Children need to grasp basic maths concepts in preschool to be proficient in later life
Educators say the way to balance the equation between more mathematically minded Asian students and their less numerate counterparts in the West is to start early
Asian students are well known for their superior performance in maths compared to their counterparts in the West. Some attribute it to cultural factors. To American cognitive development psychologist, David Geary, the difference can be avoided.
The Thomas Jefferson professor of psychology and interdisciplinary neuroscience at the University of Missouri chairs the learning processes task group under the US National Mathematics Advisory Panel.
In a 10-year longitudinal study on children's mathematical development from kindergarten to seventh grade, he found that instruction at preschool level made all the difference.
"What we found was the kids who did not have a good foundation of numbers, numerals and relations among them in the beginning of first grade were on a trajectory that will put them in trouble by adolescence," he says.
At a recent talk entitled "Early Predictors of Mathematics Achievement" at Chinese University, as the distinguished visiting scholar at the university's United College, he explained the findings of his survey of almost 300 children.
Its identification of the school-entry number knowledge needed for mathematical competencies in adolescence won him a "method to extend research in time" (Merit) award from the National Institutes of Health.
It is vital that children acquire what he calls "cardinal knowledge" - an understanding of the meaning of number words; for example, one, two, three, and Arabic numerals, and being able to associate the quantities represented by them.
Such insight is unique to humans. After thousands of trials, chimpanzees can learn to associate, for example, the Arabic numeral one with a single object. But they never have the insight of a three-year-old that one plus four equals five.
An implicit understanding of the quantities represented by numbers forms part of the basis for an ability to tackle mathematical challenges such as algebra in later school years.
A weak foundation, says Geary, contributes to low numeracy among children with the result that they will have trouble passing the qualifiying tests for reasonable blue-collar jobs, or maintaining employment in those jobs, even if their reading skills are good.
In the US, he adds, 20 to 25 per cent of the children have problems with maths. When they graduate, their maths skills will not be good enough to meet the requirements of a lot of blue-collar jobs. "I am certain the problem in Hong Kong is much lower," says Geary.
He blames it on the broad curriculum in the US. "They try to cover everything, which means each thing is only covered a little bit. Most kids will forget, or not master any of it."
"One of the things we are trying to do is to narrow it down to the core quantitative skills that kids need to know. This will set them on a trajectory to be successful in primary school."
Remedial lessons may not necessarily bring about marked improvements. "You will be lost in algebra, even if you remediate your fraction skills. The algebra curriculum has moved forward and you will always be lower in grade."
He believes Asian and Western children stand an equal chance of doing well in maths. As part of a study he did on US and Chinese students in the 1990s, comparing them from kindergarten to old age in a variety of arithmetic work, he found there was no difference in maths skills between US school graduates in the 1930s and 1940s - when US maths education was at its best - and Chinese adults.
"When you looked at the cross-generational changes you see an improvement in China and a decline in the US in terms of the maths skills."
In the Programme for International Student Assessment (Pisa) results announced last December, Hong Kong came third globally in maths, after Singapore and Shanghai, which topped the rankings for 15-year-olds in reading, maths and science.
Maths teaching in China today is far more organised than it is in the US, says Geary. The more lax culture in education in the US, where teachers are not expected to assert authority, also disadvantages schoolchildren, especially when it comes to learning maths.
"The Chinese system is very good in teaching, for example, standard algorithms, having kids practice them enough so they are fluent at it. They don't have to think about it, and they can do it very quickly," he says.
"Many American teachers and maths professors think if you give kids that much practice, it will destroy their inherent interest in the subject.
"The problem is that most people don't have an inherent interest in maths. People are inherently interested in people but not algebra. But nevertheless, being good in algebra provides opportunities for success in the modern economy that you otherwise wouldn't normally have, doing IT, computer science, statistics and engineering," he adds.
Compared to Asia, US schoolchildren have a more relaxed, possibly happier, school life. But Geary warns it is also a trade-off between low pay, due to limited maths attainment, and an easy life.
"They are happy in school, but when they get out, 25 per cent of them are not employable in anything other than the very basic minimum wage skills, even if they can read reasonably well. It's a bad trade-off."
But with the heavy drilling, maths education could be overdone on the mainland, he warns: "It is another trade-off. It is good preparation for college entry mathematics, but not every kid is going to university. A student who is going into carpentry or mechanical work needs to have some maths, but not calculus."
At a seminar organised by Yew Chung Community College last week on early childhood education, an education psychology professor from the University of Oxford, Kathy Sylva, agreed with the importance of numeracy in preschool years.
Her own research in England shows that the quality of maths teaching in preschool has lasting effects on national tests at age 11. "It is more important to acquire a good foundation in maths knowledge and skills than to have remedial classes later in life," she says.
"But it is possible, with intensive one-to-one teaching, to improve a child's maths abilities later in primary school. It is very difficult to have remedial teaching in maths when the child is in secondary school because the young person has developed a low academic self concept by then."
Maths teaching should be fun, she adds.