The Splitting Loope

Researchers have hypothesized that children’s construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors propose that splitting constitutes a psychological structure similar to that of a mathematical group (Piaget, 1970): a structure that introduces mutual reversibility of students’ partitioning and iterating operations that the authors refer to as the splitting loope. Findings from 66 sixth-grade students’ written performance on 20 tasks are consistent with hypotheses from related teaching experiments. They demonstrate that equipartitioning and the partitive unit fraction scheme mediate the construction of splitting from partitioning and iterating operations.