Expert Commentary

Early predictors of high school math achievement

2012 study from Carnegie Mellon University, University of California-Irvine and others published in Psychological Science on the link between elementary and high school math achievement.


Significant resources are invested in intervention programs to ensure student academic success at the elementary school level. Research has shown this preparation is critical for students to demonstrate academic achievement in high school, and early education is strongly linked with optimal higher education outcomes, as well as good careers and wages.

A 2012 study from Carnegie Mellon University, University of California-Irvine and others published in Psychological Science, “Early Predictors of High School Mathematics Achievement,” investigated the extent to which elementary school math performance predicted subsequent math proficiency in high school. The study used longitudinal data from two studies: the British Cohort study and the U.S.-based Panel Study of Incomes Dynamics Child Development Supplement (PSID-CDS). British elementary school students were tested on whole-number arithmetic and fractions, then retested six years later on whole-number arithmetic, fractions, algebra, and probability. Their elementary school peers in the United States were tested on whole-number arithmetic and fractions, and then retested on whole-number arithmetic, fractions, algebra, geometry, measurement and probability. The researchers also collected data on participant demographics, family background and general intelligence.

Key study findings include:

  • “Elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education.”
  • In both the United States and the United Kingdom, knowledge of fractions at age 10 was the strongest predictor of algebra knowledge and math achievement at age 16. Early whole-number division had the second strongest relationship to future math outcomes in both countries.
  • High school students’ understanding of fractions and division were highly correlated with overall mathematics achievement.
  • Although division and fractions were predictors of high school mathematics knowledge, they did not predict all intellectual outcomes — such as those related to reading — more accurately. “Moreover, in all cases but one, the pooled predictive effect of fractions and division knowledge on literacy was no greater than the pooled predictive effect of addition, subtraction, and multiplication knowledge on literacy.” However, fractions and division knowledge more accurately predicted vocabulary competency in the UK study.

The authors suggested that “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.”

A related study published in Proceedings of the National Academy of Sciences, “Number Sense across the Lifespan as Revealed by a Massive Internet Based Sample,” conducted an experiment to determine how number sense — “the cognitive system that gives rise to our basic numerical intuitions [or understandings]” — changes over time. The study found that number sense develops gradually, peaking around age 30, and that there are significant differences in number sense performance between individuals of the same age. More related findings are detailed in a 2013 study published in the journal PLoS One, “Adolescents’ Functional Numeracy Is Predicted by Their School Entry Number System Knowledge.”

Tags:  children, youth, cognition

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