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…

Empirical data relate to Bruner's and Ausubel's theories of learning concepts at different age levels. The concept of vector addition was taught to eighth, ninth, and tenth grade students. The concept was learned and retained by high ability ninth and all tenth grade students. (PS)