Essential Building Blocks of Math

Number sense is so innate to many adults that they may not remember being taught such skills, but it is crucial to mastering more complex math skills like manipulating fractions and decimals or solving equations with unknown variables, experts say. Research shows that a flexible understanding of numbers is strongly correlated to later math achievement and the ability to solve problems presented in different ways. Unlike the recent surge of evidence on science-based reading instruction, research and emphasis on number sense isn’t making its way into schools and classrooms in the same way. Students spend less time on foundational numeracy compared with what they spend on reading; elementary teachers often receive less training in how to teach math effectively; and schools use fewer interventions for students who need extra math support.

Many American students struggle in math. According to the 2024 National Assessment of Educational Progress, nearly 1 in 4 fourth graders and 39 percent of eighth graders scored “below basic,” the test’s lowest category. An analysis of state tests shows that few states have recovered students from pandemic math losses, with disadvantaged students from low-income neighborhoods hit especially hard.

For those struggling students — including those diagnosed with dyscalculia and related learning challenges — lack of number sense often plays a significant role. “For kids that have a fundamental weakness in mathematics, 80 percent or 90 percent of the time that’s going to be linked to a lack of understanding numbers,” said Ben Clarke, an early math researcher and department head of special education and clinical sciences at the University of Oregon. “If we want students to be able to access other pieces of mathematics that are really important, then they need to build this foundational understanding of numbers.”

Even in the early years of school, researchers can spot students who can make connections between numbers and use more sophisticated strategies to solve problems, just as there are some students who start school already reading. Also as with reading, gaps between students are present on the first day of kindergarten. Students from low-income and disadvantaged backgrounds arrive at school with less math knowledge than high-income students. Boston College psychologist and early math researcher Elida Laski said research has found income-based differences in how families talk about math with children before they ever reach school.

“Lower-income families are more likely to think about math as narrow, it’s counting and numbers,” Laski said. “Whereas higher-income families tend to think about math as more conceptual and around in everyday life.” These differences in thinking play out in how flexible students are with numbers in early elementary school. In one study, Laski and her team found that higher-income kindergarten and first grade students used more sophisticated problem-solving strategies than lower-income students, who more often relied on counting. The higher-income students also had more basic math facts committed to memory, like the answer to one plus two.

The memory recall and relatively advanced strategies used by higher-income students produced more efficient problem-solving and more correct answers than counting did. Also, when students from high-income families produced a wrong answer, it was often less wrong than students who were relying on strategies like counting. Laski said many of the low-income students in the study struggled with addition because they didn’t have a firm understanding of how basic concepts of numbers work. For example, “When we’d ask, ‘What’s three plus four,’ we’d get answers like ‘34,’” Laski said. “Whatever ways they’re practicing arithmetic, they don’t have the conceptual basis to make sense of it. They didn’t have the number sense, really.”

Laski said early childhood classrooms could be “far more direct” with students in teaching number sense, weaving it in explicitly when working on more concrete skills like addition. Even something as simple as counting big numbers, including hundred thousands and millions, some educators say, can help develop number sense. Counting might seem simple, but for young children it’s foundational and essential.

Allison Green
Boston Tutoring Services