Analyzing Learning Hierarchies Relative to Transfer Relationships Within Arithmetic. Final Report.

The purpose of this study was to develop and evaluate procedures for validating a learning hierarchy from test data. An initial hierarchy for the computational skills of adding rational numbers with like denominators was constructed using Gagne's task analysis. A test designed to assess mastery at each of the 11 levels in this hierarchy was administered to a large sample of elementary school children. The pass-fail relationships from this test data were analyzed with seven learning hierarchy validation procedures, and seven hierarchical orderings of the 11 subtasks were determined. Fourth grade subjects, randomly assigned to seven treatment groups determined by the seven hierarchical orderings, worked 30 minutes a day on programmed materials until they were completed. Achievement tests measured acquisition of the terminal task. On the following day a transfer test on subtraction of rational numbers was administered. Two weeks later an alternate form of the achievement test was administered as a retention test. Results of the study indicate that sequence seems to have little effect upon immediate achievement and transfer. However, longer term retention seems quite susceptible to sequence manipulation. In general, the authors report that optimal instructional sequences can be devised using learning hierarchies validated from test data. (Author/JG)