• Building on Informal Knowledge Through Instruction in a Complex Content Domain: Partitioning, Units, and Understanding Multiplication of Fractions

    Nancy K. Mack
    Six fifth-grade students came to instruction with informal knowledge related to partitioning. This knowledge initially focused on partitioning "units of measure one" into a specific number of parts. Students were able to build on their informal knowledge to reconceptualize and partition units to solve problems involving multiplication of fractions in ways that were meaningful to them. Students built their knowledge by developing mental processes related to focusing on fractional amounts and to partitioning units in different ways. Students also frequently returned to their initial focus on the number of parts and to ideas embedded in equal-sharing situations.