mathematics

Gender Differences

  • In general, males are better at spatial tasks involving mental rotation.
  • In general, females have superior verbal skills.
  • Males are far more likely to pursue math or science careers, but gender differences in math are not consistent across nations or ages.
  • A number of imaging studies have demonstrated that the brains of males and females show different patterns of activity on various tasks.
  • Nicotine has been shown to differentially alter men's and women's brain activity patterns so that the differences disappear.
  • Both estrogen and testosterone have been shown to affect cognitive function.
  • Training has been shown to bring parity to differences in cognitive performance between the sexes.
  • Age also alters the differences between men and women.

Widely cited gender differences in cognition

It is clear that there are differences between the genders in terms of cognitive function; it is much less clear that there are differences in terms of cognitive abilities. Let me explain what I mean by that.

It's commonly understood that males have superior spatial ability, while females have superior verbal ability. Males are better at math; females at reading. There is some truth in these generalizations, but it's certainly not as simple as it is portrayed.

First of all, as regards spatial cognition, while males typically outperform females on tasks dealing with mental rotation and spatial navigation, females tend to outperform males on tasks dealing with object location, relational object location memory, and spatial working memory.

While the two sexes score the same on broad measures of mathematical ability, girls tend to do better at arithmetic, while boys do better at spatial tests that involve mental rotation.

Having said that, it does depend where you're looking. The Programme for International Student Assessment (PISA) is an internationally standardised assessment that is given to 15-year-olds in schools. In 2003, 41 countries participated. Given the constancy of the gender difference in math performance observed in the U.S., it is interesting to note what happens in other countries. There was no significant difference between the sexes in Australia, Austria, Belgium, Japan, the Netherlands, Norway, Poland, Hong Kong, Indonesia, Latvia, Serbia, and Thailand. There was a clear male superiority for all 4 content areas in Canada, Denmark, Greece, Ireland, Korea, Luxembourg, New Zealand, Portugal, the Slovak Republic, Liechtenstein, Macao and Tunisia. In Austria, Belgium, the United States and Latvia, males outperformed females only on the space and shape scale; in Japan, the Netherlands and Norway only on the uncertainty scale. And in Iceland, females always consistently do better than males!

Noone knows why, but it is surely obvious that these differences must lie in cultural and educational factors.

Interestingly, the IEA Third International Mathematics and Science Study (TIMSS) shows this developing -- while significant gender differences in mathematics were found only in 3 of the 16 participating OECD countries for fourth-grade students, gender differences were found in 6 countries at the grade-eight level, and in 14 countries at the last year of upper secondary schooling.

This inconsistency is not, however, mirrored in verbal skills -- girls outperform boys in reading in all countries.

Gender differences in language have been consistently found, and hardly need reiteration. However, here's an interesting study: it found gender differences in the emerging connectivity of neural networks associated with skills needed for beginning reading in preschoolers. It seems that boys favor vocabulary sub-skills needed for comprehension while girls favor fluency and phonic sub-skills needed for the mechanics of reading.The study points to the different advantages each gender brings to learning to read.

There's a lesson there.

There are other less well-known differences between the sexes. Women tend to do better at recognizing faces. But a study has found that this superiority applies only to female faces. There was no difference between men and women in the recognition of male faces.

Moreover, pre-pubertal boys and girls have been found to be equally good at recognizing faces and identifying expressions. However, they do seem to do it in different ways. Boys showed significantly greater activity in the right hemisphere, while the girls' brains were more active in the left hemisphere. It is speculated that boys tend to process faces at a global level (right hemisphere), while girls process faces at a more local level (left hemisphere).

It's also long been recognized that women are better at remembering emotional memories. Interestingly, an imaging study has revealed that the sexes tend to encode emotional experiences in different parts of the brain. In women, it seems that evaluation of emotional experience and encoding of the memory is much more tightly integrated.

But of course, noone denies that there are differences between men and women. The big question (one of the big questions) is how much, if any, is innate.

Studies of differences, even at the neural level, don't demonstrate that. It's increasingly clear that environmental factors affect all manner of thing at the neural level. However, one study of 1-day-old infants did find that boys tended to gaze at three-dimensional mobiles longer than girls did, while girls looked at human faces longer than boys did.

Of course, even a 1-day-old infant isn't entirely free of environmental influence. In this case, the most important environmental influence is probably hormones.

Hormones and chemistry

A lot of studies in recent years have demonstrated that estrogen is an important player in women's cognition. Spatial ability in particular seems vulnerable to hormonal effects. Women do vary in their spatial abilities according to where they are in the menstrual cycle, and there is some evidence that spatial abilities (in both males and females) may be affected by how much testosterone is received in the womb.

Another study has found children exposed to higher levels of testosterone in the womb also develop language later and have smaller vocabularies at 2 years of age.

Hormones aren't the only chemical affecting male and female brains differently. Significant differences have been found in the brain activity of men and women when engaged in a broad range of activities and behaviors. These differences are more acute during impulsive or hostile acts. But — here's the truly fascinating thing — nicotine causes these brain activity differences to disappear. A study has found that among both smokers and non-smokers on nicotine, during aggressive moments, there are virtually no differences in brain activity between the sexes. A finding that supports other studies that indicate men's and women's brains respond differently to the same stimuli — for example, alcohol.

What does all this mean? Well, let's look at the question that's behind the whole issue: are men smarter than women? (or alternately, are women smarter than men?)

Is one sex smarter than the other?

Here's a few interesting studies that demonstrate some more differences between male and female brains.

A study of some 600 Dutch men and women aged 85 years found that the women tended to have better cognitive speed and a better memory than the men, despite the fact that significantly more of the women had limited formal education compared to the men. This may be due to better health. On the other hand, there do appear to be differences in the way male and female brains develop, and the way they decline.

For example, women have up to 15% more brain cell density in the frontal lobe, which controls so-called higher mental processes, such as judgement, personality, planning and working memory. However, as they get older, women appear to shed cells more rapidly from this area than men. By old age, the density is similar for both sexes.

A study of male and female students (aged 18-25) has found that men's brain cells can transmit nerve impulses 4% faster than women's, probably due to the faster increase of white matter in the male brain during adolescence.

An imaging study of 48 men and women between 18 and 84 years old found that, compared with women, men had more than six times the amount of intelligence-related gray matter. On the other hand, women had about nine times more white matter involved in intelligence than men did. Women also had a large proportion of their IQ-related brain matter (86% of white and 84% of gray) concentrated in the frontal lobes, while men had 90% of their IQ-related gray matter distributed equally between the frontal lobes and the parietal lobes, and 82% of their IQ-related white matter in the temporal lobes. Despite these differences, men and women performed equally on the IQ tests.

It has, of course, long been suggested that women are intellectually inferior because their brains are smaller. A study involving the intelligence testing of 100 neurologically normal, terminally ill volunteers found that a bigger brain size is indeed correlated with higher intelligence — but only in certain areas, and with odd differences between women and men. Verbal intelligence was clearly correlated with brain size for women and — get this — right-handed men! But not for left-handed men. Spatial intelligence was also correlated with brain size in women, but much less strongly, while it was not related at all to brain size in men.

Also, brain size decreased with age in men over the age span of 25 to 80 years, suggesting that the well-documented decline in visuospatial intelligence with age is related, at least in right-handed men, to the decrease in cerebral volume with age. However age hardly affected brain size in women.

What is all this telling us?

Male and female brains are different: they develop differently; they do things differently; they respond to different stimuli in different ways.

None of this speaks to how well information is processed.

None of these differences mean that individual brains, of either sex, can't be trained to perform well in specific areas.

Here’s an experiment and a case study which bear on this.

It's all about training

The experiment concerns rhesus monkeys. The superiority of males in spatial memory that we're familiar with among humans also occurs in this population. But here's the interesting thing — the gender gap only occurred between young adult males and young untrained females. In other words, there was no difference between older adults (because performance deteriorated with age more sharply for males), and did not occur between male and female younger adults if they were given simple training. Apparently the training had little effect on the males, but the females improved dramatically.

The “case study” concerns Susan Polgar, a chess master. You can read about her in a recent article (http://www.opinionjournal.com/la/?id=110006356 ), which I noticed because the Polgar sisters are a well-known example of “hot-housing”. I cited them in my own article on the question of whether there is in fact such a thing as innate talent. Susan Polgar and her sisters are examples of how you can train “talent”; indeed, whether there is in fact such a thing as “talent” is a debatable question. Certainly you can argue for a predisposition towards certain activities, but after that … Well, even geniuses have to work at it, and while you may not be able to make a genius, you can certainly create experts.

This article was provoked, by the way, by comments by the President of Harvard University, Lawrence Summers, who recently stirred the pot by giving a speech arguing that boys outperform girls on high school science and math scores because of genetic differences between the genders, and that discrimination is no longer a career barrier for female academics. Apparently, during Dr Summers' presidency, the number of tenured jobs offered to women has fallen from 36% to 13%. Last year, only four of 32 tenured job openings were offered to women.

You can read a little more about what Dr Summers said at http://education.guardian.co.uk/gendergap/story/0,7348,1393079,00.html, and there's a rather good response by Simon Baron-Cohen (professor in the departments of psychology and psychiatry, Cambridge University, and author of The Essential Difference) at: http://education.guardian.co.uk/higher/research/story/0,9865,1399109,00.html

References: 

  • Canli, T., Desmond, J.E., Zhao, Z. & Gabrieli, J.D.E. 2002. Sex differences in the neural basis of emotional memories. Proceedings of the National Academy of Sciences, 99, 10789-10794.
  • Everhart, D.E., Shucard, J.L., Quatrin, T. & Shucard, D.W. 2001. Sex-related differences in event-related potentials, face recognition, and facial affect processing in prepubertal children. Neuropsychology, 15(3), 329-341.
  • Fallon, J.H., Keator, D.B., Mbogori, J., Taylor, D. & Potkin, S.G. 2005. Gender: a major determinant of brain response to nicotine. The International Journal of Neuropsychopharmacology, 8(1), 17-26. (see http://www.eurekalert.org/pub_releases/2005-02/uoc--bao021705.htm)
  • Geary, D.C. 1998. Male, Female: The Evolution of Human Sex Differences. Washington, D.C.: American Psychological Association.
  • Haier, R.J., Jung, R.E., Yeo, R.A., Head, K. & Alkire, M.T. 2005. The neuroanatomy of general intelligence: sex matters. NeuroImage, 25(1), 320-327.
  • Hanlon, H. 2001. Gender Differences Observed in Preschoolers’ Emerging Neural Networks. Paper presented at Genomes and Hormones: An Integrative Approach to Gender Differences in Physiology, an American Physiological Society (APS) conference held October 17-20 in Pittsburgh.
  • Kempel, P.. Gohlke, B., Klempau, J., Zinsberger, P., Reuter, M. & Hennig, J. 2005. Second-to-fourth digit length, testosterone and spatial ability. Intelligence, 33(3), 215-230.
  • Lacreuse, A., Kim, C.B., Rosene, D.L., Killiany, R.J., Moss, M.B., Moore, T.L., Chennareddi, L. & Herndon, J.G. 2005. Sex, age, and training modulate spatial memory in the Rhesus monkey (Macaca mulatta). Behavioral Neuroscience, 119 (1).
  • Levin, S.L., Mohamed, F.B. & Platek, S.M. 2005. Common ground for spatial cognition? A behavioral and fMRI study of sex differences in mental rotation and spatial working memory. Evolutionary Psychology, 3, 227-254.
  • Lewin, C. & Herlitz, A. 2002. Sex differences in face recognition-Women's faces make the difference, Brain and Cognition, 50 (1), 121-128.
  • OECD. Learning for Tomorrow's World –First Results from PISA 2003 http://www.oecd.org/document/0/0,2340,en_2649_201185_34010524_1_1_1_1,00.html
  • Reed, T.E., Vernon, P.A. & Johnson, A.M. 2005. Confirmation of correlation between brain nerve conduction velocity and intelligence level in normal adults. Intelligence, 32(6), 563-572.
  • van Exel, E., Gussekloo, J., de Craen, A.J.M, Bootsma-van der Wiel, A., Houx, P., Knook, D.L. & Westendorp, R.G.J. 2001. Cognitive function in the oldest old: women perform better than men. Journal of Neurology, Neurosurgery & Psychiatry, 71, 29-32.
  • Witelson, S.F., Beresh, H. & Kigar, D.L. 2006. Intelligence and brain size in 100 postmortem brains: sex, lateralization and age factors. Brain, 129, 386-398.
  • Witelson, S.F., Kigar, D.L. & Stoner-Beresh, H.J. 2001. Sex difference in the numerical density of neurons in the pyramidal layers of human prefrontal cortex: a stereologic study. Paper presented to the annual Society for Neuroscience meeting in San Diego, US.

For more on this, see the research reports

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Early development

Children’s understanding, and their use of memory and learning strategies, is a considerably more complex situation than most of us realize. To get some feeling for this complexity, let’s start by looking at a specific area of knowledge: mathematics.

Children's math understanding

Here’s a math problem:

Pete has 3 apples. Ann also has some apples. Pete and Ann have 9 apples altogether. How many apples does Ann have?

This seems pretty straightforward, right? How about this one:

Pete and Ann have 9 apples altogether. Three of these belong to Pete and the rest belong to Ann. How many apples does Ann have?

The same problem, phrased slightly differently. Would it surprise you to know that this version is more likely to be correctly answered by children than the first version?

Whether or not a child solves a math problem correctly is not simply a matter of whether he or she knows the math — the way the problem is worded plays a crucial part in determining whether the child understands the problem correctly. Slight (and to adult eyes, insignificant) differences in the wording of a problem have a striking effect on whether children can solve it.

Mathematics also provides a clear demonstration of the seemingly somewhat haphazard development in cognitive abilities. It’s not haphazard, of course, but it sometimes appears that way from the adult perspective. In math, understanding different properties of the same concept can take several years. For example, children’s understanding of addition and subtraction is not an all-or-none business; adding as combining is grasped by young children quite early, but it takes some 2 to 3 years at school to grasp the essential invariants of additive relations. Multiplicative relations are even harder, with children up to age 10 or so often having great difficulty with proportion, probability, area and division.

Neurological differences between children and adults

Part of the problems children have with math stems from developmental constraints — their brains simply aren’t ready for some concepts. A recent imaging study of young people (aged 8-19 years) engaged in mental arithmetic, found that on simple two-operand addition or subtraction problems (for which accuracy was comparable across age), older subjects showed greater activation in the left parietal cortex, along the supramarginal gyrus and adjoining anterior intra-parietal sulcus as well as the left lateral occipital temporal cortex. Younger subjects showed greater activation in the prefrontal cortex (including the dorsolateral and ventrolateral prefrontal cortex and the anterior cingulate cortex), suggesting that they require comparatively more working memory and attentional resources to achieve similar levels of performance, and greater activation of the hippocampus and dorsal basal ganglia, reflecting the greater demands placed on both declarative and procedural memory systems.

In other words, the evidence suggests that the left inferior parietal cortex becomes increasingly specialized for mental arithmetic with practice, and this process is accompanied by a reduced need for memory and attentional resources.

Not just a matter of brain maturation

But this isn't the whole story. As the earlier example indicated, difficulties in understanding some concepts are often caused by the way the concepts are explained. This is why it’s so important to keep re-phrasing problems and ideas until you find one that “clicks”. Other difficulties are caused by the preconceptions the child brings with them — cultural practices, for example, can sometimes help and sometimes hinder learning.

Other domains: neurological differences between children and adults

What's true of mathematics is also true of other learning areas. When we teach children, we do need to consider developmental constraints, but recent studies suggest we may have over-estimated the importance of development.

In an intriguing imaging study, brain activity in children aged 7-10 and adults (average age 25 years) while doing various language tasks was compared. Six sub-regions in the left frontal and the left extrastriate cortex were identified as being significant. Both these areas are known to play a key role in language processing and are believed to undergo substantial development between childhood and adulthood.

Now comes the interesting part. The researchers attempted to determine whether these differences between children and adults were due to brain maturation or simply the result of slower and less accurate performance by children. By using information regarding each individual's performance on various tasks, they ended up with only two of the six sub-regions (one in the frontal cortex, one in the extrastriate cortex) showing differences that were age-related rather than performance-related (with the extrastriate region being more active in children than adults, while the frontal region was active in adults and not in children).

The researchers concluded that, yes, children do appear to use their brains differently than adults when successfully performing identical language tasks; however, although multiple regions appeared to be differentially active when comparing adults and children, many of those differences were due to performance discrepancies, not age-related maturation.

Childhood amnesia

Let's talk about childhood amnesia for a moment. "Childhood amnesia" is a term for what we all know -- we have very few memories of our early years. This is so familiar, you may never have considered why this should be so. But the reason is not in fact obvious. Freud speculated that we repressed those early memories (but Freud was hung up on repression); modern cognitive psychologists have considered immature memory processing skills may be to blame. This is surely true for the first months -- very young babies have extremely limited abilities at remembering anything for long periods of time (months), and research suggests that the dramatic brain maturation that typically occurs between 8 and 12 months is vital for long-term memory.

But an intriguing study (carried out by researchers at my old stomping ground: the University of Otago in New Zealand) has provided evidence that an important stumbling block in our remembrance of our early years is the child's grasp of language. If you don't have the words to describe what has happened, it seems that it is very difficult to encode it as a memory -- or at least, that it is very difficult to retrieve (before you leap on me with examples, let me add that noone is saying that every memory is encoded in words -- this is palpably not true).

This finding is supported by a recent study that found that language, in the form of specific kinds of sentences spoken aloud, helped 4-year-old children remember mirror image visual patterns.

The role of social interaction in memory development

Another study from my favorite university looked at the role mothers played in developing memory in their young children. The study distinguished between reminiscing (discussing shared experiences) and recounting (discussing unshared experiences). Children 40 months old and 58 months old were studied as they talked about past events with their mothers. It was found that mothers who provided more memory information during reminiscing and requested more memory information during recounting had children who reported more unique information about the events.

In general, parents seldom try to teach memory strategies directly to children, but children do learn strategies by observing and imitating what their parents do and this may in fact be a more effective means of teaching a child rather than by direct instruction.

But parents not only provide models of behavior; they also guide their children's behavior. The way they do this is likely to be influenced by their own beliefs about their children’s mnemonic abilities. If you don't believe your child can possibly remember something, you are unlikely to ask them to make the effort. But when parents ask 2 – 4 year olds to remind them to do something in the future, even 2 year olds remember to remind their parents of promised treats 80% of the time.

By 3 yrs old, children whose mothers typically asked questions about past events performed better on memory tasks than those children whose mothers only questioned them about present events. Observation of mothers as they taught their 4 year olds to sort toys, copy etch-a-sketch designs, and respond to questions regarding hypothetical situations found 3 interaction styles found that related to the child’s performance:

  • imperative-normative, in which mother gave little justification for requests or demands;
  • subjective, in which mother encouraged child to see his own behaviour from another’s point of view;
  • cognitive-rational, in which mother offered logical justifications for requests and demands.

Children whose mothers used the last two styles were more verbal and performed better on cognitive tasks.

A study of kindergarten and elementary school teachers found that children from classes where teachers frequently made strategy suggestions were better able to verbalize aspects of memory training and task performance. Although this made no difference for high achieving children, average and low achievers were more likely to continue using the trained strategy if they had teachers who frequently made strategy suggestions.

Conclusion

What lessons can we learn from all this?

First, we must note that there are indeed developmental constraints on children's capabilities that are rooted in physical changes in the brain. Some of these are simply a matter of time, but others are changes that require appropriate stimulation and training.

Secondly, the importance of language in enabling the child cannot be overestimated.

And thirdly, for children as with older adults, expectations about memory performance can reduce their capabilities. Supportive, directed assistance in developing memory and reasoning strategies can be very effective in helping even very young children.

References: 

  • Best, D.L. 1992. The role of social interaction in memory improvement. In D. Herrmann, H. Weingartner, A. Searleman & C. McEvoy (eds.) Memory Improvement: Implications for Memory Theory. New York: Springer-Verlag. pp 122-49.
  • Liston, C. & Kagan, J. 2002. Brain development: Memory enhancement in early childhood. Nature, 419, 896-896.
  • Reese, E. & Brown, N. 2000. Reminiscing and recounting in the preschool years. Applied Cognitive Psychology, 14 (1), 1-17.
  • Rivera, S.M., Reiss, A.L., Eckert, M.A. & Menon, V. 2005. Developmental Changes in Mental Arithmetic: Evidence for Increased Functional Specialization in the Left Inferior Parietal Cortex. Cerebral Cortex, 15 (11), 1779-1790.
  • Schlaggar, B.L., Brown, T.T., Lugar, H.M., Visscher, K.M., Miezin, F.M. & Petersen, S.E. 2002. Functional neuroanatomical differences between adults and school-age children in the processing of single words. Science, 296, 1476-9.
  • Vergnaud, G. 1997. The Nature of Mathematical Concepts. In T. Nunes & P. Bryant (Eds.), Learning and Teaching Mathematics: An International Perspectives (pp. 5-28). Eastern Sussex: Psychology Press Ltd.

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Finger tracing helps children doing geometry problems

  • Finger tracing key elements in worked problems seems to help some students better understand and apply mathematical concepts.

I've reported before on studies showing how gesturing can help children with mathematics and problem-solving. A new Australian study involving children aged 9-13 has found that finger-tracing has a similar effect.

Students who used their finger to trace over practice examples while simultaneously reading geometry or arithmetic material were able to complete the problems more quickly and correctly than those who didn't use the same technique.

In the first experiment, involving 52 students aged 11-13, some students were instructed to use their index fingers to trace elements of worked examples in triangle geometry, involving two angle relationships (Vertical angles are equal; Any exterior angle equals the sum of the two interior opposite angles.). Students were given two minutes to study a short instructional text on the relationships and how they can be used to solve particular problems. They were then given two minutes to study two worked examples. The tracing group were given additional instruction in how to use their index finger to trace out highlighted elements. The non-tracing group were told to keep their hands in their lap. Testing consisted of six questions, two of which were the same as the acquisition problems but with different numbers, and four of which were transfer questions, requiring more thoughtful responses.

A ceiling effect meant there was no difference between the two groups on the first two test questions. The tracing group answered significantly more transfer questions, although the difference wasn't great. There was no difference in how difficult the groups rated the test items.

In the second experiment, involving 54 Year 4 students, the instruction and problems concerned the fundamental order of operations. The tracing group were told to trace the operation symbols. The tracing group did significantly better, although again, the difference wasn't great, and again, there was no difference in assessment of problem difficulty.

In another experiment, involving 42 Year 5 students (10-11 years), students were given 5 minutes to study three angle relationships involving parallel lines (vertical angles are equal; corresponding angles are equal; the sum of co- interior angles is 180°). While answers to the 'basic' test questions failed to show significant differences, on the advanced transfer problems, the tracing group solved significantly more test questions than the non-tracing group, solved them more quickly, made fewer errors, and reported lower levels of test difficulty.

In the final experiment, involving 72 Year 5 students, on the advanced test problems, students who traced on the paper outperformed those who traced above the paper, who in turn outperformed those who simply read the material.

The researchers claim the findings support the view that tracing out elements of worked examples helps students construct good mental schemas, making it easier for them to solve new problems, and reducing cognitive demand.

As with gesturing, the benefits of tracing are not dramatic, but I believe the pattern of these results support the view that, when cognitive load is high (something that depends on the individual student as well as the task and its context), tracing key elements of worked examples might be a useful strategy.

Further research looking at individual differences would be helpful. I think greater benefits would be shown for students with low working memory capacity.

http://www.eurekalert.org/pub_releases/2016-01/uos-ftc012816.php

Reference: 

[4046] Hu F-T, Ginns P, Bobis J. Getting the point: Tracing worked examples enhances learning. Learning and Instruction [Internet]. 2015 ;35:85 - 93. Available from: http://www.sciencedirect.com/science/article/pii/S0959475214000929

[4043] Ginns P, Hu F-T, Byrne E, Bobis J. Learning By Tracing Worked Examples. Applied Cognitive Psychology [Internet]. 2015 :n/a - n/a. Available from: http://onlinelibrary.wiley.com/doi/10.1002/acp.3171/abstract

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Parents' math anxiety can undermine children's math achievement

  • 1st- & 2nd-grade children learned less math and developed more math anxiety when math-anxious parents frequently helped with their math homework.
  • Children with math-anxious parents who rarely helped with their math homework were not affected.

A study of 438 first- and second-grade students and their primary caregivers has revealed that parents' math anxiety affects their children's math performance — but (and this is the surprising bit) only when they frequently help them with their math homework.

The study builds on previous research showing that students learn less math when their teachers are anxious about math. This is not particularly surprising, and it wouldn't have been surprising if this study had found that math-anxious parents had math-anxious children. But the story wasn't that simple.

Children were assessed in reading achievement, math achievement and math anxiety at both the beginning and end of the school year. Children of math-anxious parents learned significantly less math over the school year and had more math anxiety by the year end—but only if math-anxious parents reported providing help every day with math homework. When parents reported helping with math homework once a week or less often, children’s math achievement and attitudes were not related to parents’ math anxiety. Reading achievement (included as a control) was not related to parents' math anxiety.

Interestingly, the parents' level of math knowledge didn't change this effect (although this is less surprising when you consider the basic-level of math taught in the 1st and 2nd grade).

Sadly, the effect still held even when the teacher was strong in math.

It's suggested that math-anxious parents may be less effective in explaining math concepts, and may also respond less helpfully when children make a mistake or solve the problem in a non-standard way. People with high math anxiety tend to have poor attitudes toward math, and also a high fear of failing at math. It's also possible (likely even) that they will have inflexible attitudes to how a math problem “should” be done. All of these are likely to demotivate the child.

Analysis also indicated that it is not that parents induced math anxiety in their children, who thus did badly, but that their homework help caused the child to do poorly, thus increasing their math anxiety.

Information about parental anxiety and how often parents helped their children with math homework was collected by questionnaire. Math anxiety was assessed using the short (25-item) Math Anxiety Rating Scale. The question, “How often do you help your child with their math homework?” was answered on a 7-point scale (1 = never, 2 = once a month, 3 = less than once a week, 4 = once a week, 5 = 2–3 times a week, 6 = every day, 7 = more than once a day). The mean was 5.3.

The finding points to the need for interventions focused on both decreasing parents' math anxiety and scaffolding their skills in how to help with math homework. It also suggests that, in the absence of such support, math-anxious parents are better not to help!

http://www.eurekalert.org/pub_releases/2015-08/uoc-pma080715.php

http://www.futurity.org/parents-math-anxiety-979472/

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Mathematics

Also see

Dyscalculia

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

Factors influencing math performance

Early math skills best predict school success

A review of data from six studies of close to 36,000 preschoolers has revealed that the single most important factor in predicting later academic achievement is that children begin school with a mastery of early math and literacy concepts. This was true even if they have various social and emotional problems. Children's attention-related skills also mattered. The very strongest predictor of future academic success was beginning school with a knowledge of numbers, number order and other rudimentary math concepts. The study controlled for IQ, family income, gender, temperament, type of previous educational experience, and whether children came from single or two parent families. Mastery of early math skills predicted future reading achievement as well as future math achievement. The opposite was not true.

Duncan, G.J. et al. 2007. School Readiness and Later Achievement. Developmental Psychology, 43 (6), 1428–1446. 

http://www.sciencedaily.com/releases/2007/11/071112182442.htm

Gesturing helps grade-schoolers solve math problems

Two studies of children in late third and early fourth grade, who made mistakes in solving math problems, have found that children told to move their hands when explaining how they’d solve a problem were four times as likely as kids given no instructions to manually express correct new ways to solve problems. Even though they didn’t give the right answer, their gestures revealed an implicit knowledge of mathematical ideas, and the second study showed that gesturing set them up to benefit from subsequent instruction. The findings extend previous research that body movement not only helps people to express things they may not be able to verbally articulate, but actually to think better.

Broaders, S.C., Cook, S.W., Mitchell, Z. & Goldin-Meadow, S. 2007. Making Children Gesture Brings Out Implicit Knowledge and Leads to Learning. Journal of Experimental Psychology: General, 136 (4).

http://www.eurekalert.org/pub_releases/2007-11/apa-ghg102907.php

Young children can add and subtract without arithmetic

We knew infants can judge simple mathematical relationships, such as being able to tell when there are more objects in one group compared to another. Now a new study shows that children can apply that ability to Arabic numerals after learning to count but before they learned to add and subtract. When given such problems as, "Sarah has 15 candies and she gets 19 more; John has 51 candies. Who has more?", five- and six-year-old children answered correctly 64—73% of the time. The research suggests ways to improve children’s engagement with formal arithmetic.

Gilmore, C.K., McCarthy, S.E. & Spelke, E.S. 2007. Symbolic arithmetic knowledge without instruction. Nature, 447, 589-591.

Executive function as important as IQ for math success

A study of 141 preschoolers from low-income homes has found that a child whose IQ and executive functioning were both above average was three times more likely to succeed in math than a child who simply had a high IQ. The parts of executive function that appear to be particularly linked to math ability in preschoolers are working memory and inhibitory control. In this context, working memory may be thought of as the ability to keep information or rules in mind while performing mental tasks. Inhibitory control is the ability to halt automatic impulses and focus on the problem at hand. Inhibitory control was also important for reading ability. The finding offers the hope that training to improve executive function will improve academic performance

Blair, C. & Razza, R.P. 2007. Relating Effortful Control, Executive Function, and False Belief Understanding to Emerging Math and Literacy Ability in Kindergarten. Child Development, 78 (2), 647–663.

Language affects how math is done?

A comparison of activity in the brains of Chinese and English participants doing simple arithmetic using Arabic numbers has found that, although both groups utilised the inferior parietal cortex (an area connected to quantity representation and reading), English speakers displayed more activity in the language processing area of the brain, while Chinese speakers used the area of the brain that deals with processing visual information. There was no significant difference in the reaction time and accuracy of the Chinese and English-speaking volunteers. However, an earlier study comparing Canadian and Chinese students found that the latter were better at complex maths. The findings suggest that our native language, or different teaching methods, may influence the way we solve equations.

Tang, Y. et al. 2006. Arithmetic processing in the brain shaped by cultures. Proc. Natl. Acad. Sci. USA, Published online before print June 30, 2006.

 http://www.newscientist.com/article/dn9422?DCMP=NLC-nletter&nsref=dn9422

Preschool storytelling ability linked to later mathematical ability

A new study suggests that preschool children's early storytelling abilities are predictive of their mathematical ability two years later. In the study, three-and four-year-old children were shown a book that contained only pictures and were asked to tell the story to a puppet. Their abilities were measured in a variety of ways. Two years later, the children were given a number of tests of academic achievement, including a test of mathematical achievement. It was found was that those children who scored highly on the mathematics test had also scored highly on certain measures of their storytelling ability two years earlier. "Most strongly predictive of children's mathematical performance was their ability to relate all the different events in the story, to shift clearly from the actions of one character to another, and to adopt the perspective of different characters and talk about what they were feeling or thinking." This study suggests that building strong storytelling skills early in the preschool years may be helpful in preparing children for learning mathematics when they enter school.

O’Neill, D.K. et al. 2004. Preschool children's narratives and performance on the Peabody Individualized Achievement Test - Revised: Evidence of a relation between early narrative and later mathematical ability. First Language, 24 (2), 149-184.

http://www.eurekalert.org/pub_releases/2004-07/nsae-url072904.php

Factors impairing math ability

Gender gap in math is culture-based

Data from the Trends in International Mathematics and Science Study and the Programme for International Student Assessment, representing 493,495 students ages 14-16 from 69 countries, have revealed only very small gender differences overall, but marked variation when nations are compared. For example, there are more girls in the top tier in countries such as Iceland, Thailand, and the United Kingdom–and even in certain U.S. populations, such as Asian-Americans. However, despite overall similarities in math skills, boys felt significantly more confident in their abilities than girls did and were more motivated to do well. Furthermore, although some studies have found more males than females scoring above the 95th or 99th percentile, this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Greater male variability with respect to mathematics, where it exists, correlates with several measures of gender inequality.

Hyde, J. S., & Mertz, J. E. (2009). Gender, culture, and mathematics performance. Proceedings of the National Academy of Sciences, 106(22), 8801-8807.

Else-Quest, N.M., Hyde, J.S. & Linn, M.C. 2010. Cross-national patterns of gender differences in mathematics: A meta-analysis. Psychological Bulletin, 136(1), 103-127.

http://spectrum.ieee.org/at-work/education/math-quiz-why-do-men-predominate 
http://www.physorg.com/news181915640.html

Iron deficiency may affect maths achievement in children and teens

A U.S. national study of 5,398 children aged 6 to 16 found iron deficiency in 3% of the children overall, and 8.7% of girls aged 12 to 16 (7% without anemia). Average math scores for iron-deficient children with or without anemia were about six points lower than those with normal iron levels. Among adolescent girls, the difference in scores was more than eight points. Previous research has linked iron-deficiency anemia with lower developmental test scores in young children, but there is less information on older children and on iron deficiency without anemia. It is suggested that this finding may help explain why the female superiority in maths at younger ages reverses itself in adolescence.

Halterman, J.S., Kaczorowski, J.M., Aligne, C.A., Auinger, P. & Szilagyi, P.G. 2001. Iron Deficiency and Cognitive Achievement Among School-Aged Children and Adolescents in the United States. Pediatrics, 107 (6), 1381-1386.

Math Anxiety

Positive stereotypes can offset negative stereotype effect

A number of studies have now shown that negative stereotypes can impair cognitive performance, mainly through adding to working memory load. A new study has now shown that this effect can be mitigated by the activation of a positive stereotype. The research takes advantage of the fact that we all belong to several social groups. In this case, the relevant groups were ‘female’ and ‘college student’. As usual, when (subtly) reminded of negative stereotypes for women and math, women performed worse. The interesting thing was that this didn’t happen if women were also made aware that college students performed better at math than non-college students. Moreover, this was reflected in working memory capacity. It seems that, when both a positive and a negative stereotype are offered, people will tend to choose the positive stereotype, and the effects of this will cancel out the negative stereotype. It’s also worth noting how easily these stereotypes are activated: effects could be manipulated simply by subtly changing demographic questions asked before the test (and it is not uncommon that test-takers are first required to answer some demographic questions).

Rydell, R.J., McConnell, A.R. & Beilock, S.L. 2009. Multiple social identities and stereotype threat: Imbalance, accessibility, and working memory. Journal of Personality and Social Psychology, 96(5), 949-966.

http://www.eurekalert.org/pub_releases/2009-05/iu-pob050109.php

Stereotype-induced math anxiety robs women's working memory

Another study finds evidence that being told men are better at mathematics undermines women's math performance, and extends it by demonstrating that the anxiety induced by the stereotype mainly reduced the verbal part of working memory, and that this carried over to subsequent (non-math-related) tasks. The accuracy of women exposed to the stereotype was reduced from nearly 90% in a pretest to about 80% after being told men do better in mathematics.

Beilock, S.L., Rydell, R.J. & McConnell, A.R. 2007. Stereotype threat and working memory: Mechanisms, alleviation, and spillover. Journal of Experimental Psychology: General, 136(2), 256-276.

http://www.physorg.com/news99239898.html
http://www.eurekalert.org/pub_releases/2007-05/uoc-sma052107.php

Implicit stereotypes and gender identification may affect female math performance

Relatedly, another study has come out showing that women enrolled in an introductory calculus course who possessed strong implicit gender stereotypes, (for example, automatically associating "male" more than "female" with math ability and math professions) and were likely to identify themselves as feminine, performed worse relative to their female counterparts who did not possess such stereotypes and who were less likely to identify with traditionally female characteristics. Strikingly, a majority of the women participating in the study explicitly expressed disagreement with the idea that men have superior math ability, suggesting that even when consciously disavowing stereotypes, female math students are still susceptible to negative perceptions of their ability.

Kiefer, A.K., & Sekaquaptewa, D. 2007. Implicit stereotypes, gender identification, and math performance: a prospective study of female math students. Psychological Science, 18(1), 13-18.

http://www.eurekalert.org/pub_releases/2007-01/afps-isa012407.php

Women's math performance affected by theories on sex differences

In a salutary reminder to all researchers into gender and race differences, researchers found that women who received a genetic explanation for female underachievement in math or were reminded of the stereotype about female math underachievement, performed more poorly on math tests than those who received an experiential explanation (such as math teachers treating boys preferentially during the first years of math education) or were led to believe there are no sex differences in math.

Dar-Nimrod, I. & Heine, S.J. 2006. Exposure to Scientific Theories Affects Women's Math Performance. Science, 314 (5798), 435.

http://www.eurekalert.org/pub_releases/2006-10/uobc-wmp101306.php

Anxiety over maths blocks learning

The so-called "maths block" is notorious - why do we have such a term? Do we talk about a "geography block", or a "physics block"? But we do talk of a reading block. Perhaps the reason for both is the same.
The amount of information you can work with at one time has clear limits, defined by your working memory capacity. When we are anxious, part of our working memory is taken up with our awareness of these fears and worries, leaving less capacity available for processing (which is why students who are very anxious during exams usually perform well below their capabilities). Processes such as reading and working with numbers are very sensitive to working memory capacity because they place such demands on it.
A recently reported study by Mark H. Ashcraft and Elizabeth P. Kirk, both psychologists at Cleveland (Ohio) State University, provides the first solid evidence that, indeed, math-anxious people have working memory problems as they do maths.

Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224–237. doi:10.1037/0096-3445.130.2.224

Neural substrate of mathematics

Where math takes place normally and in children with fetal alcohol spectrum disorder

An imaging study involving 21 children with fetal alcohol spectrum disorder confirms the importance of the left parietal area for mathematical tasks. Children with FASD are particularly impaired in mathematical ability. Brain activity patterns also revealed that the involvement of regions in the left cerebellum and the brainstem in math processing may be specific to children with FASD.

Lebel, C., Rasmussen, C., Wyper, K., Andrew, G., & Beaulieu, C. (2009). Brain Microstructure Is Related to Math Ability in Children With Fetal Alcohol Spectrum Disorder. Alcoholism: Clinical and Experimental Research, 9999(9999). doi: 10.1111/j.1530-0277.2009.01097.x.

http://www.eurekalert.org/pub_releases/2009-11/ace-ema111209.php

Are language and math processed separately by the brain?

Challenging the view that mathematics and language use common cognitive resources, a recent study provides support for the view that the functions of math and language are separate in the human brain. The study involved three men with severe agrammatic aphasia, which means they're unable to understand or form sentences due to brain damage. They didn't understand a reversible sentence - for example, the difference between 'John kissed Kate' and 'Kate kissed John', but they were able to understand that 5 - 2 is different from 2 – 5 (but not when it was expressed in words: two minus five). The researcher takes the results as a demonstration that we can have cognition without language, however, because the men were all normal until they sustained brain damage, it doesn’t answer the question of whether sophisticated cognition could arise without language.

Varley, R.A., Klessinger, N.J.C., Romanowski, C.A.J. & Siegal, M. 2005. Agrammatic but numerate. Proceedings of the National Academy of Sciences, 102 (9), 3519-3524.

http://education.guardian.co.uk/egweekly/story/0,,1427167,00.html
http://news.bbc.co.uk/1/hi/sci/tech/4265763.stm
http://www.nature.com/news/2005/050214/full/050214-3.html

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More evidence of the value of gesture in teaching math

A new study claims to provide ‘some of the strongest evidence yet’ for the benefits of gesturing to help students learn.

The study involved 184 children aged 7-10, of whom half were shown videos of an instructor teaching math problems using only speech, while the rest were shown videos of the instructor teaching the same problems using both speech and gestures. The problem involved mathematical equivalence (i.e., 4+5+7=__+7), which is known to be critical to later algebraic learning.

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Math skill in 1st grade linked to jobs, wages

A study involving 180 13-year-olds who had been assessed every year since kindergarten has found that their understanding of the number system in first grade predicted functional numeracy more than six years later, but skill at using counting procedures to solve arithmetic problems did not. Researchers controlled for intelligence,

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Math anxiety starts before school, impacts math achievement

"The general consensus is that math anxiety doesn't affect children much before fourth grade.” New research contests that.

Study 1: found many first grade students do experience negative feelings and worry related to math. This math anxiety negatively affects their math performance when it comes to solving math problems in standard arithmetic notation.

Study 2: found that second grade math anxiety affected second grade computations and math applications. Additionally, children with higher levels of math anxiety in second grade learned less math in third grade.

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Development of mathematics in children — a round-up of recent news

August, 2012
  • Fifth grade students' understanding of fractions and division predicted high school students' knowledge of algebra and overall math achievement.
  • School entrants’ spatial skills predicted later number sense and estimation skills.
  • Gender differences in math performance may rest in part on differences in retrieval practice.
  • ‘Math’ training for infants may be futile, given new findings that they’re unable to integrate two mechanisms for number estimation.

Grasp of fractions and long division predicts later math success

One possible approach to improving mathematics achievement comes from a recent study finding that fifth graders' understanding of fractions and division predicted high school students' knowledge of algebra and overall math achievement, even after statistically controlling for parents' education and income and for the children's own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication.

The study compared two nationally representative data sets, one from the U.S. and one from the United Kingdom. The U.S. set included 599 children who were tested in 1997 as 10-12 year-olds and again in 2002 as 15-17-year-olds. The set from the U.K. included 3,677 children who were tested in 1980 as 10-year-olds and in 1986 as 16-year-olds.

You can watch a short video of Siegler discussing the study and its implications at http://youtu.be/7YSj0mmjwBM.

Spatial skills improve children’s number sense

More support for the idea that honing spatial skills leads to better mathematical ability comes from a new children’s study.

The study found that first- and second-graders with the strongest spatial skills at the beginning of the school year showed the most improvement in their number line sense over the course of the year. Similarly, in a second experiment, not only were those children with better spatial skills at 5 ½ better on a number-line test at age 6, but this number line knowledge predicted performance on a math estimation task at age 8.

Hasty answers may make boys better at math

A study following 311 children from first to sixth grade has revealed gender differences in their approach to math problems. The study used single-digit addition problems, and focused on the strategy of directly retrieving the answer from long-term memory.

Accurate retrieval in first grade was associated with working memory capacity and intelligence, and predicted a preference for direct retrieval in second grade. However, at later grades the relation reversed, such that preference in one grade predicted accuracy and speed in the next grade.

Unlike girls, boys consistently preferred to use direct retrieval, favoring speed over accuracy. In the first and second grades, this was seen in boys giving more answers in total, and more wrong answers. Girls, on the other hand, were right more often, but responded less often and more slowly. By sixth grade, however, the boys’ practice was paying off, and they were both answering more problems and getting more correct.

In other words, while ability was a factor in early skilled retrieval, the feedback loop of practice and skill leads to practice eventually being more important than ability — and the relative degrees of practice may underlie some of the gender differences in math performance.

The findings also add weight to the view being increasingly expressed, that mistakes are valuable and educational approaches that try to avoid mistakes (e.g., errorless learning) should be dropped.

Infants can’t compare big and small groups

Our brains process large and small numbers of objects using two different mechanisms, seen in the ability to estimate numbers of items at a glance and the ability to visually track small sets of objects. A new study indicates that at age one, infants can’t yet integrate those two processes. Accordingly, while they can choose the larger of two sets of items when both sets are larger or smaller than four, they can’t distinguish between a large (above four) and small (below four) set.

In the study, infants consistently chose two food items over one and eight items over four, but chose randomly when asked to compare two versus four and two versus eight.

The researchers suggest that educational programs that claim to give children an advantage by teaching them arithmetic at an early age are unlikely to be effective for this reason.

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Gender differences in effects of anxiety on performance

July, 2012

Two studies indicate that, while anxiety is present in both sexes, it only impairs performance in females.

A British study looking at possible gender differences in the effects of math anxiety involved 433 secondary school children (11-16 years old) completing customized (year appropriate) mental mathematics tests as well as questionnaires designed to assess math anxiety and (separately) test anxiety. These sources of anxiety are often confounded in research studies (and in real life!), and while they are indeed related, reported correlations are moderate, ranging from .30 to .50.

Previous research has been inconsistent as regards gender differences in math anxiety. While many studies have found significantly greater levels of math anxiety in females, many studies have found no difference, and some have even found higher levels in males. These inconsistencies may stem from differences in how math anxiety is defined or measured.

The present study looked at a rather more subtle question: does the connection between math anxiety and math performance differ by gender? Again, previous research has produced inconsistent findings.

Findings in this study were very clear: while there was no difference between boys and girls in math performance, there were marked differences in both math and test anxiety. Girls showed significantly greater levels of both. Both boys and girls showed a positive correlation between math anxiety and test anxiety, and a negative correlation between math anxiety and math performance, and test anxiety and performance. However, these relationships between anxiety and performance were stronger for girls than boys, with the correlation between test anxiety and performance being only marginally significant for boys (p<0.07), and the correlation between math anxiety and performance disappearing once test anxiety was controlled for.

In other words, greater math anxiety was linked to poorer math performance, but it was significant only for girls. Moreover, anxiety experienced by boys may simply reflect test anxiety, rather than specific math anxiety.

It is worth emphasizing that there was no gender difference in performance — that is, despite laboring under the burden of greater levels of anxiety, the girls did just as well as boys. This suggests that girls might do better than boys if they were free of anxiety. It is possible, however, that levels of anxiety didn’t actually differ between boys and girls — that the apparent difference stems from girls feeling more free to express their anxiety.

However, the finding that anxiety is greater in girls than boys is in line with evidence that anxiety (and worry in particular) is twice as prevalent in women as men, and more support for the idea that the girls are under-performing because of their anxiety comes from another recent study.

In this study, 149 college students performed a relatively simple task while their brain activity was measured. Specifically, they had to identify the middle letter in a series of five-letter groups. Sometimes the middle letter was the same as the other four ("FFFFF") while sometimes it was different ("EEFEE"). Afterward the students completed questionnaires about their anxiety and how much they worry (Penn State Worry Questionnaire and the Anxious Arousal subscale of the Mood and Anxiety Symptom Questionnaire).

Anxiety scores were significantly negatively correlated with accuracy on the task; worry scores were unrelated to performance.

Only girls who identified themselves as particularly anxious or big worriers recorded high brain activity when they made mistakes during the task (reflecting greater performance-monitoring). Although these women performed about the same as others on simple portions of the task, their brains had to work harder at it. Then, as the test became more difficult, the anxious females performed worse, suggesting worrying got in the way of completing the task.

Greater performance monitoring was not evident among anxious men.

[A reminder: these are group differences, and don't mean that all men or all women react in these ways.]

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