Maddie\u27s Units Coordinating Across Contexts

Units coordinating has emerged as an important construct for understanding students’ mathematical thinking, particularly their concepts of multiplication and fractions. We conducted an eleven-session constructivist teaching experiment with a pair of sixth-grade students to investigate how children coordinate whole number and fractional units across quantitative contexts. In this paper, we focus on one student, Maddie, who was assessed as reasoning with three levels of whole number units at the onset of the teaching experiment. We illustrate Maddie\u27s units coordinating with fractional units over the course of the teaching experiment: it began with incorrect responses that indicated she had yet to coordinate three levels of fractional units; it progressed through her coordination of three levels of fractional units in situations for which she had a tangible referent for partitioning. We describe how students’ ways of experiencing quantitative situations are important considerations in their development of units coordinating structures