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Knowledge of fractions and long division “key to later mathematics success”

16 July 2012

Secondary school pupils’ maths performance could be substantially improved if children gained a better understanding of fractions and long division in primary school, an important international research study that involved the Institute of Education has concluded.

The study found that primary pupils’ knowledge of fractions and division at age 10 is a uniquely accurate predictor of their attainment in algebra and overall maths performance five or six years later.

Understanding of whole-number division and fractions has a stronger relation to maths achievement than does knowledge of whole-number addition, subtraction, and multiplication; verbal IQ; working memory; and parental income and education, the researchers say.

The study was conducted by seven US academics and Dr Kathryn Duckworth of the IOE. They examined two nationally representative longitudinal data sets – one British, the other American.

The larger of the two was the 1970 British Cohort Study (BCS), which is managed by the IOE’s Centre for Longitudinal Studies. The total BCS sample includes more than 17,000 people born in Britain in a single week of 1970. A subsample of 3,677 cohort members with test scores at age 10 and 16 was analysed in this research. The smaller US data set involved 599 children who were tested in 1997 as 10 to 12-year-olds and in 2002 as 15 to 17-year-olds.

Professor Robert Siegler of Carnegie Mellon University in Pittsburgh, Pennsylvania, the research team’s leader, said: “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. 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.”

The fact that the UK and US analyses produced very similar findings despite differences in the samples, the tests, and the times at which the data were obtained provides further support for their findings, the researchers say in an online article published by the journal of Psychological Science. “The correlation between knowledge of fractions in elementary school and achievement in algebra and mathematics overall in high school was expected,” they add. “But the relation between early knowledge of division and later mathematical knowledge was not.”

There are several reasons why knowledge of division at age 10 is such a good predictor of future maths skills, the researchers believe. One is that mastery of whole-number division, like mastery of fractions, is required to solve many algebra problems.

Professor Siegler and his colleagues also speculate that poor knowledge of division and fractions might lead pupils to give up trying to understand maths, and rely instead on rote memorisation. They add that some might argue that understanding of fractions and division is a uniquely strong indicator of future performance because these are more difficult areas of maths than addition, subtraction, and multiplication. They can therefore be used to measure more advanced thinking.

The researchers do not, however, believe that this is the case. If it were, knowledge of fractions and division would also help to predict a child’s future literacy skills, they say. However, in most cases it does not.

“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,” said Dr Duckworth of the IOE.

“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. The conclusion must therefore be 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 study’s findings appear in “Early Predictors of High School Mathematics Achievement” by Robert S. Siegler, Greg J. Duncan, Pamela E. Davis-Kean, Kathryn Duckworth, Amy Claessens, Mimi Engel, Maria Ines Susperreguy, and Meichu Chen.

There is also a YouTube video of Professor Siegler speaking about the study.

Coverage in TESpro magazine

This story was covered by tespro magazine: "Fractions and division predict maths success" by Kerra Maddern on 17 August 2012.

Further information:

Meghan Rainsberry
Centre for Longitudinal Studies
Institute of Education
University of London
020 7612 6530
075 3186 4481

David Budge
Centre for Longitudinal Studies
Institute of Education
University of London
020 7911 5349
07881 415362

Notes for editors:

  1. The research was supported by grants from the US Department of Education’s Institute of Education Sciences and by the National Science Foundation’s Developmental and Learning Science Group at the Social, Behavioral and Economic Directorate.
  2. Mathematics proficiency at age 10 was assessed by performance on the Friendly Maths Test, which examined knowledge of whole-number arithmetic and fractions. Mathematics proficiency at age 16 was assessed by the APU (Applied Psychology Unit) Arithmetic Test, which measured knowledge of whole-number arithmetic, fractions, algebra, and probability. General intelligence was assessed at age 10 by performance on the British Ability Scale, which included measures of verbal and non-verbal intellectual ability, vocabulary, and spelling. Parents provided information about their education and income and their children’s gender, age, and number of siblings.
  3. The US data set used was the Panel Study of Income Dynamics-Child Development Supplement.
  4. The Institute of Education is a college of the University of London that specialises in education and related areas of social science and professional practice. In the most recent Research Assessment Exercise two-thirds of the Institute’s research activity was judged to be internationally significant and over a third was judged to be “world leading”. The Institute was recognised by Ofsted in 2010 for its “high quality” initial teacher training programmes that inspire its students “to want to be outstanding teachers”. The IOE is a member of the 1994 Group, which brings together 15 internationally renowned, research-intensive universities. More at
  5. The Centre for Longitudinal Studies (CLS) is an Economic and Social Research Council (ESRC) resource centre based at the Institute of Education, University of London. The ESRC is the UK's largest organisation for funding research on economic and social issues. It supports independent, high quality research which has an impact on business, the public sector and the third sector. The ESRC’s total budget for 2012-13 is £205 million. At any one time the ESRC supports over 4,000 researchers and postgraduate students in academic institutions and independent research institutes. More at