Early Predictors of High School Mathematics Achievement

Abstract

Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that 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. Implications of these findings for understanding and improving mathematics learning are discussed.

Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents

“…Hypothesis 2). These results are in line with the major findings of previous studies with U.S. samples (see Bailey et al, 2012;Booth & Newton, 2012;Siegler et al, 2012;Siegler & Pyke, 2013;Siegler et al, 2011) and thus indicate that prior findings on this topic are not limited to the U.S.…”

“…Also as with whole numbers, fraction magnitude understanding has proved to be quite strongly correlated with other aspects of mathematics learning. On top of this correlational evidence, recent investigations provide evidence for predictive relations between earlier fraction magnitude understanding and subsequent knowledge of fraction arithmetic, algebra and overall math achievement (Bailey et al, 2012;Booth & Newton, 2012;Siegler et al, 2012). To cite one example, Siegler et al (2012) demonstrated that 5 th graders' fraction knowledge predicts their mastery of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after controlling for IQ, reading achievement, working memory, family income and education, and whole number knowledge.…”

“…First, the moderate correlations between fraction magnitude understanding and fraction arithmetic skill, and also the non-significant contribution of fraction arithmetic skill to general math achievement scores when magnitude understanding was statistically controlled, argue against the possibility that the relations among arithmetic, magnitude knowledge, and overall achievement that we observed in the present study were only due to shared relations to IQ. Moreover, recent empirical investigations on this topic have demonstrated that fraction understanding is strongly related to fraction arithmetic and mathematical achievement, even after statistically controlling for IQ, reading level, executive functioning, and knowledge of all four whole number operations (Bailey et al, in press;Siegler et al, 2012;Siegler & Pyke, 2013). Notwithstanding these findings and arguments, future studies should take into account students' general intellectual capacities when analysing the pivotal role of fraction magnitude understanding in their further math development.…”

“…Understanding fractions is crucial for mathematics learning: It not only requires a deeper understanding of numbers than is ordinarily gained through experience with whole numbers, it is also predictive for students' mathematical achievement years later (Bailey, Hoard, Nugent, & Geary, 2012;Booth & Newton, 2012;Siegler et al, 2012). Despite increasing research interest in the domain of fractions, almost all studies of the role of fraction magnitude understanding in mathematics learning have been conducted in the U.S., limiting the generality of the findings to only U.S. students and adults.…”

“…However, to the best of our knowledge, all previous behavioural studies of the role of fraction magnitude understanding in mathematics learning have been conducted in the U.S. --with the one exception of Siegler et al (2012), which included both U.S. and U.K. samples.…”