ heads are like wiretaps, each eavesdropping on a population of several hundred thousand nerve cells and reporting back to a computer.

In the study, participants’ actions were also monitored by video cameras throughout their stay. This allowed the researchers later to correlate patients’ voluntary activities in a real-life setting with nerve-cell behavior in the monitored brain region.

As part of the study, volunteers answered true/false questions that popped up on a laptop screen, one after another. Some questions required calculation — for instance, is it true or false that 2+4=5? — while others demanded what scientists call episodic memory — true or false: I had coffee at breakfast this morning. In other instances, patients were simply asked to stare at the crosshairs at the center of an otherwise blank screen to capture the brain’s so-called “resting state.”

Consistent with other studies, Parvizi’s team found that electrical activity in a particular group of nerve cells in the intraparietal sulcus spiked when, and only when, volunteers were performing calculations.

Afterward, Parvizi and his colleagues analyzed each volunteer’s daily electrode record, identified many spikes in intraparietal-sulcus activity that occurred outside experimental settings, and turned to the recorded video footage to see exactly what the volunteer had been doing when such spikes occurred.

They found that when a patient mentioned a number — or even a quantitative reference, such as “some more,” “many” or “bigger than the other one” — there was a spike of electrical activity in the same nerve-cell population of the intraparietal sulcus that was activated when the patient was doing calculations under experimental conditions.

That was an unexpected finding. “We found that this region is activated not only when reading numbers or thinking about them, but also when patients were referring more obliquely to quantities,” said Parvizi.

“These nerve cells are not firing chaotically,” he said. “They’re very specialized, active only when the subject starts thinking about numbers. When the subject is reminiscing, laughing or talking, they’re not activated.” Thus, it was possible to know, simply by consulting the electronic record of participants’ brain activity, whether they were engaged in quantitative thought during nonexperimental conditions.

Any fears of impending mind control are, at a minimum, premature, said Greely. “Practically speaking, it’s not the simplest thing in the world to go around implanting electrodes in people’s brains. It will not be done tomorrow, or easily, or surreptitiously.”

Parvizi agreed. “We’re still in early days with this,” he said. “If this is a baseball game, we’re not even in the first inning. We just got a ticket to enter the stadium.”

(Source: med.stanford.edu)