What ten-year-olds know about fractions predicts their algebra grade at sixteen
Robert Siegler tracked 4,276 children for six years. The skill at age ten that predicted their algebra grade at sixteen wasn't IQ, working memory, or arithmetic. It was fractions. Most parents worry about times tables. They are worrying about the wrong thing.
In 2012, Robert Siegler and his colleagues did something that should have changed how primary maths is taught, and largely did not. They tracked 3,677 children in the UK and 599 in the United States for six years. They tested everything they could think of: IQ, reading age, working memory, whole-number arithmetic, family income, parental education. They wanted to find the single skill at age ten that best predicted who would be good at algebra at sixteen.
It was fractions.
The correlation that broke the assumption
Children who understood fractions at ten outperformed their peers in algebra and overall mathematics at sixteen, even after every other variable had been statistically removed. The effect held in both countries. It held across income groups. By the time the children were sixteen, the correlation between fraction knowledge and overall maths performance exceeded 0.80, which in education research is the kind of number you double-check before publishing.
The study did not just measure whether a child could write 1/2 as 0.5. It measured whether they understood that 3/4 was a single number with a place on the number line, larger than 2/3 and smaller than 7/8. It tested fraction comparison, fraction arithmetic, and the ability to place fractions on a number line correctly. Children who could do these things at ten went on to do algebra at sixteen. Children who could not, did not.
Why fractions and not anything else
This is the part that needs explaining. The curriculum spends far more time on times tables, long division and arithmetic facts. Why does fraction knowledge predict so much more than any of those?
The answer is that fractions are the first time a child meets a number that is not a count. Three apples is a count. Four cars is a count. Whole-number arithmetic, however clever, is fundamentally about counting things and combining them. A child who is good at whole-number arithmetic has learned the rules of counting very well.
Three-quarters is not a count. It is a relationship between two numbers. You cannot point at three-quarters of a thing without first agreeing on what the whole is. Once a child understands that, they have done the cognitive work algebra will later assume.
Algebra is full of relationships dressed up as numbers. The variable x is not a count. The expression 2x/3 is not a count. A child who is comfortable with fractions is already comfortable with the idea that a number can describe how two quantities relate to each other. A child who is not, will spend the next six years quietly confused.
What the study did not prove
Siegler's data is correlational, and he is careful about this. Fraction skill at ten does not cause algebra skill at sixteen the way that planting a seed causes a tree. It is more accurate to say that the children who get fractions have already done the thinking algebra requires, and the children who do not, have not.
The prediction is also robust. Two countries, two large samples, controls for nearly every confounding variable a reviewer could think of. It fits with other longitudinal work: Oxford scanned 87 sixteen-year-olds and found those who had stopped studying maths had measurably less of a specific brain chemical, a finding with relevance further back down the age range than its headline suggests. What is in dispute is what schools and parents should do about it.
What this looks like if your child is eight
Most parents who worry about their child's maths worry about times tables. Times tables are useful but they are recoverable. A child with wobbly times tables at eight will, with practice, have adequate times tables at ten. The window does not close. Fractions aren't the only quiet foundation parents tend to overlook: spatial reasoning predicts maths performance years before the curriculum names it, and the curriculum doesn't tell parents to build it.
Fractions are different. They are the moment when maths stops being arithmetic and starts being something more abstract. A child who arrives at secondary school without fluency in fractions has not just fallen behind on one topic. They have not made the cognitive move the rest of secondary maths assumes.
The practical implication is small but meaningful. Time spent on fractions is not interchangeable with time spent on arithmetic drill. They are different categories of learning, and the research suggests they are not equally important to the rest of the child's mathematical life.
If your eight-year-old has wobbly times tables, they will catch up. If your ten-year-old does not yet know what three-quarters means as a number rather than a phrase, that is the conversation worth having.
Full study: Siegler et al. (2012), "Early Predictors of High School Mathematics Achievement", Psychological Science. https://journals.sagepub.com/doi/10.1177/0956797612440101
