mathematics

Dyscalculia

Older news items (pre-2010) brought over from the old website

Right parietal lobe implicated in dyscalculia

By temporarily knocking out an area in the right parietal lobe (the right intraparietal sulcus), researchers have induced dyscalculia in normal subjects, providing strong evidence that dyscalculia is caused by malfunction in this area. These findings were further validated by testing participants suffering from developmental dyscalculia. Although less well-known, dyscalculia is as prevalent as dyslexia and attention deficit hyperactivity disorder (around 5%).

Kadosh, R.C. et al. 2007. Virtual Dyscalculia Induced by Parietal-Lobe TMS Impairs Automatic Magnitude Processing. Current Biology, online ahead of print March 22

http://www.sciencedaily.com/releases/2007/03/070322132931.htm
http://www.eurekalert.org/pub_releases/2007-03/ucl-tro032107.php

Scientists find brain function most important to math ability

A finding that an area of the brain widely thought to be involved in processing number information generally, in fact has two very separate functions, may be the key to diagnosing dyscalculia. One function is responsible for counting 'how many' things are present and the other is responsible for knowing 'how much'. The brain activity specific to estimating numbers of things is thought to be the brain network that underlies arithmetic and may be abnormal in dyscalculics.

[1336] Castelli, F., Glaser D. E., & Butterworth B.
(2006).  Discrete and analogue quantity processing in the parietal lobe: A functional MRI study.
Proceedings of the National Academy of Sciences of the United States of America. 103(12), 4693 - 4698.

http://www.eurekalert.org/pub_releases/2006-03/ucl-sfb030606.php

Calculation difficulties in children of very low birthweight

Learning difficulties, including problems with numeracy, are common in Western populations. Many children with learning difficulty are survivors of preterm birth. Although some of these children have neurological disabilities, many are neurologically normal. A neuroimaging study of neurologically normal adolescent children who had been born preterm at 30 weeks gestation or less found an area in the left parietal lobe where children without a deficit in calculation ability have more grey matter than those who do have this deficit.

[1281] Isaacs, E. B., Edmonds C. J., Lucas A., & Gadian D. G.
(2001).  Calculation difficulties in children of very low birthweight: A neural correlate.
Brain. 124(9), 1701 - 1707.

http://brain.oupjournals.org/cgi/content/abstract/124/9/1701
http://news.bbc.co.uk/hi/english/sci/tech/newsid_1512000/1512664.stm
http://www.independent.co.uk/story.jsp?story=90945

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The effect of stress on performance depends on individual and situational factors

September, 2011

A new study shows how stress only impacts math performance in those with both higher working memory capacity and math anxiety, while another shows that whether or not pressure impacts your performance depends on the nature of the pressure and the type of task.

Working memory capacity and level of math anxiety were assessed in 73 undergraduate students, and their level of salivary cortisol was measured both before and after they took a stressful math test.

For those students with low working memory capacity, neither cortisol levels nor math anxiety made much difference to their performance on the test. However, for those with higher WMC, the interaction of cortisol level and math anxiety was critical. For those unafraid of math, the more their cortisol increased during the test, the better they performed; but for those anxious about math, rising cortisol meant poorer performance.

It’s assumed that low-WMC individuals were less affected because their performance is lower to start with (this shouldn’t be taken as an inevitability! Low-WMC students are disadvantaged in a domain like math, but they can learn strategies that compensate for that problem). But the effect on high-WMC students demonstrates how our attitude and beliefs interact with the effects of stress. We may all have the same physiological responses, but we interpret them in different ways, and this interpretation is crucial when it comes to ‘higher-order’ cognitive functions.

Another study investigated two theories as why people choke under pressure: (a) they’re distracted by worries about the situation, which clog up their working memory; (b) the stress makes them pay too much attention to their performance and become self-conscious. Both theories have research backing from different domains — clearly the former theory applies more to the academic testing environment, and the latter to situations involving procedural skill, where explicit attention to the process can disrupt motor sequences that are largely automatic.

But it’s not as simple as one effect applying to the cognitive domain, and one to the domain of motor skills, and it’s a little mysterious why pressure could have too such opposite effects (drawing attention away, or toward). This new study carried out four experiments in order to define more precisely the characteristics of the environment that lead to these different effects, and suggest solutions to the problem.

In the first experiment, participants were given a category learning task, in which some categories had only one relevant dimension and could be distinguished according to one easily articulated rule, and others involved three relevant dimensions and one irrelevant one. Categorization in this case was based on a complex rule that would be difficult to verbalize, and so participants were expected to integrate the information unconsciously.

Rule-based category learning was significantly worse when participants were also engaged in a secondary task requiring them to monitor briefly appearing letters. However it was not affected when their secondary task involved them explicitly monitoring the categorization task and making a confidence judgment. On the other hand, the implicit category learning task was not disrupted by the letter-monitoring task, but was impaired by the confidence-judgment task. Further analysis revealed that participants who had to do the confidence-judgment task were less likely to use the best strategy, but instead persisted in trying to verbalize a one- or two-dimension rule.

In the second experiment, the same tasks were learned in a low-pressure baseline condition followed by either a low-pressure control condition or one of two high-pressure conditions. One of these revolved around outcome — participants would receive money for achieving a certain level of improvement in their performance. The other put pressure on the participants through monitoring — they were watched and videotaped, and told their performance would be viewed by other students and researchers.

Rule-based category learning was slower when the pressure came from outcomes, but not when the pressure came from monitoring. Implicit category learning was unaffected by outcome pressure, but worsened by monitoring pressure.

Both high-pressure groups reported the same levels of pressure.

Experiment 3 focused on the detrimental combinations — rule-based learning under outcome pressure; implicit learning under monitoring pressure — and added the secondary tasks from the first experiment.

As predicted, rule-based categories were learned more slowly during conditions of both outcome pressure and the distracting letter-monitoring task, but when the secondary task was confidence-judgment, the negative effect of outcome pressure was counteracted and no impairment occurred. Similarly, implicit category learning was slowed when both monitoring pressure and the confidence-judgment distraction were applied, but was unaffected when monitoring pressure was counterbalanced by the letter task.

The final experiment extended the finding of the second experiment to another domain — procedural learning. As expected, the motor task was significantly affected by monitoring pressure, but not by outcome pressure.

These findings suggest two different strategies for dealing with choking, depending on the situation and the task. In the case of test-taking, good test preparation and a writing exercise can boost performance by reducing anxiety and freeing up working memory. If you're worried about doing well in a game or giving a memorized speech in front of others, you instead want to distract yourself so you don't become focused on the details of what you're doing.

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Simple estimation abilities predict better math understanding in preschoolers

August, 2011

New research linking a better number sense to greater math understanding in preschoolers emphasizes the role of parents and caregivers in giving children a head start in math.

Mathematics is a complex cognitive skill, requiring years of formal study. But of course some math is much simpler than others. Counting is fairly basic; calculus is not. To what degree does ability at the simpler tasks predict ability at the more complex? None at all, it was assumed, but research with adolescents has found an association between math ability and simple number sense (or as it’s called more formally, the "Approximate Number System" or ANS).

A new study extends the finding to preschool children. The study involved 200 3- to 5-year-old children, who were tested on their number sense, mathematical ability and verbal ability. The number sense task required children to estimate which group had more dots, when seeing briefly presented groups of blue and yellow dots on a computer screen. The standardized test of early mathematics ability required them to verbally count items on a page, to tell which of two spoken number words was greater or lesser, to read Arabic numbers, as well as demonstrate their knowledge of number facts (such as addition or multiplication), calculation skills (solving written addition and subtraction problems) and number concepts (such as answering how many sets of 10 are in 100). The verbal assessment was carried out by parents and caregivers of the children.

The study found that those who could successfully tell when the difference between the groups was only one dot, also knew the most about Arabic numerals and arithmetic. In other words, the findings confirm that number sense is linked to math ability.

Because these preschoolers have not yet had formal math instruction, the conclusion being drawn is that this number sense is inborn. I have to say that seems to me rather a leap. Certainly number sense is seen in human infants and some non-human animals, and in that sense the ANS is assuredly innate. However what we’re talking about here is the differences in number sense — the degree to which it has been developed. I’d remind you of my recent report that preschoolers whose parents engage in the right number-talk develop an understanding of number earlier, and that such understanding affects later math achievement. So I think it’s decidedly premature to assume that some infants are born with a better number sense, as opposed to having the benefit of informal instruction that develops their number sense.

I think, rather, that the finding adds to the evidence that preschoolers’ experiences and environment have long-lasting effects on academic achievement.

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How parents can improve their preschoolers’ understanding of number

July, 2011

A new study shows that preschoolers whose parents engage in the right number-talk develop an understanding of number earlier. Such understanding affects later math achievement.

At every level, later math learning depends on earlier understanding. Previous research has found that the knowledge children have of number before they start school predicts their achievement throughout elementary school.

One critical aspect of mathematical development is cardinal-number knowledge (e.g. knowing that the word ‘three’ refers to sets of three things). But being able to count doesn’t mean the child understands this principle. Children who enter kindergarten with a good understanding of the cardinal principle have been found to do better in mathematics.

Following research indicating an association between children’s knowledge of number and the amount of number talk their parents engage in, a new study recorded parental interactions for 44 young children aged 14-30 months. Five 90-minute sessions, four months apart, were recorded in the children’s home, and each instance in which parents talked about numbers with their children was noted and coded. The children were then (at nearly four years) tested on their understanding of the cardinal principle.

The study found that parents’ number talk involving counting or labeling sets of visible objects related to children’s later cardinal-number knowledge, whereas other types of parent number talk were not. Talk of larger sets, containing more than 3 objects, was particularly important. This is probably because children can recognize number sets of three or less in a holistic way.

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Exercise improves executive function and math in sedentary children

February, 2011
  • A three-month trial comparing the effects of exercise programs on cognitive function in sedentary, overweight children, has found dose-related benefits of regular aerobic exercise.

A study involving 171 sedentary, overweight 7- to 11-year-old children has found that those who participated in an exercise program improved both executive function and math achievement. The children were randomly selected either to a group that got 20 minutes of aerobic exercise in an after-school program, one that got 40 minutes of exercise in a similar program, or a group that had no exercise program. Those who got the greater amount of exercise improved more. Brain scans also revealed increased activity in the prefrontal cortex and reduced activity in the posterior parietal cortex, for those in the exercise group.

The program lasted around 13 weeks. The researchers are now investigating the effects of continuing the program for a full year. Gender, race, socioeconomic factors or parental education did not change the impact of the exercise program.

The effects are consistent with other studies involving older adults. It should be emphasized that these were sedentary, overweight children. These findings are telling us what the lack of exercise is doing to young minds. I note the report just previous, about counteracting what we have regarded as “normal” brain atrophy in older adults by the simple action of walking for 40 minutes three times a week. Children and older adults might be regarded as our canaries in the coal mine, more vulnerable to many factors that can affect the brain. We should take heed.

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Review makes clear no gender differences in math ability

November, 2010

Analysis of hundreds of studies has found no difference between male and female in terms of their math skills.

A meta-analysis of 242 articles assessing the math skills of 1,286,350 people found no difference between the two sexes. This was confirmed in an analysis of the data from several large surveys of American adolescents (the National Longitudinal Surveys of Youth, the National Education Longitudinal Study of 1988, the Longitudinal Study of American Youth, and the National Assessment of Educational Progress).

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[1924] Lindberg, S. M., Hyde J S., Petersen J. L., & Linn M. C.
(2010).  New trends in gender and mathematics performance: A meta-analysis..
Psychological Bulletin. 136(6), 1123 - 1135.

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Child's 'mental number line' affects memory for numbers

October, 2010

Young children’s memory for numbers reflects their understanding that numbers, however big, are all evenly spaced.

When children learn to count, they do so by rote. Understanding what the numbers really mean comes later. This is reflected in the way children draw a number line. In the beginning, they typically put more space between the smaller numbers, with the larger numbers all scrunched up at the end (a logarithmic number line). Eventually they progress to a number line where the numbers are evenly spaced (linear number line).

Now a series of experiments with preschoolers and second graders has revealed that the more linear the child's magnitude representations (as seen on the number line as well as in other tasks), the better the child was at remembering numbers (for example, from a story with some numbers included).

This was true for preschoolers for numbers from 1-20 and for elementary school children for numbers from 1-1000, and for four different number tasks measuring numerical-magnitude representations (categorization and number-line, measurement, and numerosity estimation). Other types of numerical knowledge—numeral identification and counting—were unrelated to remembering numbers.

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Negative stereotypes affect learning, not just performance

August, 2010

Following on from several studies showing that being reminded of a negative stereotype for your group (be it race or gender) affects your test performance, a new study shows it also impairs learning.

A number of studies have demonstrated that negative stereotypes (such as “women are bad at math”) can impair performance in tests. Now a new study shows that this effect extends to learning. The study involved learning to recognize target Chinese characters among sets of two or four. Women who were reminded of the negative stereotypes involving women's math and visual processing ability failed to improve at this search task, while women who were not reminded of the stereotype got faster with practice. When participants were later asked to choose which of two colored squares, imprinted with irrelevant Chinese characters, was more saturated, those in the control group were slower to respond when one of the characters had been a target. However, those trained under stereotype threat showed no such effect, indicating that they had not learned to automatically attend to a target. It’s suggested that the women in the stereotype threat group tried too hard to overcome the negative stereotype, expending more effort but in an unproductive manner.

There are two problems here, it seems. The first is that people under stereotype threat have more invested in disproving the stereotype, and their efforts may be counterproductive. The second, that they are distracted by the stereotype (which uses up some of their precious working memory).

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[1686] Rydell, R. J., Shiffrin R. M., Boucher K. L., Van Loo K., & Rydell M. T.
(2010).  Stereotype threat prevents perceptual learning.
Proceedings of the National Academy of Sciences.

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Women teachers transfer their fear of doing math to girls

January, 2010

A study involving first- and second-grade teachers found that boys' math performance was not related to their (female) teacher's math anxiety while girls' math achievement was.

Consistent with studies showing that gender stereotypes can worsen math performance in females, a year-long study involving 17 first- and second-grade teachers and their 52 boy and 65 girl students has found that boys' math performance was not related to their (female) teacher's math anxiety while girls' math achievement was. Early elementary school teachers in the United States are almost exclusively female. Math achievement was unrelated to teacher math anxiety in both boys and girls at the beginning of the school year. Moreover, achievement was negatively associated with belief in gender stereotypes. Girls who confirmed a belief that boys are better in math than girls scored six points lower in math achievement than did boys or girls who had not developed a belief in the stereotype (102 versus 108). Research has found that elementary education majors have the highest rate of mathematics anxiety of any college major.

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[1450] Beilock, S. L., Gunderson E. A., Ramirez G., & Levine S. C.
(2010).  Female teachers’ math anxiety affects girls’ math achievement.
Proceedings of the National Academy of Sciences. 107(5), 1860 - 1863.

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Children with home computers likely to have lower test scores

July, 2010

An American study suggests that getting a home computer can have a negative effect on reading and math scores in middle-grade students, particularly those from disadvantaged families.

Data from North Carolina's mandated End-of-Grade tests (2000-2005), which includes student reports on how frequently they use a home computer for schoolwork, watch TV or read for pleasure, reveals that students in grades five through eight (c.10-13), particularly those from disadvantaged families, tended to have lower reading and math scores after they got a home computer. The researchers suggest that the greater negative effect in disadvantaged households may reflect less parental monitoring.

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[1635] Vigdor, J. L., & Ladd H. F.
(2010).  Scaling the Digital Divide: Home Computer Technology and Student Achievement.
National Bureau of Economic Research Working Paper Series. No. 16078,

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