Why Do Males Continue to be Superior at Math?

Despite shoddy pseudo-scholarly attempts by feminist ideologues to disprove the obvious statistical sex differences in math reasoning and advanced math ability, males continue to be over-represented in fields requiring advanced mathematical abilities.

Proportion Female in Various Fields _HBD Chick _via_ Complexity Simplified

So, why are males superior at math? Let's be more specific, since the reality is a bit mixed:

In late elementary school, females outperform males on several verbal skills tasks: verbal reasoning, verbal fluency, comprehension, and understanding logical relations (Hedges & Nowell, 1995). Males, on the other hand, outperform females on spatial skills tasks such as mental rotation, spatial perception, and spatial visualization (Voyer, Voyer, & Bryden, 1995). Males also perform better on mathematical achievement tests than females. However, gender differences do not apply to all aspects of mathematical skill. Males and females do equally well in basic math knowledge, and girls actually have better computational [arithmetic _ ed.] skills. Performance in mathematical reasoning and geometry shows the greatest difference (Fennema, Sowder, & Carpenter, 1999). _Education

In fact, recent research shows that males begin to take a qualitatively different approach to math thinking from an early age:

In a University of Missouri study, girls and boys started grade school with different approaches to solving arithmetic problems, with girls favoring a slow and accurate approach and boys a faster but more error prone approach. Girls’ approach gave them an early advantage, but by the end of sixth grade boys had surpassed the girls....

“Developing mathematical skill may be part ‘practice makes perfect’ and part ‘perfect makes practice,’” Bailey said. “Attempting more answers from memory gives risk-takers more practice, which may eventually lead to improvements in accuracy. It also is possible that children who are skilled at certain strategies are more likely to use them and therefore acquire more practice.” _MU News

The greater boldness exhibited by boys in math class is likely a testosterone effect, which is exhibited in so many other behavioural differences between males and females in childhood, adolescence, and early to middle adulthood.

The male superiority in spacial skills tasks and advanced math reasoning is likely to derive from far more subtle changes in the brain than those that lead to greater male boldness. But those more subtle changes are also largely due to testosterone effect.

These brain changes occur over time -- slowly in childhood, and at a faster rate in adolescence. All levels of brain activity -- from gene expression to physiological parameters to brain structure to cognitive function -- are involved.

Recent feminist-inspired studies which compare male : female math skills in childhood or very early in adolescence are unable to detect the most significant brain transformations, and are thus likely to fail to detect very real differences. Likewise, studies which focus upon comparisons of basic arithmetic skills, fail to detect the male advantages in spatial skills and in advanced mathematical reasoning.

Fortunately, better tools for detecting brain activity and differences at all levels -- from gene expression to fine brain structure to the neurological correlates of cognition -- are all in development.

A fascinating new brain imager which combines MEG (magnetoencephalography) with MRI (magnetic resonance imaging) will allow an unprecedented degree of simultaneous spatial and temporal imaging of brain structure and activity.

Functional brain imaging has already developed to the point where it can be used as an objective, culture-free test for cognitive function and speed. It is only a matter of time before such crude objective measures of cognition can be fine-tuned to look at distinct types of cognition, including mathematical and spatial reasoning.

When it comes to brain, cognition, and behaviour, hormones have consequences. The sooner human academics can grow beyond their political correctness to look at these issues objectively and honestly, the sooner we can find ways for all of us to move ahead.

More from La Griffe du Lion

More on math sex gap at secondary level (PDF)

Lubos Motl provides colour commentary on the La Griffe du Lion article linked above, paying particular attention to cross-cultural views of the math sex gap.

Inborn Number Sense and Math Skills, Genes for IQ?

12 August 2011: More findings on genes and IQ

...the study -- published online in a recent issue of Developmental Science -- indicates that math ability in preschool children is strongly linked to their inborn and primitive "number sense," called an "Approximate Number System" or ANS. _SD

Johns Hopkins psychologists have found a connection between a child's innate "number sense" and his ability to master math skills. The "number sense" was tested using a computer screen of flashing blue and yellow dots, similar to the image below. Children had to tell the researchers whether there were more blue or yellow dots, for a number of different dot combinations.

Panamath: More Yellow or Blue Dots?

Some comparisons were easy (like comparing five yellow versus 10 blue dots). Others were much harder (like comparing five yellow versus six blue dots). Children were informed of right or wrong answers via a high- or low-pitched beep. (You can take a test similar to the one administered to the children online here: http://www.panamath.org/testyourself.php )


The children also were given a standardized test of early mathematics ability that measures numbering skills (verbally counting items on a page), number-comparison (determining which of two spoken number words is greater or lesser), numeral literacy (reading Arabic numbers), mastery 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.) This standardized test is often given to children between the ages of 3 and 8 years.


...According to the researchers, this means that inborn numerical estimation abilities are linked to achievement (or lack thereof) in school mathematics.


"Previous studies testing older children left open the possibility that differences in instructional experience is what caused the difference in their number sense; in other words, that some children tested in middle or high school looked like they had better number sense simply because they had had better math instruction," Libertus said. "Unlike those studies, this one shows that the link between 'number sense' and math ability is already present before the beginning of formal math instruction."


Still in question, of course, is the root cause of the link between number sense and math ability. _SD

These findings share some similarities with those of a recent U. of Missouri study, highlighted in an earlier Al Fin posting. Innate number sense would represent one of the "confounders" which Al Fin warned the U. Missouri researchers about.

Abstract for Johns Hopkins study discussed above

The controversy over whether human intelligence can be partially inherited, or whether cognitive ability is purely an environmental trait, rages behind the scenes in universities around the world. Academics who have been indoctrinated into pure egalitarian philosophies often balk at the idea that much of human cognitive aptitude is inherited. And yet the evidence continues to accumulate.

Not that it has been easy to find so-called "intelligence genes." Not at all. No one said it would be easy.

Scientists who hunt for "intelligence genes" used to think there were fewer than half a dozen of them.


In recent years, they determined there may be at least 1,000 - each with just a tiny effect on the differences in people's IQ. A study released Tuesday found new evidence that many genes play a role in intelligence, but scientists still couldn't pinpoint the specific genes involved.


...Previous work involving twins and adopted children has found that genes have a significant influence on differences in IQ scores, producing about half the difference between adults in general. The influence of genes on IQ appears to grow from childhood to adulthood.


Scientists have come to realize that, as with height, differences in intelligence come not from a few genes, but rather the overall effect of many genes, each with only tiny influence. That makes them hard to tease out.


The new DNA study, reported online Tuesday in the journal Molecular Psychiatry, came to similar conclusions. Many genes work together to shape intelligence much like the different instruments of an orchestra that play in sync. Unless there's a soloist playing, it's often difficult to decipher the contributions of individual instruments.


...Researchers didn't ID any genes affecting IQ. But they estimated that they found a genetic influence that accounts for at least 40 percent to 50 percent of the differences on intelligence test scores in the 3,511 unrelated adults in their study who were tested on knowledge and problem-solving skills.


They focused on more than 500,000 places in the participants' DNA, looking for evidence that IQ-influencing genes lay close to those places. They concluded that the overall effect was coming from many scattered genetic differences, each of only small influence.


The latest work adds to evidence that even the most powerful of these has only weak influence. Deary said that future studies will probably need to involve millions of people to detect the genetic effects.


Robert Plomin of the Institute of Psychiatry in London, who's looked for intelligence-related genes for 15 years but didn't participate in the new study, isn't surprised by the latest findings.


"We've got a century of twin and adoption studies," such as those comparing twins reared in different families, that support the notion that about half of IQ differences come from DNA, he said.


...Turkheimer, the Virginia psychologist [author of above study], thinks other types of research such as brain scans might have better luck in understanding what intelligence is.


Those methods are better than "pinning your hopes on adding together a bunch" of small effects from individual genes, he said. _Physorg

Turkheimer certainly has a good point, suggesting that brain scans may offer a faster method for objectively measuring intelligence and cognitive aptitude, as compared to genetic studies. But in reality, all approaches must be taken, in order to fill in as many gaps in our knowledge about human intelligence as possible.

Only the most foolhardy and die-hard of HBD deniers can fail to acknowledge the powerful effect which genes play on the variability of human cognitive skills displayed statistically by different human populations. And yet in a modern academic milieu of egalitarian multiculturalist political correctness, there are plenty of die-hard HBD deniers around at all levels of academia and its human and pseudo-intellectual effluence.

When Is a Child's Brain Ready for Maths?

The newest study examined 90 children recruited from a variety of schools. Half had just completed second grade; the other half had just completed third grade. All children had normal intelligence and had math reasoning scores between the 25th and 98th percentile. On average, the third-graders were one year older than the second-graders and had significantly better math-reasoning skills.

...The scientists found that children in third grade showed much more differentiated brain responses between complex and simple problems. They found significant change in the responses of two key regions of the brain to the different types of addition problems.Greater responses to complex addition problems were seen in third-graders’ brains in both the dorsolateral prefrontal cortex, a brain area responsible for manipulating information in working memory, and in the intraparietal sulcus, a posterior brain region essential for representing numerical quantity. _Vinod Menon et al described in Physorg

MyNextBrain_Taken from Brain Age PDF
It appears that significant changes in brain function occur in children sometime between grades 2 and 3, measured by fMRI. At least some of these changes in brain activity appear to allow more sophisticated maths reasoning in children.

Compared to 2nd graders, 3rd graders showed greater activity in dorsal stream parietal areas right SPL, IPS and angular gyrus (AG) as well as ventral visual stream areas bilateral lingual gyrus (LG), right lateral occipital cortex (LOC) and right parahippocampal gyrus (PHG). Significant differences were also observed in the prefrontal cortex (PFC), with 3rd graders showing greater activation in left dorsal lateral PFC (dlPFC) and greater deactivation in the ventral medial PFC (vmPFC). Third graders also showed greater functional connectivity between the left dlPFC and multiple posterior brain areas, with larger differences in dorsal stream parietal areas SPL and AG, compared to ventral stream visual areas LG, LOC and PHG. No such between-grade differences were observed in functional connectivity between the vmPFC and posterior brain regions. These results suggest that even the narrow one-year interval spanning grades 2 and 3 is characterized by significant arithmetic task-related changes in brain response and connectivity, and argue that pooling data across wide age ranges and grades can miss important neurodevelopmental changes. _Abstract Menon et al via ScienceDirect

It is likely that another similar maths-facilitating change occurs during puberty, at least partially triggered by testosterone surge. Understanding these age specific developmental brain changes is critical to the study of group differences and the efficacy of interventions in maths learning.

Abstract from an earlier collaboration between David Geary and Vinod Menon dealing with counting and retrieval strategies in early maths learning.

Modern high tech societies are based upon technologies which require sophisticated maths skills. Various commercial methods from maths learning have been developed in an attempt to assure a plentiful supply of talent for engineering and science training programs of the future. Most of these programs fail to compensate for the huge weaknesses of the government educational system as a whole, which limits their usefulness.

Music learning is another activity which displays a developmental learning window in childhood, at least for highly proficient musical skills and abilities. Not coincidentally, musical skills and math skills overlap significantly. This interesting study looks at brain networks in music, and how they come into play during everyday "segmentation of the neural stream." In other words, good and timely early childhood training in language, maths, music -- and probably many other skills not properly delineated -- can make a crucial difference in the skillful execution of ordinary moment to moment thinking processes.

This page links to a sophisticated analysis (PDF Thesis Download 6MB) of fMRI analysis of mental patterns from a whole-brain spatio-temporal perspective. Only for those most curious.

Modern educators and neuroscientists do not actually understand how children learn, nor do they know the best ways of assisting children in the crucial learning processes. In fact, modern educational practises are so infused with politicised dogma and indoctrination, that a mainstream education is apt to do as much harm as good in the average student.

If you are the parent of a young or adolescent child, DO NOT LEAVE your child's education up to the system. To you, your child is your life. To the system, your child is a statistic, prone to currents of political favouritism and neglect.

Computer Assisted Tutoring Especially Helpful for Maths?

A new Carnegie Mellon University and Worcester Polytechnic Institute study indicates that grammar school students who receive mathematics tutoring assistance from computer programs score higher in year-to-year achievement, than their untutored cohorts.

Year-end test scores of Massachusetts middle school students whose teachers used a Web-based tutoring platform called ASSISTments as a central part of their mathematics instruction were significantly better than those of students whose teachers did not use the platform, according to a recent study published in the Journal of Educational Computing Research. Conducted by Neil T. Heffernan, PhD, of Worcester Polytechnic Institute (WPI), and Kenneth R. Koedinger, PhD, and Elizabeth A. McLaughlin, both of Carnegie Mellon University, the study examined data collected from 1,240 seventh grade students in four schools in an urban Massachusetts school district.

The study (http://tinyurl.com/34j4ylj) compared students’ seventh-grade year-end test scores to their comparable scores at the end of sixth grade. Students at three schools where ASSISTments was used were shown to significantly outperform their peers at the fourth school, where it was not used. The improvement in test scores was pronounced for all students in the schools where ASSISTments was used... _ScienceBlog

One up and coming online approach to math tutoring for children is "Mathletics."

Mathletics portends of the education system that is to come. Beyond its strong approach to pushing students to love math, it is also digitally equipped in ways that give it a clear edge over previous programs. Students can login anytime 24/7, from any internet-capable computer, and continue their lessons. Not quite as good as having a teacher available at all hours of the day, but still pretty good. The reward system takes a note from many popular video games on the market, allowing students to build virtual avatars they can customize by earning more points. There’s also intelligent response from the system – Mathletics adapts to students during exercises, adjusting difficulty to match progress so far. Students can track their personal progress and, when ready, compete against their peers on a global scale. That gives each mathlete the feeling that they are part of something bigger, a sense of belonging that could transform math from a fun challenge to a purposeful part of their lives. _SingularityInstitute

One of the reasons why web-based programs may be particularly suitable for mathematics tutoring, is the personalised nature of mathematical "understanding." The Eureka! or Aha! moment of comprehending a mathematical concept is less social and more personal. It is nice when such personal moments can be shared, but that is not necessarily how it happnes. Due to the uniqueness of each individual brain -- and the brain's historical experiences -- the moment of cohesive comprehension for one brain is not likely to occur at the same time as for another brain. Mathematics is both more logical and more emotional than many human endeavours. This makes it a more delicate subject to teach.

Personal tutoring almost always involves some level of interpersonal tension or pressure to perform. Sometimes a student says he understands a point, just to keep things moving. When it subsequently becomes clear that the student does not understand, interpersonal tensions can ratchet upwards. With computers, such tension is typically absent.

Most learning software is still abysmally primitive and uninformed -- in terms of how children and adolescents learn. As more people with a deep insight into learning psychology come together to create improved approaches to computer tutoring, better learning should take place in several new areas besides just maths.

Digits, Dots, and the Numeric Brain

French scientists at INSERM studied 10 human volunteers to determine how the human brain encodes number. Using fMRI, the scientists scanned the volunteers' brains while showing them either images of certain numbers of dots, or a numeric symbol representing the same number.

This experiment reveals that the brain codes number symbols and fundamental numerical quantities slightly differently, he adds.

Coauthor Evelyn Eger of the French research institute INSERM and her colleagues scanned the brains of 10 volunteers using fMRI while showing them collections of dots. Computer analyses revealed that viewing different quantities of dots led to distinct brain activity patterns. Then the team showed the volunteers either collections of dots or digits of the same value. Analyses revealed slightly different brain activation patterns for digits and dots of the same numerical value, Eger says.

In both cases, activity was primarily in the parietal cortex. And the analyses used to evaluate the patterns revealed there was some overlap. A volunteer’s brain activation signature from viewing numbers could predict how many dots a subject had viewed, but not the other way around.

The researchers also found that the brain patterns shifted gradually with increasing numbers of dots, suggesting that numbers that are close in value activate patches of neurons that are close to each other in the brain. Digits, on the other hand, did not create this pattern of change in brain activity as numbers increased. _ScienceNews

It is interesting that early childhood math training at the Better Baby Institute in Philadelphia utilises large "flash cards" containing various numbers of dots.

Since the parietal lobe handles numbers of dots and equivalent numerical symbols differently, it is likely that other types of mental metaphor for number and quantity would likewise reveal distinctions in the neural correlates via scans. Very interesting research.

Khhaaann!!! No, Not that Khan! Khan Academy -- An Amazing Place for At-Home Learning at Any Age Anywhere on Earth

Khan Academy is a free online library of over 700 learning videos that make learning easy. This marvelous intutive-learning website is a labour of love from Salman Khan, investment professional and holder of multiple advanced degrees from Harvard and MIT.

Perfect for the homeschool student who is studying for the SAT, for the budding young engineer or scientist, or for anyone wanting to get better at math, physics, management, finance, banking, probability, pre-engineering etc. Example: have you been curious about Singapore Math? Khan Academy offers a series of videos to give you a good idea of what the program is all about.

Every homeschool parent should be aware of Khan Academy, as should anyone studying for the SAT or GMAT, or anyone who needs a better understanding of math, physics, probability or finance.

"Number Sense": As Common as Common Sense?

A simple test administered to children via computer graphic may be a better predictor of his subsequent performance in mathematics than his SAT. The Johns Hopkins University researchers who devised the test believe that most mammals also have an inherent "number sense" that allows them to estimate relative numbers in groups. It is a matter of degree, for humans, as to whose number sense will allow them to excel in mathematics.

Good "number sense" at age 14 correlates with higher scores on standardized math tests throughout a child's life up to that point and weaker "number sense" at 14 predicts lower scores on those standardized tests, said Justin Halberda, assistant professor of psychological and brain sciences in the university's Krieger School of Arts and Sciences.

"We discovered that a child's ability to quickly estimate how many things are in a group significantly correlates with that child's performance in school math for every single year, reaching all the way back to when he or she was in kindergarten..."

..."What this seems to mean is that the very basic number sense that we humans share with animals is related to the formal mathematics that we learn in school," Halberda concludes. "The number sense we share with the animals and the formal math we learn in school may interact and inform each other throughout our lives."
_SD

The researchers ad the obligatory PC disclaimer that "nothing in this research suggests that math ability is innate or genetic." As if at this stage in understanding of human biodiversity there is still anyone with an IQ above 100 who still believes in "The Blank Slate" hypothesis.

What is obvious is that it is possible to devise fairly simple tests to distinguish between children with higher and lower aptitudes at various cognitive skills. The fact that these tests have high predictive power for the future of the respective children, is something that should not be ignored, covered up, or euphemised.