Fraction arithmetic development: a longitudinal study on students' growth and errors during the intermediate grades
Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
Fractions serve as an obstacle in many students’ mathematics education. Mastery of fractions, including fraction arithmetic, is critical for supporting not only a variety of personal benefits (e.g., cooking, finances, and understanding health risk ratios), but also students’ success in advanced mathematics courses (e.g., algebra) and the larger field of science, technology, engineering, and mathematics (STEM). Unfortunately, many U.S. students demonstrate difficulties on even the most basic fraction arithmetic problems despite several years of instruction (NAEP, 2013; NMAP, 2008). To shed light on why students find fraction arithmetic so difficult, the current study examined the development of students’ (N = 536) common denominator addition/subtraction skills from the third through sixth grades; the educational period when students receive most of the fraction instruction. The study particularly sought to uncover whether students display empirically distinct growth trajectories in the development of their fraction arithmetic skills, as well as factors that predict differential growth in these skills. ☐ Students were assessed on a variety of cognitive and mathematics-specific skills in the third grade, including language, nonverbal reasoning, working memory, attentive behavior, reading fluency, calculation fluency, and whole number line estimation skills. They were also administered a set of addition/subtraction common denominator fraction arithmetic word problems five times (i.e., fall and spring of fourth grade, fall and spring of fifth grade, and winter of sixth grade) during the study to assess their fraction arithmetic skills. ☐ Latent class growth analyses revealed three distinct fraction arithmetic growth classes: High Growth, Low Growth, and Consistently Accurate. Age and calculation fluency predicted membership in both the High Growth and Consistently Accurate class relative to those in the Low Growth class. Language and nonverbal reasoning skills were also identified as predictors of student membership in the Consistently Accurate versus Low Growth class. ☐ Error analyses revealed that students who demonstrated poor accuracy across time (i.e., Low Growth) displayed greater whole number bias errors (i.e., over generalization of whole number arithmetic strategies to fractions) that were less systematic compared to those who made growth. Low Growth students also demonstrated a mixture of conceptually inappropriate procedures that were further compounded by poor whole number calculation fluency and reflected misunderstandings of fraction notation, magnitude, and differentiation between whole versus fraction portions of mixed numbers. ☐ These findings inform the fields’ understanding of students’ fraction arithmetic development as well the underlying heterogeneity of these skills. Identification of predictors of fraction arithmetic growth and related student errors provides insight for why some students persistently struggle with fraction arithmetic but others do not. Information regarding these barriers to students’ fraction arithmetic learning can inform the development of screeners to identify those at risk for persistent fraction difficulties, as well as skills and fraction misconceptions that should be targeted in both interventions and general classroom instruction to support students’ fraction arithmetic learning.
Description
Keywords
Arithmetic learning, Fractions, Student errors, STEM, Student development