Finding their way: students’ fraction misconceptions and errors over two years of fraction learning

Purpose.
This study examined the longitudinal stability and consistency of student misconceptions across five fraction subconstructs during two years of mathematics instruction.

Method.
In this study, 1,055 students (546 boys; Mage = 9.8 years) were assessed at four time points in Grades 4 and 5 across five subconstructs: part-whole, measurement, quotient, operator, and density. Using a methodical pre-registered error-classification framework, supplemented by exploratory mixed-effects modelling, we examined the frequency and stability of student errors.

Results.
Results revealed a clear distinction in conceptual stability across domains. Part-whole meanings were mastered early in instruction and remained stable over time, whereas tasks involving magnitude and density were characterized by high response entropy and frequent strategy shifts. Students simultaneously held multiple misconceptions, which were highly dependent on the specific subconstruct being assessed. For example, in fraction arithmetic, errors varied across representations and operations. While accuracy generally improved, the progression of errors was often variable, with students frequently reverting from correct responses to whole number bias or unique, unclassified strategies when new topics, such as decimals, were introduced.

Conclusion.
These patterns indicate that a correct response at a single time point is not always a sign of stable understanding. Instead, the high degree of variation suggests that early fraction knowledge is context-dependent and that unique error patterns often signal active conceptual reorganization. These findings suggest that because misconceptions are a moving target, interventions must be adaptive and responsive to the specific errors that emerge as students transition between new fraction concepts.