Students’ partitive reasoning

In building models of students’ fractions knowledge, two prominent frameworks have arisen: Kieren's rational number subconstructs, and Steffe's fractions schemes. The purpose of this paper is to clarify and reconcile aspects of those frameworks through a quantitative analysis. In particular, we focus on the measurement subconstruct and the partitive fraction scheme, as well as the role splitting operations play in their construction. Our findings indicate a strong connection between students’ measurement conceptions and their construction of partitive unit fraction schemes. On the other hand, generalizing the partitive unit fraction scheme to partitive reasoning with non-unit fractions seems to require conceptions that exceed most researchers’ descriptions of measurement. Such a generalization also seems to require mental operations beyond splitting.

Research highlights▶ Key conceptions of measurement coincide with the construction of partitive unit fraction schemes (PUFSs). ▶ Partitive reasoning with non-unit fractions is not a simple generalization of PUFS. ▶ Students who construct PUFS in earlier grades seem to construct splitting operations with no further instructional support. ▶ Counter to previous hypotheses, splitting operations seem to precede the construction of a general partitive fraction scheme.