Reported is a study to determine the relative effectiveness of a meaningful concrete and a meaningful symbolic model in learning a selected mathematics principle. Subjects were from a second grade population and they were assigned to three treatments. Students assigned to Treatment 1 received instruction in the principle with a meaningful symbolic model and students assigned to Treatment 2 received instruction in the principle with a meaningful concrete model. Students assigned to Treatment 3 did not participate in the instructional portion of the study. At the end of the instructional period, learning was evaluated by four tests that measured the dependent variables. The results indicated that children in this study were not able to generalize their learning to demonstrating a learned principle on an unfamiliar concrete device. Meaningful learning alone does not ensure that the application of a learned mathematical principle can be recognized. (RP)