mathematics

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. The Polgar sisters are a well-known example of “hot-housing”. I cited them in my 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

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.