Is a Picture Worth 1,000 Words? Investigating Fraction Magnitude Knowledge Through Analysis of Student Representations

The present study examines the features and quality of visual representations (VRs) created by middle school students with learning disabilities and difficulties in mathematics in response to a released fraction item from the National Assessment of Educational Progress (NAEP). Relations between VR quality and scores on other measures of fraction knowledge are also investigated. Results show that students used circular area models most frequently to represent the NAEP item, but used bar models most accurately. Based on results, bar models may be the most efficient and effective area model VRs for use in fractions instruction. Representation quality was associated with problem-solving accuracy, as well as with performance on fraction number line estimation and fraction magnitude comparison. Implications for practice are discussed.