1. Study suggests positive attitude toward math predicts math achievement in kids

    February 9, 2018 by Ashley

    From the Stanford University Medical Center press release:

    For the first time, scientists have identified the brain pathway that links a positive attitude toward math to achievement in the subject.

    In a study of elementary school students, researchers at the Stanford University School of Medicine found that having a positive attitude about math was connected to better function of the hippocampus, an important memory center in the brain, during performance of arithmetic problems.

    The findings will be published online Jan. 24 in Psychological Science.

    Educators have long observed higher math scores in children who show more interest in math and perceive themselves as being better at it. But it has not been clear if this attitude simply reflects other capacities, such as higher intelligence.

    The new study found that, even once IQ and other confounding factors were accounted for, a positive attitude toward math still predicted which students had stronger math performance.

    ‘Attitude is really important’

    “Attitude is really important,” said Lang Chen, PhD, the study’s lead author and a postdoctoral scholar in psychiatry and behavioral sciences. “Based on our data, the unique contribution of positive attitude to math achievement is as large as the contribution from IQ.”

    The scientists had not expected the contribution of attitude to be so large, Chen said. The mechanism underlying its link to cognitive performance was also unexpected.

    “It was really surprising to see that the link works through a very classical learning and memory system in the brain,” said the study’s senior author, Vinod Menon, PhD, professor of psychiatry and behavioral sciences. Researchers had previously hypothesized that the brain’s reward centers might drive the link between attitude and achievement — perhaps children with better attitudes were better at math because they found it more rewarding or motivating. “Instead, we saw that if you have a strong interest and self-perceived ability in math, it results in enhanced memory and more efficient engagement of the brain’s problem-solving capacities,” Menon said.

    The researchers administered standard questionnaires to 240 children ages 7 to 10, assessing demographics, IQ, reading ability and working-memory capacity. The children’s level of math achievement was measured with tests of their knowledge of arithmetic facts and ability to solve math word problems. Parents or guardians answered surveys about the children’s behavioral and emotional characteristics, as well as their anxiety about math and general anxiety. Children also answered a survey that assessed their attitude toward math, including questions about interest in math and self-perceived math ability, as well as their attitude toward academics in general.

    Forty-seven children from the group also participated in MRI brain scans while performing arithmetic problems. Tests were conducted outside the MRI scanner to discern which problem-solving strategies they used. An independent group of 28 children also was given MRI scans and other assessments in an attempt to replicate the findings from the cohort previously given brain scans.

    Opening the door

    Math performance correlated with a positive attitude toward math even after statistically controlling for IQ, working memory, math anxiety, general anxiety and general attitude toward academics, the study found. Children with poor attitudes toward math rarely performed well in the subject, while those with strongly positive attitudes had a range of math achievement.

    A positive attitude opens the door for children to do well but does not guarantee that they will; that depends on other factors as well,” Chen said.

    From the brain-imaging results, the scientists found that, when a child was solving a math problem, his or her positive-attitude scores correlated with activation in the hippocampus, an important memory and learning center in the brain. Activity in the brain’s reward centers, including the amygdala and the ventral striatum, was not linked to a positive attitude toward math. Statistical modeling of the brain imaging results suggested that the hippocampus mediates the link between positive attitude and efficient retrieval of facts from memory, which in turn is associated with better problem solving abilities.

    Having a positive attitude acts directly on your memory and learning system,” Chen said. “I think that’s really important and interesting.”

    The study could not disentangle the extent to which a positive attitude came from a child’s prior success in math. “We think the relationship between positive attitude and math achievement is mutual, bi-directional,” Chen said. “We think it’s like bootstrapping: A good attitude opens the door to high achievement, which means you then have a better attitude, getting you into a good circle of learning. And it can probably go the other way and be a vicious circle, too.”

    The findings may provide a new avenue for improving academic performance and learning in children who are struggling, Menon said, cautioning that this idea still needs to be tested through active interventions.

    “Typically, we focus on skill learning in individual academic domains, but our new work suggests that looking at children’s beliefs about a subject and their self-perceived abilities might provide another inroad to maximizing learning,” Menon said. The findings also offer a potential explanation for how a particularly passionate teacher can nurture students’ interest and learning capacities for a subject, he added. Inspiring teachers may be instinctively sharing their own interest, as well as instilling students in the belief that they can be good at the subject, building a positive attitude even if the student did not have it before.


  2. Study suggests engaging children in math at home equals a boost in more than just math skills

    November 23, 2017 by Ashley

    From the Purdue University press release:

    Preschool children who engage in math activities at home with their parents not only improve their math skills, but also their general vocabulary, according to research from Purdue University.

    “Exposure to basic numbers and math concepts at home were predictive, even more so than storybook reading or other literacy-rich interactions, of improving preschool children’s general vocabulary,” said Amy Napoli, a doctoral student in the Department of Human Development and Family Studies who led the study. “And one of the reasons we think this could be is the dialogue that happens when parents are teaching their children about math and asking questions about values and comparisons, which helps these young children improve their oral language skills.”

    The findings are published online in the Journal of Experimental Child Psychology.

    “It’s never too early to talk about numbers and quantities. One of the first words young children learn is ‘more,'” said David Purpura, an assistant professor in the Department of Human Development and Family Studies, and senior author of the study.

    There are a number of ways parents can encourage math learning at home, such as talking about counting, connecting numbers to quantities and comparing values — more and less. It also helps to focus on counting as purposeful, such as “there are three cookies for a snack” rather than “there are cookies for a snack.”

    “This focus on math typically isn’t happening at home, but this shows that when parents do include math concepts it can make a difference,” said Napoli, who is working on tools to help parents improve math-related instruction at home. “When working with families, there is a math-related anxiety aspect and that is probably why more parents focus on literacy than on math. But, if you can count, then you can teach something to your child.”

    This study evaluated 116 preschool children, ages 3-5. The researchers assessed the children’s math and language skills in the fall and spring of the preschool year and examined how what their parents reported about math and literacy activities at home predicted children’s improvement over time. Napoli and Purpura do caution that these findings are only correlational and the future experimental work is needed to evaluate the causal nature of these findings. This research is ongoing work supported by Purdue’s Department of Human Development and Family Studies.


  3. Students’ self-concepts of ability in math, reading predict later math, reading attainment

    September 29, 2017 by Ashley

    From the Society for Research in Child Development press release:

    Educational and developmental psychologists have tried to understand how skills and motivation are linked to academic achievement. While research supports ties between individuals’ concepts of their abilities and their achievement, we lack a complete picture of how these relations develop from childhood to adolescence. A new longitudinal study looked at how youths’ self-concepts are linked to their actual academic achievement in math and reading from middle childhood to adolescence. The study found that students’ self-concepts of their abilities in these two academic domains play an important role in motivating their achievements over time and across levels of achievement.

    The findings come from researchers at Pontificia Universidad Catolica de Chile and the University of Michigan. They appear in the journal Child Development.

    “Our study shows that youths’ perceptions of their abilities in middle childhood are important in promoting their later achievement in math and reading,” explains Maria Ines Susperreguy, assistant professor in the Faculty of Education at Pontificia Universidad Catolica de Chile, who led the study. “This relation is not limited to students who perform at the top levels, but extends to students with different levels of achievement in math and reading. Even the lowest-performing students who had a more positive view of their math and reading abilities had higher levels of achievement in math and reading.”

    The researchers looked at three data sets of children ages 5 to 18 — the Avon Longitudinal Study of Parents and Children (13,901 British children), the National Institute of Child Health and Human Development Study of Early Child Care and Youth Development (1,354 American children), and the Panel Study of Income Dynamics-Child Development Supplement (237 American children). Each data set included measures of self-concept and standardized assessments of early and later academic achievement.

    Students’ self-concept was defined as their perceptions of their capabilities to succeed on academic tasks. The study considered children’s earlier achievement as well as their characteristics and backgrounds, including birth weight, race/ethnicity, gender, age, and their mother’s education.

    The study found that children’s beliefs about their math and reading abilities explain some of the variance in their later math and reading achievement, after controlling for demographics and children’s characteristics, as well as prior academic achievement. The study also revealed that children’s self-concept of their ability in math predicted later math achievement, and that their self-concept of their ability in reading predicted later reading achievement, but not vice versa. This finding suggests that the links between self-concept of ability and later achievement are specific to domains; that is, there is a link from students’ self-concept about reading to reading achievement, and from students’ self-concept about math to match achievement. The findings apply to students of all levels of achievement.

    “When trying to understand the issues of low academic performance, we often examine what additional skills children need to succeed in school,” says Pamela Davis-Kean, professor of psychology and research professor at the Institute for Social Research at the University of Michigan, who coauthored the study. “Our findings, replicated across three data sets, show that it is important to understand the relation between children’s perceptions of their abilities and later achievement.”


  4. Preschoolers learn from math games, to a point

    July 23, 2017 by Ashley

    From the Massachusetts Institute of Technology press release:

    What is the best way to help poor schoolchildren succeed at math? A study co-authored by researchers at MIT, Harvard University, and New York University now sheds light on the ways preschool activities may — or may not — help children develop cognitive skills.

    The study, based on an experiment in Delhi, India, engaged preschool children in math games intended to help them grasp concepts of number and geometry, and in social games intended to help them cooperate and learn together.

    The results contained an unexpected wrinkle. Children participating in the math games did retain a superior ability to grasp those concepts more than a year later, compared to children who either played only the social games or did not participate. However, the exercises did not lead to better results later, when the children entered a formal classroom setting.

    “It’s very clear you have a significant improvement in the math skills” used in the games, says Esther Duflo, the Abdul Latif Jameel Professor of Poverty Alleviation and Development Economics at MIT and co-author of the study. “We find that the gains are persistent … which I think is quite striking.”

    However, she adds, by the time the children in the study were learning formal math concepts in primary school, such as specific number symbols, the preschool intervention did not affect learning outcomes.

    “All the kids [in primary school] had learned, but they had learned [those concepts] equally,” says Duflo, who is a co-founder of MIT’s Abdul Latif Jameel Poverty Action Lab (J-PAL), which conducts field experiments, often in education, around the globe.

    A paper detailing the results of the study, “Cognitive science in the field: A preschool intervention durably enhances intuitive but not formal mathematics,” is being published in the journal Science.

    The authors are Duflo; Moira R. Dillon, an assistant professor in New York University’s Department of Psychology; Harini Kannan, a postdoc at J-PAL South Asia; Joshua T. Dean, a graduate student in MIT’s Department of Economics; and Elizabeth Spelke, a professor of psychology and researcher at the Laboratory for Developmental Studies at Harvard University.

    It’s a numbers game

    The results bear on the question of how early-childhood educational interventions can help poor children access the same educational concepts that more privileged children have before entering primary school.

    Spelke, an expert in cognitive development among children, notes that around age 5, children “transition from developing knowledge in a common-sense, spontaneous manner, to going to school, where they have to start grappling with formal subjects and building formal skills.” She adds that this can be a highly challenging transition for children living in poverty whose parents had no schooling themselves.

    To address that, the researchers developed a field experiment involving 1,540 children, who were 5 years old on average and enrolled in 214 Indian preschools.

    Roughly one-third of the preschool children were put in groups playing math games exposing them to concepts of number and geometry. For instance, one game the children played allowed them to estimate numbers on cards and sort the cards on that basis.

    Another one-third of the preschool children played games that focused on social content, encouraging them to, for instance, estimate the intensity of emotional expressions on cards and sort the cards on that basis. In all, the games were “fun, fast-paced, and social” and “encouraged a desire to play together,” Dillon says.

    Meanwhile, the final one-third of the preschoolers had no exposure to either type of game; these children formed another control group for the study.

    The researchers then followed up on the abilities of children from all three groups, soon after the intervention, as well as six and 12 months later. They found that even after the first year of primary school, children who had played the math games were better at the skills that those games developed, compared to children from the other groups. The intervention using social games had effects on social skills but did not produce a comparable effect on math skills; the effects of the math games were specific to their math content.

    Despite these effects, the early exposure to numerical concepts such as one-to-one correspondence, and geometrical concepts such as congruence and parallelism did not produce an advantage for the first group of students when it came to achievement in primary school. As the paper states, “Although the math games caused persistent gains in children’s non-symbolic mathematical abilities, they failed to enhance children’s readiness for learning the new symbolic content presented in primary school.”

    Not adding up

    The researchers have been analyzing why the intervention did not produce improvements in school results. One possibility, Duflo observes, is that children in Delhi primary schools learn math in a rote style that may not have allowed the experiment’s set of games to have an effect. Kids in these schools, she observes, “are [only] learning to sing ‘1 times 1 is 1, 1 times 2 is 2.'” For this reason, Duflo notes, the greater understanding of the concepts provided by the preschool math games might be more beneficial when aligned with a different kind of curriculum.

    Or, Spelke puts it, “the negative thing that we learned” from the study is that lab work is not necessarily “sufficient to establish what actually causes knowledge to grow in the mind of a child, over timespans of years in the environments in which children live and learn.”

    With that in mind, the research team is designing follow-up studies in which the games will segue more seamlessly into the curriculum being used in a particular school district.

    “We want to include in the games themselves some element of bridging between the intuitive knowledge of mathematics and the formal knowledge they will be actually exposed to,” Duflo says. J-PAL is currently engaged in developing projects along these lines in both India and the U.S.

    The larger goal of helping disadvantaged preschool children remains intact, Duflo emphasizes: “If we could take the poorest kids and instead of sending them to school with a [learning deficit], because they haven’t been to preschool or been to very good preschools, or their parents have not been able to help them out in the schoolwork, why couldn’t we try to use the best cognitive science available and bring them to school with a slight advantage?”


  5. Study suggests counting on fingers may be important part of math learning

    July 10, 2017 by Ashley

    From the Frontiers press release:

    Is it OK for children to count on their fingers? Generations of pupils have been discouraged by their teachers from using their hands when learning maths. But a new research article, published in Frontiers in Education shows using fingers may be a much more important part of maths learning than previously thought.

    The article, by Professor Tim Jay of Sheffield Hallam University and independent researcher Dr Julie Betenson, confirms what parents have long felt instinctively — that the sorts of finger games children often play at home are central to their education.

    The researchers worked with 137 primary pupils aged between six and seven. All the children were given different combinations of counting and number games to play — but only some were given exercises which involved finger-training.

    Some pupils played games involving number symbols, such as dominoes, shut-the-box, or snakes and ladders.

    Other pupils were asked to play finger games: such being asked to hold up a given number of fingers, or numbering fingers from 1 — 5 and then having to match one of them by touching it against the corresponding finger on the other hand, or tracing coloured lines using a particular finger.

    Both these groups did a little better in maths tests than a third group of pupils who had simply had ‘business as usual’ with their teachers. But the group which did both the counting and the finger games fared significantly better.

    “This study provides evidence that fingers provide children with a ‘bridge’ between different representations of numbers, which can be verbal, written or symbolic. Combined finger training and number games could be a useful tool for teachers to support children’s understanding of numbers,” Professor Jay said.

     


  6. Study suggests poor understanding of ratios leads to bad shopping decisions

    June 12, 2017 by Ashley

    From the University of Miami press release:

    Consumers make poor purchase decisions when they need to work with ratios to assess a product’s value, says a new study published in the May 2017 of the Journal of Marketing Behavior, from the University of Miami School of Business Administration. In situations where consumers must average ratio information, such as comparing the fuel efficiency of two cars using the ratio miles per gallon, they often flub the numbers by incorrectly assuming the mathematic equation to find miles per gallon would be to average the sum of the mileage of both cars and then divide by two, instead of using a more complex equation needed to accurately compare ratios. This incorrect way of crunching the numbers leads to only 25-30 percent of shoppers getting the correct answer.

    “People rely heavily on the ‘normal’ way to compute an average and if they simply had ready access to software that calculates the average of ratios, they could make more informed decisions about many big-ticket purchases, such as cars,” said Michael Tsiros, professor of marketing at the University of Miami School of Business Administration. “If you think about how many different ways we miscalculate the average of ratios, you’d realize how much of an impact this likely has on our stock purchase decisions that can also suffer from the same bias given they can also be compared as ratios,” said Tsiros, who conducted the study with a colleague from Texas A&M University.

    Methodology

    The researchers conducted two studies to demonstrate consumers’ difficulty in dealing with ratios. In the first study, participants were assigned word problems that, in order to arrive at the correct answer, required them to use the formula for averaging ratios. The majority, 53 percent of the participants selected the response that reflected the arithmetic average vs. the average of ratios. In the second study, participants received information on the cash ?ow, discount rate, and growth rate of three stocks and were asked to allocate $1,000 across them. Similar to the first study, 48 percent of participants’ selections reflected the incorrect use of the arithmetic average formula.

    “Whether the decision is about allocating funds properly to a 401K plan or finding a washer and dryer that uses a lower ratio of water per load, this study points to the significant need for something like a ratio calculator built on to relevant shopping websites or perhaps in-store,” continued Tsiros. “Maybe it’s an easy mobile app. Whatever it may be, the return that comes with going the extra mile for your customer, especially those making big-ticket purchases, is a smart business decision.”


  7. Cognitive scientist suggests numerical cognition is not biologically endowed

    May 26, 2017 by Ashley

    From the University of California San Diego press release:

    Clocks and calendars, sports scores and stock-market tickers — our society is saturated with numbers. One of the first things we teach our children is to count, just as we teach them their ABCs. But is this evidence of a biological drive? No, says cognitive scientist Rafael Nunez of the University of California San Diego. It is evidence of our cultural preoccupations. “Numerical cognition,” he says, “is not biologically endowed.”

    Writing in the June 2017 issue of Trends in Cognitive Sciences, Nunez takes on the conventional wisdom in the field right now — a widely accepted view in cognitive neuroscience, child psychology and animal cognition that there is a biologically evolved capacity for number and arithmetic that we share with other species.

    For example, Alex the African grey parrot wowed millions with his mathematical genius, not only on YouTube and TV but in scientific journals as well. Respected researchers are publishing studies suggesting that not only Alex but an incredible array of other animals can deal with numbers, too, from our evolutionary cousins the chimpanzees to more distant relatives like newborn chicks, salamanders and even mosquitofish. Human babies have also been shown to discriminate between different quantities at ages so young that it would seem language and culture couldn’t have yet played much of a role.

    That all points to a primordial ability for math, right? We’re wired for it like we are for language? Not so fast, says Nunez, professor of cognitive science in the UC San Diego Division of Social Sciences and director of the Embodied Cognition Laboratory.

    He believes that part of the problem is muddled terminology. There is a difference, he says, between number and quantity, between doing math and perceiving relative amounts of things. We — human and nonhuman animals alike — do seem to have a shared ability, grounded in our biology and helped along by evolutionary pressures, to tell apart “some” and “many” or even small amounts of something. But numbers, more strictly speaking, he says, need a symbolic system and the scaffold of culture.

    In the same issue of the journal, neuroscientist Andreas Nieder writes a rebuttal to Nunez. And Nunez, in turn, rebuts the rebuttal. Is this an argument for the birds, though? A debate only a specialist could love? Nunez says the implications go far beyond the field. As society seeks to apply findings from neuroscience to solve problems in education, for example, we need a clearer view of where to look for solutions.

    To support his argument that we and other animals don’t have an evolved capacity for number per se, Nunez cites several different strands of research in the current literature, including experimental work with humans from non-industrialized cultures, which suggests an imprecise approach to quantity.

    Many of the world’s languages, he points out, don’t bother with exact terms for numbers larger than a few and rely on quantifiers like “several” or “many.” People can get along surprisingly well with just those kinds of words and occasional linguistic emphasis like “really” to distinguish between “a lot” and “really a lot.” A survey of 193 hunter-gatherer languages from different continents found that most of these languages stop at the number five or below: 61 percent in South America, 92 percent in Australia and 41 percent in Africa. Nunez suspects that until the need arose to make precise counts of commodities, most humans throughout history just worked with “natural quantifiers.”

    He points also to brain-imaging research that shows native speakers of Chinese and native speakers of English process the same Arabic numerals in different parts of their brains, suggesting that language and culture influence even which neurons are recruited to deal with numbers.

    According to Nunez, as much as we might be wowed by what some trained animals can do, we have to remember that doesn’t necessarily point back to an evolved capacity. They are trained over many hours and months, and they’re trained by humans. “A circus seal may jump through a burning ring but it doesn’t tell us anything about the animal’s ability to deal with fire in its natural environment,” he said.

    To drive home his point about humans, Nunez uses what he describes as the “absurd” analogy of snowboarding. To be able to snowboard, we need our biology- “we need our limbs and our vestibular system for balance, we need optic flow navigation, but those don’t give an account of snowboarding and no one argues that we evolved to do it.” Without a culture that allows for thermal suits and ski lifts, he said, we wouldn’t be on the slopes at all.

    Nunez calls on researchers to become more precise with their terms and suggests that it could be productive to investigate “what seems to be nearly universal in human cultures and in many nonhuman animals too: a ‘quantical‘ ability and not a numerical one.”

    “Quantical skills,” he said, are a good candidate for more intensive study and might even be informative for education. We study early ability to count and draw correlations with later achievement in school. Perhaps there are even stronger correlations with the ability to quantify, he said.


  8. Parents’ motivation influences students’ academic outcomes

    May 13, 2017 by Ashley

    From the University of Tübingen press release:

    Whether parental help has positive or negative effects on students’ academic outcomes depends on the motivation and involvement of their parents. Results of a study conducted by the Hector Research Institute of Education Sciences and Psychology suggest that students whose parents are interested in math and perceive their own math competencies to be high perform better than students with parents who show a low interest in math and regard their competencies in the domain as equally low — regardless of the intensity of the help students receive at home. The results have now been published in Child Development.

    Family background plays a crucial role in the development of students’ academic motivation and achievement. Previous research suggested that parents’ academic involvement is, on average, associated with better academic outcomes, but the pattern of results was far from being unequivocal and it also remained unclear what kind of help is actually helpful and what is harmful. For example, excessive parental involvement may be perceived by students as controlling behavior. This can have a detrimental effect on their academic confidence and correspondingly on achievement. Thus, researchers at the University of Tübingen set out to investigate which family characteristics have a positive effect on academic outcomes and which characteristics can be more of a hindrance. To this end, they collected data from more than 1,500 ninth-grade students and their parents.

    Parents answered questions on the degree of their academic involvement in math such as homework help, family math interest, their math competencies, their child’s need for support in math, and the time and energy they invest in their child’s academic life. Students filled out questionnaires at the beginning as well as five months later, in which they reported on their own competencies, their effort, and their interest in math. In addition, their math grades and their achievement in standardized achievement tests were assessed.

    The results confirmed the researchers’ assumption that parental involvement per se does not result in higher academic outcomes. Instead, there are very specific family characteristics that promote high achievement. “A favorable pattern of students’ academic outcomes was found when families were interested in math and perceived their own math competence to be high, regardless of their amount of academic involvement,” says Isabelle Häfner, lead author of the study. Thus, it would be problematic to attribute high or low achievement solely to whether parents help students with their homework or not.

    The most unfavorable conditions for academic achievement were found for students from deeply involved families who considered their child needed support in math, showed low levels of family math interest, and perceived their own math competencies as low. Students from these ‘involved but unmotivated’ families not only performed poorly in math, but also showed low levels of motivation. “Helicopter moms can impair their child’s performance if they are not themselves interested in the subject they want to support their child in,” explains Häfner. This complex interplay of favorable and unfavorable factors with regard to students’ academic achievement will be investigated in further studies.


  9. Simple Numbers Game Seems to Make Kids Better at Math

    June 22, 2016 by Ashley

    From the Johns Hopkins University media release:

    math_problemAlthough math skills are considered notoriously hard to improve, Johns Hopkins University researchers boosted kindergarteners’ arithmetic performance simply by exercising their intuitive number sense with a quick computer game.

    “Math ability is not static — it’s not the case that if you’re bad at math, you’re bad at it the rest of your life. It’s not only changeable, it can be changeable in a very short period of time,” said Jinjing “Jenny” Wang, a graduate student in the Krieger School of Arts and Science’s Department of Psychological and Brain Sciences. “We used a five-minute game to change kids’ math performance.”

    The findings are due to appear in the July issue of the Journal of Experimental Child Psychology.

    Humans and animals are born with an intuitive sense of quantities and can demonstrate this knowledge as infants. For instance, when presented with a choice between a plate with a few crackers and another with more of them, even a baby will gravitate to the option with more. This intuition about numbers is called the “approximate number system.”

    Although this primitive sense of number is imprecise, and therefore quite different than the numerical exactitude of mathematics, studies have shown the two abilities are linked. For instance, researchers from this same Johns Hopkins research group have demonstrated that a strong early gut sense of approximate number can predict math ability later when a child attends school. But until now, no one has shown that grooming that gut sense could make a child better at math.

    “That’s the big question,” Wang said. “If we can improve people’s intuitive number ability, can we also improve their math ability?

    The researchers created a five-minute computer game to train the intuitive number sense of 40 five-year-olds. Blue dots and yellow dots flashed on a laptop screen; the children were asked to indicate whether there were more blue ones or more yellow ones — and to do so quickly, without counting. Children received feedback after each trial. After correct responses, a pre-recorded voice told them, “That’s right.” After wrong answers, they heard, “Oh, that’s not right.”

    Some of the kids started with easier questions that gradually became harder. Other kids started with the hard questions, and a third group worked through a mix of hard and easy problems.

    After the dots game, the researchers gave all of the children a vocabulary quiz or a math quiz. With the math quiz, derived from a standardized math ability assessment test, the kids were asked to count backward, to judge the magnitude of spoken numbers (“Which is more, 7 or 6?”), to calculate answers to word problems (“Joey has one block and gets two more; how many does he have?”), and to write down numbers.

    Though researchers detected no change in any of the children’s vocabulary skills, the kids who performed the dots game in the proper training fashion — easiest to hardest — scored much higher on the math test, getting about 80 percent of the answers correct.

    The kids given the hardest dot questions first got just 60 percent of the math test right, while the control group kids who got the mix of easy and hard questions got scored about a 70 percent.

    It was clear that improving the children’s number sense with the game helped their math scores, at least in the short term, said Lisa Feigenson, professor of psychological and brain sciences and a senior author of the study. The next step will be to figure out if there’s a way to use the technique for lasting results.

    “These findings emphasize the sense in which core cognition, seen across species and across development, serves as a foundation for more sophisticated thought,” Feigenson said. “Of course, this raises the question of whether this kind of rapid improvement lasts for any significant duration, and whether it enhances all types of math abilities. We’re excited to follow up on these questions.”

    The research team also included Darko Odic, a former graduate student in psychology, and Justin Halberda, a professor of psychological and brain sciences, both at Johns Hopkins.

    This research was supported by National Institutes of Health grant R01 HD057258.