The goal of this study was to describe fraction-calculation errors among fourth-grade students and to determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low-, average-, or high-achieving). We specifically addressed whether mathematics-achievement status was related to students’ tendency to operate with whole-number bias. We extended this focus by comparing low-performing students’ errors in 2 instructional settings that focused on 2 different types of fraction understandings: core instruction that focused on part-whole understanding versus small-group tutoring that focused on magnitude understanding. Results showed students across the sample were more likely to operate with whole-number bias on problems with unlike denominators. Students with low or average achievement (who participated only in core instruction) were more likely to operate with whole-number bias than students with low achievement who participated in small-group tutoring. We suggest instruction should emphasize magnitude understanding to sufficiently increase fraction understanding for all students in the upper elementary grades.
