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 schools, that have a track record. If these and similar efforts find traction in schools, experts say, they could transform teaching from the bottom up  giving the ancient craft a modern scientific compass.

Beyond Counting

In a typical preschool class, children do very little math. They may practice counting, and occasionally look at books about numbers, but that is about it. 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.

“They decide they’re no good at math  ‘I’m not a math person,’ they say  and pretty soon the school agrees, the parents agree,” Dr. Clements said.

“Everyone agrees.”

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). Teachers can tailor the Building Block lesson to a student’s individual ability.

On a recent Wednesday afternoon at the Makowski center, Buffalo’s Public School 99, Pat Andzel asked her preschool class a question:

“How many did you count?”

She had drilled them on the number seven. She held up a sign with “7” and asked her students what number they saw (“seven!”); had the group jump seven times, counting; then had them touch their nose seven times. As the class finished counting seven objects on a poster, she asked again:

“How many?”

“I never used to ask that,” Ms. Andzel said in an interview after the lesson. She asks it all the time now, she said, because it drives home a subtle but crucial idea: that the last number they said in counting is the quantity; it is the answer.