This exploratory study applied two new cognitively sensitive measurement models to constructed-response quantitative data. The models, intended to produce qualitative characteristics of examinee performance, were fitted to algebra word problem solutions produced by 285 examinees taking the Graduate Record Examinations (GRE) General Test. The two types of response data modeled, error diagnoses and partial-credit scores, were produced by an expert system. Error diagnosis, analyzed using K. Yamamoto's (1989) Hybrid model, detected a class of examinees who tended to miss important pieces of the problem solution, but made relatively few errors of other types. Comparisons with matched examinees whose response patterns were better captured by the unidimensional item response theory model suggested subtle differences in error frequency rather than sharp qualitative distinctions. In contrast with the error data, partial-credit scores modeled using D. A. Rock's Hierarchically Ordered Skills Test (Rock and J. Pollack, 1987) procedure did not fit well, in part owing to limitations of the task theory being tested. Implications for the development of refined task and error theories, improvements to expert-system scoring procedures, and response modeling are discussed. Three figures and 11 tables present analysis results. Four appendixes present items, the scoring rubric, and information about bugs. (Contains 36 references.) (Author/SLD)