An Analysis of the Fragion Concept into a Hierarchy of Seleged Subconcepts and the Testing of the Hierarchical Dependencies

The fraction concept was analyzed into a set of 16 selected subconcepts, which were arranged into a hypothesized hierarchy. A Fraction Concept Test of 68 items, constructed to measure students' attainment of the 16 selected subconcepts was administered to 279 students in grades 4, 5, and 6. The data were analyzed by using two ratios to determine sequencing validity. 18 of the 23 dependencies in the hypothesized hierarchy were supported. On the basis of these results, it was concluded that certain stated subconcepts were prerequisite to others.