SEATTLE — 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.
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, 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.
Humans take those conceptions develop 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, they would hold up four fingers, count their fourth finger and then their thumb, 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.”
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.
