By BENEDICT CAREY


FOR MUCH OF THE last century, educators and many scientists believed that children could not learn math at all before the age of five, that their brains simply were not ready.

But recent research has challenged that assumption - along with conventional wisdom about geometry, reading, language and self-control in class. The findings, mostly from a branch of research called cognitive neuroscience, are helping to clarify when young brains are able to grasp fundamental concepts.

In one recent study, for instance, researchers found that most entering preschoolers could perform rudimentary division, by distributing candies among two or three play animals. In another, scientists found that the brain’s ability to link letter combinations with sounds may not be fully developed until age 11 - much later than many have assumed.


Neuroscience is challenging assumptions about early education. Students in Buffalo, New York, get an introduction to math. / RYAN COLLERD FOR THE NEW YORK TIMES


The teaching of basic academic skills, until now largely the realm of tradition and guesswork, is giving way to approaches based on cognitive science. In several American cities, including Boston, Washington and Nashville, schools have been experimenting with new curriculums to improve math skills in preschoolers. In others, teachers have used techniques developed by brain scientists to help children overcome dyslexia.

And schools in about a dozen states have begun to use a program intended to accelerate the development of young students’ frontal lobes, improving selfcontrol in class.

“Teaching is an ancient craft, and yet we really have had no idea how it affected the developing brain,” said Kurt Fischer, director of the Mind, Brain and Education program at Harvard University. “Well, that is beginning to change, and for the first time we are seeing the fields of brain science and education work together.”





This relationship is new and still awkward, experts say, and there is more hyperbole than evidence surrounding many “brain-based” commercial products on the market. But there are others, like an early math program taught in Buffalo, New York, schools, that have a record of success. If these and similar efforts find supporters in the schools, experts say, they could transform teaching from the bottom up - giving the ancient craft a modern scientific compass.

In a typical preschool class, children do very little math. Many classes devote mere minutes a day to math instruction or no time at all, recent studies have found - far less than most children can handle, and not nearly enough to prepare those who, deprived of math-related games at home, quickly fall behind in kindergarten.

“Once that happens, it can be very hard to catch up,” said Julie Sarama, a researcher in the graduate school of education at the University at Buffalo who, with her colleague and husband, Doug Clements, a professor in the same department, developed a program called Building Blocks to enrich early math education.

In a Building Blocks classroom, numbers are in artwork, on computer games and in lessons, sharing equal time with letters. Like “Sesame Street,” Building Blocks has children play creative counting games; but it also focuses on other number skills, including cardinality (how many objects are in a set) and one-to-one correspondence (matching groups of objects, like cups and saucers).

On a recent afternoon at the Stanley M. Makowski Early Childhood Center at Buffalo’s Public School 99, the curriculum included a variety of mathbased lessons and activities, as well as software programs, all drawing on findings from cognitive science.

When it comes to understanding numbers, for example, recent research suggests that infants can distinguish one object from two, and two from three.

By preschool, the brain can handle larger numbers and is struggling to link three crucial concepts: physical quantities (seven marbles, seven centimeters) with abstract digit symbols (“7”), with the corresponding number words (“seven”).

Children begin recognizing geometric shapes as early as 18 months, studies find; by preschool, the brain can grasp informal geometric definitions.

It can when taught properly, that is.

In a study published last year, scientists at Carnegie Mellon University in Pittsburgh reported that playing what seems a simple childhood game, similar to Chutes and Ladders (sometimes called Snakes and Slides), accelerates the understanding of numbers for lowincome preschoolers.

A crude “number instinct” is hardwired into the anatomy of the brain, recent research has found. Mammals can quickly recognize differences in quantity, choosing the tree or bush with the most fruit. Human beings, even if they live in remote cultures with no formal math education, have a general grasp of quantities as well, anthropologists have found.

In a series of recent imaging studies, scientists have discovered that a sliver of the parietal cortex, on the surface of the brain about 2.5 centimeters above the ears, is particularly active when the brain judges quantity.

In this area, called the intraparietal sulcus, clusters of neurons are sensitive to the sight of specific quantities, research suggests. Some fire vigorously at the sight of five objects, for instance, less so at the sight of four or six, and not at all at two or nine. Others are most active in response to one, two, three, and so on.

When engaged in a lesson or exercise, these regions actively communicate with areas of the frontal lobe, where planning and critical thinking are centered.

“This is what we believe focused math education does: It sharpens the firing of these quantity neurons,” said Stanislas Dehaene, a cognitive neuroscientist at the College de France in Paris.

Students are taught to recognize patterns at an early childhood center in Buffalo, New York. / RYAN COLLERD FOR THE NEW YORK TIMES