Seven forms of a programmed booklet based on an eleven-level hierarchy for addition of fractions were developed. One hundred forty-two fourth graders were randomly assigned to treatments; achievement, transfer, retention, and time were compared. No treatment was consistently superior, but developing sequences from hierarchies validated by test…

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…