Development of fraction knowledge: a longitudinal study from third through sixth grade
Date
2015
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Publisher
University of Delaware
Abstract
Fractions are a difficult mathematics topic for many elementary and middle school students. Addressing difficulties with fractions is a priority, not only because fraction knowledge affects daily living (e.g., budgeting, understanding mortgage rates, and doing home repairs), but also because it predicts success in advanced mathematics. With an eye toward understanding why students find fractions so hard, the present study investigated the development of fraction concepts and procedures longitudinally on a large cohort of students (N=536) from third through sixth grade. In particular, the study identified empirically distinct patterns of growth in fraction knowledge as well as the factors that predict growth. In third grade, students were assessed on the following skills: language, working memory, nonverbal reasoning, attention, reading fluency, whole number line estimation, and calculation fluency. They also were given a fraction concepts assessment twice yearly from third through sixth grade and a fraction procedures assessment twice yearly from fourth through sixth grade. Growth curve analyses showed that, on average, students grew in a linear fashion on fraction concepts and fraction procedures. Although a constellation of demographic, general cognitive, and mathematics-related variables uniquely predicted outcomes, whole number line estimation, addition fluency, and attention were particularly important to fraction achievement. Latent class growth analyses revealed five distinct growth classes, both for fraction concepts and fraction procedures. Below average addition fluency, language, attention, whole number line estimation, and working memory predicted membership in a low-growth trajectory for fraction concepts, while addition fluency and attention predicted membership in a low-growth trajectory for fraction procedures. Analyses of performance of students who made little growth in fractions during the study period identified several barriers to fraction learning. These low-growth students struggled with problems involving understanding the relationship between the numerator and the denominator, comparing fractions, and placing fractions on the number line. They also lagged behind their peers on fraction addition and subtraction problems with like denominators. The findings contribute to our understanding of the development of fraction knowledge by identifying the typical trajectory of fraction learning as well as by identifying subgroups of children who differ from that trajectory. The study also identified predictors of growth and achievement that can be used to develop measures that screen for fraction difficulties as well as intervention approaches.