Presents a framework for analyzing what it means to understand an intellectual skill, particularly in science or mathematics: (1) types of knowledge, (2) knowledge associated with intellectual skills, (3) classification system for this knowledge, (4) application of the system to two protocols, and (5) instructional prescriptions. Gagne's learning…

The compound nature of Gagne's original definition of learning hierarchies leads to two methods of validation, the positive and negative methods. Sections of a hierarchy that had been validated by the negative method were subjected to test by the more cumbersome positive method, and again were found to be valid. (Author/RD)

A correspondence exists between a simplified data collection method employing results from a post test for graphic skills in kinematics, and a rigourous validation method. Examination of test responses for discrepant instances yielded further information of value. Hierarchical patterns of learning and remembering are identical. (Author/CP)