The Emergence of Quotient Understandings in a Fifth-Grade Classroom: A Classroom Teaching Experiment.

This study investigates the development of 5th grade children's understanding of quotient and the classroom norms and practices that constrain or enable that understanding. It reports not only how the children's understandings develop, but also why and under what conditions they develop. The results of this study indicate that children progressed from treating fractions as exclusively part-whole to having at least two parallel conceptions: part-whole and fair share while at the same time beginning to conceive of the division operation as generalizable to any pair of whole numbers. Some children began to see the operation as generalizable to division by fraction. The general learning trajectory of the class is discussed. (KHR)