Primary school pupils' knowledge of fractions and division predicts their overall achievement in maths at secondary school five or six years later, according to a new study.
Children's performance in the subject could be substantially improved if lessons in these areas were bettered, academics say.
The discovery that understanding of fractions and division at age 10 is a predictor of future proficiency in maths highlights the need for the teaching of these topics to be as strong as possible, they write in the report Early Predictors of High School Mathematics Achievement.
The research was carried out by academics at the University of London's Institute of Education and colleagues from various US universities. The academics hope that the study will improve maths education and the theoretical understanding of maths development.
Maths test scores of high school students in the US have "barely budged" in 30 years. These new findings "imply that mastery of fractions and division is needed if substantial improvements in understanding of algebra and other aspects of high school mathematics are to be achieved", the report says.
"One likely reason for students' limited mastery of fractions and division is that many US teachers lack a firm conceptual understanding of fractions and division," it explains.
This means that "many students lack even the basic mathematics competence needed to succeed in typical jobs in a modern economy", particularly those from poorer backgrounds or ethnic minorities.
For the research, academics used two different sets of data: the British Cohort Study (BCS) and the US Panel Study of Income Dynamics Child Development Supplement.
The BCS sample included 3,677 children born in the UK in a single week of 1970. Their ability in maths was tested in 1980 and in 1986.
The US survey provided a nationally representative sample of 599 American children who were tested in 1997 as 10- to 12-year-olds and in 2002 as 15- to 17-year-olds. Academics statistically controlled for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education.
In the UK, fractions knowledge at the age of 10 was the strongest of five mathematical predictors of algebra knowledge and mathematics achievement at age 16. A similar trend was seen in the US.
"There are substantial correlations between early and later knowledge in other academic subjects as well, but differences in children's mathematics knowledge are even more stable than differences in their reading and other capabilities," the report says.
Researchers chose fractions because they occupy "a central position within mathematical development", allowing children to learn about the properties of numbers and complete algebraic equations. They also found that early knowledge of division was "consistently" related to later mathematics proficiency.
"To the best of our knowledge, relations between elementary school children's division knowledge and their mathematics proficiency in high school have not been documented previously," the report says.
"The correlation between knowledge of fractions in elementary school and achievement in algebra and mathematics overall in high school was expected, but the relation between early division knowledge and later mathematical knowledge was not," it explains.
But knowledge of fractions and division did not accurately predict intellectual outcomes in other subjects.
"Knowledge of fractions and knowledge of division were not uniquely predictive of most subsequent literacy skills, as should have been the case if their predictive value was due solely to their greater difficulty," the academics say.
"The unique predictive value of early fractions and division knowledge seems to be due to many students not mastering fractions and division and to those operations being essential for more advanced mathematics, rather than simply to fractions and division being relatively difficult to master," they add.
Siegler, R.S. et al. "Early Predictors of High School Mathematics Achievement".
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WHAT TO DO
Professor Robert Siegler of Carnegie Mellon University in Pittsburgh, US, was the leader of the research team.
"The clear message is that we need to improve instruction in long division and fractions, which will require helping teachers to gain a deeper understanding of the concepts that underlie these mathematical operations," he says. "At present, many teachers lack this understanding.
"Because mastery of fractions, ratios and proportions is necessary in a high percentage of contemporary occupations we need to start making these improvements now."
Dr Kathryn Duckworth, of the University of London's Institute of Education, says that all pupils "need to have a better understanding of fractions and division if they're going to succeed in maths throughout secondary school and do well in maths GCSE.
"The unique predictive value of early fractions and division knowledge seems to be due to many students not mastering fractions and division and to those operations being essential for more advanced mathematics, rather than simply to fractions and division being relatively difficult to master," she says.
"Our results also show that a solid grasp of fractions and division early on matters for pupils across all ability levels and not just those performing at the top end of the distribution," she adds.