The development of a psychological hierarchy for learning density principles

This study was designed to determine if a task could be analyzed into behavioral components and these components ordered into a sequence in which they are learned. The terminal tasks involved the ability to apply specific gravity rules to determine whether materials would float or sink when placed in a liquid. A hierarchy of logical behavioral prerequisites was constructed. Each behavior in the logical hierarchy was evaluated with a short test designed to yield pass-fail data. Analysis of the results of each pair of tests in a four-fold table facilitated the ordering of behaviors. A series of ratios and a significant correlation coefficient between two behaviors were used to establish one behavior as prerequisite to another. The logical hierarchy was found to be not valid, and an empirical sequence was established based on the consistency ratio described by Walbesser and a necessity ratio defined by the investigator. It was demonstrated that two conditions were satisfied for each behavior in the sequence: (1) most subjects who possessed a behavior also possessed behaviors lower in the sequence, and (2) most subjects who did not possess a behavior did not possess a behavior higher in the sequence. Because several instances of behaviors with unexpected prerequisites were identified, the analysis of a logical hierarchy is considered a less effective procedure than comparison of results for each pair of tests. If all behaviors considered relevant to the terminal behavior are included in the testing sequence, construction of a complete logical hierarchy may not be necessary, since analysis procedures provide a basis for determining which behaviors are relevant to the sequence. Hierarchial analysis can and should be applied to other curriculum areas. Hierarchies with common elements can then be related to provide a valid basis for curriculum design.