Students’ strategy profiles in fraction comparison: A cross-sectional study [Author Accepted Manuscript]

When comparing fractions, students draw on different reasoning processes, ranging from intuitive, biased reasoning often rooted in natural numbers knowledge, to more magnitude-based reasoning. These processes give rise to distinct comparison strategies, and the extent to which each strategy is used is highly person-dependent, showing large interindividual differences. This cross-sectional study examined how students’ strategy use differs across primary and secondary education (ages 10-18 or grades 5–12), through a theory-driven Bayesian classification based on accuracies and reaction times. In total, 889 students completed a fraction comparison task designed to elicit natural number-based reasoning, gap thinking and benchmarking. Analyses of both accuracy and reaction time data classified students into pre-defined, theory-based profiles, which not only reflected specific strategies or combinations thereof, but also identified guessers and proficient solvers. Our results revealed age-related shifts: the classification based on accuracy scores showed that younger students were more often classified into biased profiles, while older students were increasingly profiled as capable solvers who probably relied more on magnitude-based reasoning. However, even in upper secondary education some students still employed biased comparison strategies. No clear age-related differences emerged in the reaction time-based classification. The findings highlight substantial individual differences in strategy use between and within age groups, underscoring the need for personalized instruction that targets specific misconceptions. This need extends to older students, as some still demonstrate these misconceptions, indicating that a well-developed conceptual understanding of fractions cannot be taken for granted at higher grade levels.