Co-construction of fractions schemes and units coordinating structures

• We describe methods for assessing multiplicative concepts and fraction schemes.
• Interviews with 50 6th graders suggest co-construction of levels of units structures.
• We discuss ways to support learning multiplicative structure in middle grades.

A growing body of research implicates students’ ability to coordinate multiple levels of numerical units as an important aspect of their mathematical development. In this paper, we consider relationships between the ways students coordinate units with whole numbers (their multiplicative concepts) and the ways students coordinate units with fractions (their fractions schemes). Interviews with 50 sixth-grade students suggest commonality in the number of levels of units-within-units structures that students construct for the two contexts, consistent with Steffe's (2001. The Journal, of Mathematical Behavior, 20(3), 267) reorganization hypothesis. The results suggest that fractions may be a fertile domain for elementary and middle grades students to continue to develop whole number understandings.