New research sheds light on how children’s brains memorize facts

The scientists also saw changes in the degree to which the hippocampus was connected to other parts of children’s brains, with several parts of the prefrontal, anterior temporal cortex and parietal cortex more strongly connected to the hippocampus after one year. Crucially, the stronger these connections, the greater was each individual child’s ability to retrieve math facts from memory, a finding that suggests a starting point for future studies of math-learning disabilities.

Although children were using their hippocampus more after a year, adolescents and adults made minimal use of their hippocampus while solving math problems. Instead, they pulled math facts from well-developed information stores in the neocortex.

Memory scaffold

“What this means is that the hippocampus is providing a scaffold for learning and consolidating facts into long-term memory in children,” said Menon, who is also the Rachel L. and Walter F. Nichols, MD, Professor at the medical school. Children’s brains are building a schema for mathematical knowledge. The hippocampus helps support other parts of the brain as adultlike neural connections for solving math problems are being constructed. “In adults this scaffold is not needed because memory for math facts has most likely been consolidated into the neocortex,” he said. Interestingly, the research also showed that, although the adult hippocampus is not as strongly engaged as in children, it seems to keep a backup copy of the math information that adults usually draw from the neocortex.

The researchers compared the level of variation in patterns of brain activity as children, adolescents and adults correctly solved math problems. The brain’s activity patterns were more stable in adolescents and adults than in children, suggesting that as the brain gets better at solving math problems its activity becomes more consistent.

The next step, Menon said, is to compare the new findings about normal math learning to what happens in children with math-learning disabilities.

“In children with math-learning disabilities, we know that the ability to retrieve facts fluently is a basic problem, and remains a bottleneck for them in high school and college,” he said. “Is it that the hippocampus can’t provide a reliable scaffold to build good representations of math facts in other parts of the brain during the early stages of learning, and so the child continues to use inefficient strategies to solve math problems? We want to test this.”

Not too early for maths

Bad maths grades, poor participation in class, no interest in arithmetic. Preterm children often suffer from dyscalculia – at least according to some scientific studies. A misunderstanding, claims developmental psychologist Dr Julia Jäkel, who has been studying the performance of preterm children.

Thanks to modern medicine, the percentage of preterm survivors is constantly increasing. On the cognitive level, these children frequently have long-term problems such as poor arithmetic skills and difficulty concentrating. For a long time, research focused on high-risk children, born before 32 weeks gestational age or with less than 1,500 gram. Current studies from the most recent years, however, show that this approach is too short-sighted.

Dr Julia Jäkel from the Department of Developmental Psychology has analysed cognitive abilities of children born between 23 and 41 weeks gestation. In doing so, she covered the entire spectrum, ranging from extremely preterm to healthy term born infants. For this purpose, she used data of the Bavarian Longitudinal Study, which has been following a birth cohort from the late 80s until today. “Having access to such a comprehensive long-term study is a dream come true for every developmental psychologist,” says the Bochum researcher. Over the course of the study, all children underwent a whole battery of tests that assessed their cognitive and educational abilities, and their parents were interviewed in depth.

The RUB researcher has so far mainly focused on data collected at preschool and early school age. For different test tasks, she assessed their cognitive workload, a criterion for the complexity of a given task. The data showed that preterm children had greater difficulties with tasks that demanded higher working memory resources. Moreover, results revealed that not only high-risk children had significant difficulties. On average, the more preterm a child had been born, the poorer were his or her abilities to solve complex tasks.

But what exactly is the nature of these difficulties? It has been frequently suggested that preterm children suffer from dyscalculia. A phenomenon that Julia Jäkel examined more closely. “Mathematical deficiencies, maths learning disorder, dyscalculia, innumeracy – these terms’ definitions vary slightly,” she explains, but there are no standardised, internationally consistent diagnostic criteria. In order to assess specific maths deficiencies, children in Germany are assessed with a number of tests. If their results fall below a certain cut off value in maths while their cognitive skills (IQ) are in the normal range, they are diagnosed with “maths learning disorder” or “dyscalculia”.

“The problem with preterm children, however, is that they often have general cognitive deficits,” Julia Jäkel points out. “According to current criteria, these children can’t be diagnosed.” Together with Dieter Wolke from the University of Warwick, UK, she compared different diagnostic criteria for dyscalculia in her analysis. The aim of the study was to identify specific maths deficiencies in preterm children that were independent of general cognitive impairments. With surprising results: “There is no specific maths deficit in preterm children if their general IQ is factored in,” says the researcher.

This means that preterm children do not suffer from dyscalculia more often than term children. However, they often have maths difficulties and these may not be recognized. This is because the current criteria make it impossible to diagnose dyscalculia if a child also has general cognitive deficits. Thus, these children do not receive specific help in maths although they may be in urgent need. “We need reliable and consistent diagnostic criteria,” demands Julia Jäkel. “And we’ve got to find ways to actually deliver support in schools.”

Together with her British team, the psychologist compared the results of the Bavarian Longitudinal Study with “EPICure” data, a similar study that commenced in the UK in the 1990s, following a cohort of extremely preterm children. The researchers focus on mathematical and educational performance. British preterm children had similar cognitive and basic numerical skills as German preterm children. In terms of maths achievement, however, they showed significantly better results. “We explain this with the fact that, unlike in Germany, in the UK it has not been possible for children to delay school entry,” explains Julia Jäkel. “In addition, special schools are attended by only a small percentage of extremely disabled children. All other children are integrated into normal classes in regular schools and receive targeted support there.”

The developmental psychologist has already demonstrated that assistance at primary-school age can really make a difference. Parents who support their preterm children with sensitive scaffolding can compensate the negative cognitive effects of preterm birth. It is helpful, for example, if parents give their children appropriate feedback to homework tasks and suggest potential solutions, rather than solving the tasks for the child. However, Julia Jäkel believes that a lot of research is yet to be done as far as intervention is concerned: “A large percentage of parents is very dedicated and has resources to help their children,” she says. “But research has not yet produced anything that would ensure successful results in the long-term.” Together with colleagues from the university hospital in Essen, the RUB researcher plans to investigate the benefits of computer-aided working memory training for preterm children’s school success, which has already been successfully applied on an international level.

It would also be helpful if findings from related disciplines, such as developmental psychology, educational research, and neonatal medicine were better integrated. This is, for example, because neonatal medical treatment can significantly affect later cognitive performance. Together with her interdisciplinary team, Julia Jäkel used a comprehensive model to analyse to what extent different neonatal medical indicators affect cognitive development at age 20 months, attention abilities at age six, and maths abilities at age eight years. In her analyses, she factored in child sex and socio-economic status.

Results showed that neonatal medical variables, e.g., the duration of mechanical ventilation, predicted cognitive abilities at age 20 months. Both factors together predicted attention regulation at age six years. And all those precursors, in turn, affected long-term general maths abilities.

Subsequently, Julia Jäkel analysed the data once again from a different perspective, in order to predict specific maths skills that were independent of the child’s IQ. In that model, only two variables had direct impact: the duration of mechanical ventilation and hospitalisation after birth. In the 1980s, when children participating in the Bavarian Longitudinal Study were born, German doctors often used invasive ventilation methods. Today, less invasive methods are available, but to what extent they may affect long-term cognitive performance has not yet been investigated.

“Both too high and too low oxygen concentrations are harmful to brain development,” explains Julia Jäkel. “The neonatologist in charge is faced with the great challenge of determining the right dose for each infant, depending on individually changing situations.” This is why it is so important to integrate psychological models with neonatal intensive care research. The joint objective is to offer preterm children the chance of a successful school career, high quality of life and social participation.

Gesturing with hands is a powerful tool for children’s math learning

Children who use their hands to gesture during a math lesson gain a deep understanding of the problems they are taught, according to new research from University of Chicago’s Department of Psychology.

Previous research has found that gestures can help children learn. This study in particular was designed to answer whether abstract gesture can support generalization beyond a particular problem and whether abstract gesture is a more effective teaching tool than concrete action.

“We found that acting gave children a relatively shallow understanding of a novel math concept, whereas gesturing led to deeper and more flexible learning,” explained the study’s lead author, Miriam A. Novack, a PhD student in psychology.

The study, “From action to abstraction: Using the hands to learn math,” is published online by Psychological Science.

The researchers taught third-grade children a strategy for solving one type of mathematical equivalence problem, for example, 4 + 2 + 6 = ____ + 6. They then tested the students on similar mathematical equivalence problems to determine how well they understood the underlying principle.

The researchers randomly assigned 90 children to conditions in which they learned using different kinds of physical interaction with the material. In one group, children picked up magnetic number tiles and put them in the proper place in the formula. For example, for the problem 4 + 2 + 6 = ___ + 6, they picked up the 4 and 2 and placed them on a magnetic whiteboard. Another group mimed that action without actually touching the tiles, and a third group was taught to use abstract gestures with their hands to solve the equations. In the abstract gesture group, children were taught to produce a V-point gesture with their fingers under two of the numbers, metaphorically grouping them, followed by pointing a finger at the blank in the equation.

The children were tested before and after solving each problem in the lesson, including problems that required children to generalize beyond what they had learned in grouping the numbers. For example, they were given problems that were similar to the original one, but had different numbers on both sides of the equation.

Children in all three groups learned the problems they had been taught during the lesson. But only children who gestured during the lesson were successful on the generalization problems.

“Abstract gesture was most effective in encouraging learners to generalize the knowledge they had gained during instruction, action least effective, and concrete gesture somewhere in between,” said senior author Susan Goldin-Meadow, the Beardsley Ruml Distinguished Service Professor in Psychology. “Our findings provide the first evidence that gesture not only supports learning a task at hand but, more importantly, leads to generalization beyond the task. Children appear to learn underlying principles from their actions only insofar as those actions can be interpreted symbolically.”

Mathematical beauty activates same brain region as great art or music

People who appreciate the beauty of mathematics activate the same part of their brain when they look at aesthetically pleasing formula as others do when appreciating art or music, suggesting that there is a neurobiological basis to beauty.

There are many different sources of beauty - a beautiful face, a picturesque landscape, a great symphony are all examples of beauty derived from sensory experiences. But there are other, highly intellectual sources of beauty. Mathematicians often describe mathematical formulae in emotive terms and the experience of mathematical beauty has often been compared by them to the experience of beauty derived from the greatest art.

In a new paper published in the open-access journal Frontiers in Human Neuroscience, researchers used functional magnetic resonance imaging (fMRI) to image the brain activity of 15 mathematicians when they viewed mathematical formulae that they had previously rated as beautiful, neutral or ugly. 

The results showed that the experience of mathematical beauty correlates with activity in the same part of the emotional brain – namely the medial orbito-frontal cortex – as the experience of beauty derived from art or music.

Professor Semir Zeki, lead author of the paper from the Wellcome Laboratory of Neurobiology at UCL, said: “To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintescence of beauty. The beauty of a formula may result from simplicity, symmetry, elegance or the expression of an immutable truth. For Plato, the abstract quality of mathematics expressed the ultimate pinnacle of beauty.”

“This makes it interesting to learn whether the experience of beauty derived from such as highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources.”

In the study, each subject was given 60 mathematical formulae to review at leisure and rate on a scale of -5 (ugly) to +5 (beautiful) according to how beautiful they experienced them to be. Two weeks later they were asked to re-rate them while in an fMRI scanner.

The formulae most consistently rated as beautiful (both before and during the scans) were Leonhard Euler’s identity, the Pythagorean identity and the Cauchy-Riemann equations. Leonhard Euler’s identity links five fundamental mathematical constants with three basic arithmetic operations each occurring once and the beauty of this equation has been likened to that of the soliloquy in Hamlet.

Mathematicians judged Srinivasa Ramanujan’s infinite series and Riemann’s functional equation as the ugliest.

Professor Zeki said: “We have found that activity in the brain is strongly related to how intense people declare their experience of beauty to – even in this example where the source of beauty is extremely abstract. This answers a critical question in the study of aesthetics, namely whether aesthetic experiences can be quantified.”

Professor Zeki added: “We have found that, as with the experience of visual or musical beauty, the activity in the brain is strongly related to how intense people declare their experience of beauty to be – even in this example where the source of beauty is extremely abstract. This answers a critical question in the study of aesthetics, one which has been debated since classical times, namely whether aesthetic experiences can be quantified.”

Quality of white matter in the brain is crucial for adding and multiplying

‘Grey’ cells process information in the brain and are connected via neural pathways, the tracts through which signals are transferred.

"Neural pathways are comparable to a bundle of cables. These cables are surrounded by an isolating sheath: myelin, or ‘white matter’. The thicker the isolating sheath and the more cables there are, the more white matter. And the more white matter, the faster the signals are transferred," explains educational neuroscientist Bert de Smedt.

While the correlation between arithmetic and white matter tracts linking certain brain regions is known, very little research has been done to test this correlation in normally-developing children. Nor has previous research teased out differences in neuroactivity when carrying out different arithmetic operations, e.g., adding, subtracting, multiplying and dividing.

In this study, the researchers had 25 children solve a series of different arithmetic operations while undergoing a brain scan. They then compared the quality of the children’s white matter tracts with their arithmetic test performance.

"We found that a better quality of the arcuate fasciculus anterior – a white matter tract that connects brain regions often used for arithmetic – corresponds to better performance in adding and multiplying, while there is no correlation for subtracting and dividing.”

“A possible explanation for this is that this white matter bundle is involved in rote memorization, whereas when we subtract and divide, such memorization plays less of a role. When subtracting and dividing we are more likely to use intermediary steps to calculate the solution, even as adults.”

Nursery rhymes

These findings also add insight into the link between reading and arithmetic, explains Professor De Smedt: “Reading proficiency and arithmetic proficiency often go hand-in-hand. The white matter tract that we studied also plays an important role in reading: when we learn to read, we have to memorize the correspondence between particular letters and the sound they represent. It is likely that a similar process occurs for addition and multiplication. Just think of the notorious times-table drills we all memorized as schoolchildren; it is almost like learning a nursery rhyme. Some of us can even auto-recall these sums.”

"This also might explain why we often see arithmetic problems in children with dyslexia. Likewise, children with dyscalculia often have trouble reading," says Professor De Smedt.

The researchers now aim to explore how these results relate to children with impairments such as dyscalculia or head trauma. In a next step, the team will also investigate how white matter tracts can be strengthened through extra arithmetic training.

Preschoolers’ Counting Abilities Relate to Future Math Performance

Along with reciting the days of the week and the alphabet, adults often practice reciting numbers with young children. Now, new research from the University of Missouri suggests reciting numbers is not enough to prepare children for math success in elementary school. The research indicates that counting, which requires assigning numerical values to objects in chronological order, is more important for helping preschoolers acquire math skills.

“Reciting means saying the numbers from memory in chronological order, whereas counting involves understanding that each item in the set is counted once and that the last number stated is the amount for the entire set,” said Louis Manfra, an assistant professor in MU’s Department of Human Development and Family Studies. “When children are just reciting, they’re basically repeating what seems like a memorized sentence. When they’re counting, they’re performing a more cognitive activity in which they’re associating a one-to-one correspondence with the object and the number to represent a quantity.”

“Counting gives children stronger foundations when they start school,” Manfra said. “The skills children have when they start kindergarten affect their trajectories through early elementary school; therefore, it’s important that children start with as many skills as possible.”

The study, “Associations between Counting Ability in Preschool and Mathematic Performance in First Grade among a Sample of Ethnically Diverse, Low-Income Children,” will be published in an upcoming issue of the Journal of Research in Childhood Education.

When people worry about math, the brain feels the pain

Mathematics anxiety can prompt a response in the brain similar to when a person experiences physical pain, according to new research at the University of Chicago.

Using brain scans, scholars determined that the brain areas active when highly math-anxious people prepare to do math overlap with the same brain areas that register the threat of bodily harm—and in some cases, physical pain.

“For someone who has math anxiety, the anticipation of doing math prompts a similar brain reaction as when they experience pain—say, burning one’s hand on a hot stove,” said Sian Beilock, professor of psychology at the University of Chicago and a leading expert on math anxiety.

Surprisingly, the researchers found it was the anticipation of having to do math, and not actually doing math itself, that looked like pain in the brain. “The brain activation does not happen during math performance, suggesting that it is not the math itself that hurts; rather the anticipation of math is painful,” added Ian Lyons, a 2012 PhD graduate in psychology from UChicago and a postdoctoral scholar at Western University in Ontario, Canada.

The two report their findings in a paper, “When Math Hurts: Math Anxiety Predicts Pain Network Activation in Anticipation of Doing Math,” in the current issue of PLOS One.

Higher-math skills entwined with lower-order magnitude sense

The ability to learn complex, symbolic math is a uniquely human trait, but it is intricately connected to a primitive sense of magnitude that is shared by many animals, finds a study to be published by the Proceedings of the National Academy of Sciences (PNAS).

"Our results clearly show that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system," says lead author Stella Lourenco, a psychologist at Emory University. "We were able to show how variations in both advanced arithmetic and geometry skills specifically correlated with variations in our intuitive sense of magnitude."

Babies as young as six months can roughly distinguish between less and more, whether it’s for a number of objects, the size of objects, or the length of time they see the objects. This intuitive, non-verbal sense of magnitude, which may be innate, has also been demonstrated in non-human animals. When given a choice between a group of five bananas or two bananas, for example, monkeys will tend to take the bigger bunch.

"It’s obviously of adaptive value for all animals to be able to discriminate between less and more," Lourenco says. "The ability is widespread across the animal kingdom – fish, rodents and even insects show sensitivity to magnitude, such as the number of items in a set of objects."

Memory vs. Math: Same brain areas show inverse responses to recall and arithmetic

Scientists have historically relied on neuroimaging – but not electrophysiological – data when studying the human default mode network (DMN), a group of brain regions with lower activity during externally-directed tasks and higher activity if tasks require internal focus. Recently, however, researchers at Stanford University School of Medicine recorded electrical activity directly from a core DMN component known as the posteromedial cortex (PMC) during both internally- and externally-directed waking states – specifically, autobiographical memory and arithmetic calculation, respectively. The data they recorded showed an inverse relationship – namely, the degree activation during memory retrieval predicted the degree of suppression during arithmetic calculation – which they say provides important anatomical and temporal details about DMN function at the neural population level.