An Intraconcept Analysis of Rational Number Subtraction: A Validation Study.

The purpose of this study was: (a) to develop a learning hierarchy for rational number subtraction using intraconcept analysis, and (b) to validate that hierarchy using the Walbesser technique and pattern analysis. Skills required to complete tasks within the hierarchy were operationally defined and ordered from both a mathematical and psychological point of view. A test utilizing an item for each level in the hierarchy was administered to a sample of 200 children in grades four through eight. The final hierarchy generated and important implications for prescriptive instruction relative to subtraction of rationals are discussed. The specific tasks used in the study are appended. The initial hypothesized ordering of these tasks and the empirically determined hierarchy are presented. (Author/SD)