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 to 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 tests 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 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. Together, these results suggest that while fraction conceptual and procedural knowledge distinguish whole-number bias students from reverse-bias and high-performing students, only rational magnitude processing distinguishes between students with flawed strategies and high-performing students.
Romero et al. (Fri,) studied this question.