High School Students’ Fraction Comparison Strategy Profiles Relate to Rational Number Difficulties and Cognitive Outcomes

Students often rely on flawed strategies to compare fractions, focusing on individual components rather than rational magnitudes. Only a handful of studies have explored whether these strategies result in difficulties in other fraction domains or whether they are the consequence of reduced cognitive capacities or attending the wrong numerical distances (e.g., numerator and denominator distances). Mexican high school students (N=76, mean age=16.18 years) completed a fraction comparison task with pairs either compatible with whole-number rules (e.g., 18/19 vs. 12/19) or misleading (e.g., 23/49 vs. 23/30). Participants completed conceptual and procedural fraction knowledge assessments and three executive function tasks. First, cluster analyses revealed that almost half of the students used flawed componential fraction comparison strategies. Particularly, we found two biased (whole-number bias and reverse bias) groups and a third group with overall high performance. Notably, whole-number biased students had lower math achievement, conceptual and procedural fraction knowledge, and cognitive flexibility than reverse biased or high-performance students. Next, we probed differences in rational and componential magnitude processing between these groups. Remarkably, both biased groups showed neither rational nor componential distance effects. In contrast, high-performing students' performance was better explained by robust rational distance effects. These results suggest that students who use flawed comparison strategies have not only impaired rational magnitude processing but also deficits in other fraction domains and the cognitive capacities that support their learning.