A child's ability to understand and manipulate sets of numbers in 1st grade predicts how well he or she will succeed in the math required both in secondary school and for day-to-day living, according to a study published in the current online edition of the journal PLOS One. Yet math tests in the early grades focus instead on how well and how quickly students can solve basic arithmetic problems, often using counting—a skill less connected to students' later math achievement, the study found.
In "Adolescents' Functional Numeracy Is Predicted by Their School Entry Number-System Knowledge" researchers at the University of Missouri, Columbia, and Carnegie-Mellon University, in Pittsburgh, tracked 180 students in 12 elementary schools who were participating in a larger longitudinal study of kindergarten through 9th grade.
Annually, from 1st grade, the students were given an online math battery, including simple and complex arithmetic problems (for example, 2+2 versus 6+19), comparing fractions, and solving word problems. The children were also asked to solve problems relating to sets of numbers. In one, the students identified different sets of numbers that could make up a target number; for example, for a target 7, a student might list 4 with 3 and 1 with 6.
The researchers found that students who could identify and work with sets of numbers in 1st grade performed significantly better on a test of functional numeracy given years later in 7th grade, which assesses math skills needed for the workforce. by contrast, students' ability at the start of school to perform arithmetic based on counting absolute values of numbers had little bearing on their later math skills.
As the chart below shows, students who performed well in early tests of number systems had much larger growth through grade 5 than students who had lower number-systems understanding early in their schooling.
"Children who begin school behind their peers in the use of counting procedures tend to catch up with other children within one or two years," the authors noted. By contrast, "It is very likely that competence at using more complex mathematical procedures, as in borrowing or carrying to solve multi-column arithmetic problems, contributes to functional numeracy."
At the same time, the researchers noted that math tests in the early grades tend to focus on counting skills and very simple arithmetic, rather than problems such as fractions, which require students to think about how numbers operate in sets. That gives an intriguing potential explanation for another recent study showing that parents can boost students' math skills by discussing math problems of this sort at home.
More than one in five American adults are considered "functionally innumerate," unable to solve 8th-grade mathematics problems, and the study's findings suggest early instruction in how sets of numbers interact could give students a leg up.