Fourth Graders Design a New Rod

This analytic describes the representations, reasoning, and justification used by students to express their understanding of fraction ideas while building solutions to a set of tasks. These tasks were introduced during the second session of a research intervention that was conducted over twenty-five sessions to study how students build fraction ideas prior to their introduction through the school’s curriculum. Of these sessions, seventeen were focused primarily on building basic fraction concepts including fractions used as operators, fractions as numbers, equivalence of fractions, comparison of fractions, and operations with fractions. Although students, prior to the fourth grade, were introduced to strong ideas related to fraction as operator, in this school district fraction operations were not a part of the 4th grade curriculum at that time. Rather, fraction operations were formally introduced in grade 5. The students in this class session investigated these ideas about fractions through a series of open-ended problem tasks. In this analytic, the researcher, Carolyn Maher, asks the students to design a rod that can be called one half when the blue rod is given the number name one. Erik and Alan discuss how an existing rod cannot be used, and other students suggest configurations of the new rod that could be designed to meet the specifications. In the whole class discussion Michael, David, Brian F., and Meredith discuss if it is possible to design a set of rods that contain a rod that can be called one half for any given rod that is called one