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 comprehension is the ability to evaluate their numerical magnitude. Here, we use a number-to-line task, where students point to the location of a number on a graduated line, to characterize errors in fraction comprehension. A total of ∼ 26,000 French pupils from 6th to 10th grade were tested (U.S. equivalent grades). Error rates were high, almost 80 % in 6th grade and 45 % in 10th grade. Errors could be classified into seven dominant patterns, whose frequency varied by grade level and individual performance. Younger and lower-performing children mostly confused fractions with decimals. Older and higher-performing children often confused a fraction ab and its inverse ba. All grades also confused the roles of the numerator and the denominator. We propose a theoretical framework suggesting that errors arise as bugs 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 patterns as stemming from inappropriate strategy selection, flawed execution, or incorrect corrective steps due to flawed execution. Our analysis provides a deeper understanding of the various traps that students face when interpreting a fraction's magnitude, the frequency of these errors, and their sequential order.