Fractions: Could they really be the gatekeeper’s doorman?

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.…”

“…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.…”

Persistent and Pernicious Errors in Algebraic Problem Solving

“…This is surprising, given that fraction knowledge has been shown to be highly predictive of future math achievement (Siegler et al, 2012), critical for algebra readiness (Booth & Newton, 2012), performance, and learning (Booth, Newton, & Twiss-Garrity, 2014), and is hypothesized to be one of the most important factors in algebra achievement (NMAP, 2008). One reason for the apparent discrepancy may be that scholars have identified foundational knowledge of the magnitudes of fractions, and the understanding of fractions as numbers, as the critical knowledge components impacting algebra (e.g., Booth et al, 2014;Empson & Levi, 2011).…”

Student Magnitude Knowledge of Negative Numbers

“…Future studies might also examine older students' magnitude knowledge of negative numbers and whether their performance on a negative number line task is associated with algebra success and/or later math achievement -something which has been found true for estimates on positive number lines (e.g. Booth & Newton, 2012;Booth, Newton, & Twiss-Garrity, 2014;Booth & Siegler, 2006, 2008. The current study has provided a first stepping stone towards understanding students' magnitude knowledge of negative numbers and has left much room for further efforts to help understand this unique area of mathematical cognition.…”