Characterizing error types in the comprehension of fractions: the number line test

Understanding fractions is a major hurdle for many students. A key aspect of fraction comprehensionis the ability to evaluate their numerical magnitude. Here, we use a number-to-line task, wherestudents point to the location of a number on a graduated line, to characterize errors in fractioncomprehension. A total of ~26,000 French pupils from 6th to 10th grade were tested. Error rates werehigh, almost 80% in 6th grade and 45% in 10th grade. Errors could be classified into seven dominantpatterns, whose frequency varied by grade level and individual performance. Younger andlower-performing children mostly confused fractions with decimals. Older and higher-performing𝑎𝑏children often confused a fraction 𝑏 and its inverse 𝑎 . All grades also confused the roles of thenumerator and the denominator. We propose a theoretical framework suggesting that errors arise asbugs in the execution of one of two main strategies: children converting the fraction into a decimal,or partitioning the line into units and counting them. This model explains the observed error patternsas stemming from inappropriate strategy selection, flawed execution, or incorrect corrective stepsdue to flawed execution. Our analysis provides a deeper understanding of the various traps thatstudents face when interpreting a fraction’s magnitude, the frequency of these errors, and theirsequential order.