From Parts to Wholes: Investigating Fraction Division through Partitioning Strategies

Fraction division is considered one of the most difficult concepts in learning fractions. This study aims to investigate students’ understanding of fraction division through a partition division conceptualization, utilizing their understanding of fractions as parts of a whole. To achieve this, we designed a hypothetical learning trajectory, in which students engaged with incomplete partition task. This article reports on a two-week design research intervention involving 21 fifth-grade students. The students’ written works, transcripts of teaching experiment recordings, and observational notes were retrospectively analyzed to examine the hypothetical learning trajectory. The study revealed that the students’ primary challenge was recognizing the correct whole during the teaching experiment. This study suggests that incorporating a stronger focus on proportional reasoning and varying fraction sizes in instructional approaches may help address this obstacle.