Major efforts of this project fall into four categories: (1) investigations were performed on the relationship between the dimensionality of a dataset and its underlying cognitive processes; (2) two approaches for diagnosing erroneous rules of operation were developed (an "error vector" system for constructing error diagnostic programs for signed-number arithmetic and fraction addition problems, and a series of logical statements for constructing diagnostic programs for fraction problems); (3) to circumvent the problems encountered in the construction of error diagnostic programs, two indices based on deterministic Guttman theory were formed and used to detect aberrant response patterns; and (4) the necessity for dealing quantitatively with variations in errors and changing rules of operation led to the investigation of probabilistic models for error diagnosis based on item response theory. (Author/PN)