Seattle children start school less prepared in math than in reading. Brain research says we underestimate how much math kids that age can do.

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On a recent morning in South Seattle, Kristin Alfonzo challenged her preschoolers to make the number 7 using beads strung across two rows of pipe cleaners.

One 5-year-old boy slid four beads across the top and three across the bottom. Another did the reverse, and one kid pushed all seven on one row.

“I see many different ways of making 7!” Alfonzo said over the ruckus of kids counting out loud.

Preschools typically leave math for grade school, in the belief that 4- and 5-year-olds aren’t old enough to understand what 7 stands for. Decades of brain science now show that waiting is a mistake.

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Even in the crib, research shows, infants can tell the difference between eight dots and 16 using an innate “number sense” we share with other species that helps us make some size comparisons without counting.

By the time they are preschool age, students like the ones in Alfonzo’s class can grasp simple addition — three beads plus four beads makes seven beads — even if they can’t yet write the equations.

They’re getting a strong start in math with games and playful activities that show all the ways they can use numbers and shapes to describe and measure differences and relationships between things.

Overall, 95 percent of the kindergartners at South Shore PreK-8 — a combination preschool and elementary school — arrive with the basic skills they’ll need for elementary-school math, the highest rate in the district and far above the state average, which stands at about 53 percent.

That figure is even more impressive given almost two-thirds of South Shore’s students live in low-income families, a group that, on average, tend to arrive behind rather than ahead.

Such success — at South Shore and a growing number of preschools across the nation — is fueling big changes in how math is taught to young children, which typically gets little class time and doesn’t go any deeper than basic counting and memorizing a few shapes.

The city of Seattle’s new subsidized preschool program, which voters approved last year, wants to boost math instruction in many more places, using an approach that’s similar to the one used at South Shore — and in Boston Public Schools, an urban district that has boosted third-grade math scores by improving how math is taught to 4-year-olds.

Such investments may reap gains in reading, too. A groundbreaking study in 2007, done by Northwestern University professor Greg Duncan and others, found that math skills in kindergarten predict third-grade test scores in both reading and math — a surprising result that scientists are still working to understand.

But it suggests that a good start in math is key because research also shows that kids who start out behind in the early grades don’t tend to catch up.

Boston and South Shore educators aren’t swapping play time for flashcard drills and work sheets, the fear of those who worry that preschool is becoming too focused on academics.

Instead, teachers infuse math into games such as “not my way” — which Alfonzo plays with her students after they’ve warmed up by making the number 7.

Alfonzo made the number 4 with her beads, but clutched the board close to her chest, challenging the class to guess how she did it. The kids groaned each time she checked a student’s board and said, “That’s a good way to make 4 … but it’s not my way.”

Then she called on the 5-year-old with the kitten-ears hair band.

“Rose, how did you do it?”

“I put two on the top and two on the bottom,” Rose said.

“She did it my way!” Alfonzo said.

Boston’s example

When the city of Boston launched its universal preschool program 10 years ago, educators searched for ways to teach young kids math in an age-appropriate, but rigorous way.

They understood that the Swiss psychologist Jean Piaget — a towering figure in early-childhood development in the 20th century — had mistakenly led educators to vastly underestimate what 4-year-olds can understand about numbers.

Based on his research, Piaget thought children under the age of 7 didn’t understand what numbers represented. In his experiments, for example, he found that children believed the number of objects in a row increased if those objects were spread out to make the row longer.

Researchers have since shown that children are not fooled if experimenters explain the problem in simpler language, and use objects kids care about — like M&M’s.

“Since Piaget’s days, the field has changed completely and people now recognize that children come to school with quite rich conceptions of number,” said Daniel Ansari, a neuroscientist at the University of Western Ontario who studies how the brain gets wired for math.

Yet Boston educators also understood that Piaget was right about the need for preschoolers to learn through play, and looked for a curriculum with lots of games and puzzles.

They settled on one called Building Blocks, which has received the highest effectiveness rating from the U.S. Department of Education. The department based that rating on two studies in New York state that showed that kids in a number of Building Blocks preschools learned as much as students who receive individual tutoring.

A recent analysis in Boston shows that district is getting results, too — on third-grade math tests, the passing rates of students in Building Block preschools were 10 percentage points higher than those who may have attended preschool elsewhere but weren’t enrolled in the city’s program.

I expect them to pick up scientific words like ‘waterproof,’ so why not teach them the word ‘rhombus’ ... right from the start?” - Laura Shea, preschool teacher

With Building Blocks, students don’t just learn to count and add. One key part of the curriculum is geometry, which its co-creator, University of Denver professor Douglas Clements, says is key for understanding mathematical relationships. Boston preschoolers are taught, for example, that triangles don’t always resemble a witch’s hat, the only version most kids their age see.

“I expect them to pick up scientific words like ‘waterproof,’ so why not teach them the word rhombus … right from the start?” said Laura Shea, a preschool teacher at the Curley K-8 School in Boston’s Jamaica Plain neighborhood.

She and other teachers help students learn those terms using a game called “feely box.”

In that exercise, the teacher places a thin foam shape in a box that has holes on two sides. The students slip their hands in the holes, then try to get classmates to guess what it is by describing what they feel.

“It has four L [right] angles and four sides,” said Hoang-Son, a boy at Everett Elementary, as he cupped his hand around a rhombus.

“Can you tell us anything else about the sides?” asked his teacher, Sara Gardner.

“All the sides are the same length,” he said.

Brain researchers say that preschoolers can learn more math than they're usually taught.

Someone guessed correctly that it was a square, but Gardner pushed for more, until Hoang-Son confirmed that the equal sides meant it was a rhombus, too.

Starting in the crib

The Building Blocks curriculum is rooted in decades of research into how children learn math, starting in the crib.

Researchers have shown that infants’ ability to tell the difference between two groups of dots is part of an ancient perceptual system we share with mammals and birds.

German neuroscientists, for example, recently found that crows have specialized neurons that fire when they see a specific number of dots on a touch-sensitive computer screen. The birds could indicate, by pecking at a screen, whether the number of dots they saw (between one and five) matched a previous display.

Crows, of course, can’t write equations. Humans develop that skill through developing new connections in different parts of the brain that tie our natural intuition about numbers to the words and symbols of formal mathematics.

How fast children make those connections depends on many factors, including genetics and learning opportunities at home.

Wealthier children tend to build them more quickly because, on average, they talk more with their parents about the differences in quantity — noticing which tree in the park is tallest or measuring flour and sugar to make cupcakes.

One big step in children’s mathematical development occurs when they realize that the last M & M they count in a handful is special because it represents the total quantity — the principal known as cardinality. That’s also a concept that children learn through board games, when they don’t count the square they’re sitting on because it was counted in the previous turn.

Children typically learn that by age 3 or 4, but some struggle with it late into elementary school.

Sharon Griffin, a cognitive psychologist and leading authority on early-childhood math, said she often saw children from low-income homes who couldn’t do simple addition because they hadn’t mastered that concept.

When asked to add 4 and 2 in their heads, they would include the number 4 in their count and say the answer is 5, said Griffin, professor emerita of education and psychology at Clark University in Massachusetts.

Preschools, many believe, can help prevent that, by infusing playful math instruction throughout the day.

In Boston, teachers have found that students love math games as much as listening to stories.

“It’s just math,” a 5-year-old gushed one June morning at Everett Elementary.

“You can count whatever you want: insects, butterflies, rubber duckies, even rubber people. I count how many sisters I have. Guess how many sisters I have? Six, and I have one brother.”

A matter of training

There’s no guarantee that Seattle’s preschool program will see the same results as the one in Boston.

One key to Boston’s success is that the school district provides most of the city-funded preschool classes, and keeps a tight leash on quality. In Seattle, preschool classes will be run by a number of organizations.

While Seattle’s providers will get coaching, it may not be as intensive as the training teachers get in Boston — or even at South Shore, which benefits from a private annual grant of $1 million.

And Seattle did not choose Building Blocks, although its new preschools will use approaches that draw from the same well of research and have been used successfully elsewhere.

In New Jersey, for example, fifth-grade students who spent two years in state-funded preschools were ahead of other classmates by about three-quarters of a year, according to a 2013 study.

No one approach will work on the same timetable for all kids.

In Alfonzo’s class, for example, one girl still had trouble understanding numbers past four near the end of the year.

But the hope is to ensure that most are like Zachary, a South Shore 5-year-old who, in making 10 in the “not my way,” game, slid two groups of five beads across in a single push, without counting.

Correction:  The original version of this story, published Aug. 2nd, has been corrected. Children who haven’t mastered a key math concept often struggle when adding in their heads or counting spaces on a game board.  The story incorrectly said they often make that error when counting on their fingers.