The report is a review of research results which concern sequencing (procedures for validating the hypothesized ordering of the subordinate tasks in a learning hierarchy) and practical applications of learning hierarchies in instructional design. Indirect versus direct validation procedures are examined in detail. (Author)

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…

A hierarchy for learning to solve different types of addition with fractions problems was hypothesized on the basis of both content analysis and psychological considerations. Problem types were defined according to the relationship of the two denominators to each other (e.g., equal, prime, etc.) Students in grades 4 through 8 were each given 45…