The transition from whole numbers to rational numbers and the associated mastery of the multiplicative conceptual field constitute an important development in lower secondary schooling. This study draws primarily on the theory of conceptual fields as a framework that is mathematical and enables a cognitive perspective by identifying the concepts- and theorems-in-action that lead to underlying concepts and theorems. Application of the Rasch model configures the location of both item difficulty and learner proficiency on one scale. These insights permit teacher interventions specific to each learner subSet.