Identifying learning difficulties with fractions: A longitudinal study of student growth from third through sixth grade

- This study examined fraction development from third to sixth grade.
- We identified distinct growth classes for fraction concepts and procedures.
- One group of children made little progress between third and sixth grades.
- Cognitive and math-specific measures predicted growth trajectory membership.
- Students with learning difficulties struggled with fraction comparison and equivalence problems.

The present longitudinal study examined growth in fraction knowledge between third and sixth grades (N = 536). Students were administered fraction concepts and procedures measures twice yearly through sixth grade. Analyses revealed empirically distinct growth classes on both measures. Of particular interest were students who started low and made little progress after three years of instruction in fractions, compared to those who started low but made good progress. Poorer language, attention, whole number line estimation, and calculation fluency in third grade significantly increased the odds of membership in a low-growth trajectory class for fraction concepts, while poorer attention and calculation fluency predicted membership in a low-growth trajectory class for fraction procedures. Students classified as receiving special education services in school, many of whom had diagnosed learning disabilities, were 2.5 times more likely to experience low growth in fraction concepts than their peers who were not receiving special education and 11.5 times more likely to experience low growth in fraction procedures. Students with persistent difficulties in fraction knowledge also were much less likely to meet state standards on a mathematics achievement test, portending problems in more advanced mathematics.