DISTRIBUTIVE PARTITIONING OPERATION IN MATHEMATICAL SITUATIONS INVOLVING FRACTIONAL QUANTITIES

In the present study, we describe a participating student’s (Carol’s) distributive partitioning scheme and operations along with Steffe’s and his colleagues’ studies about children’s constructions of fraction knowledge as a particular model of mathematical learning. Analysis of Carol’s mathematical behaviors indicates that an operationally common mathematical behavior (distributive partitioning operation) was revealed in various mathematical problem situations such as fraction multiplication, fraction division, and multiplicative transformation between fractional quantities. It both provides a rationale for why becoming versed in one mathematical subject could facilitate working with another mathematical subject and also implies the necessity of describing and defining students’ mathematical behaviors from an operational view of knowledge, which might lead to building foundations of a substantial cognitive map for students’ mathematical development.