Diagnostic classification models (DCMs) hold great potential for applications in summative and formative assessment by providing discrete multivariate proficiency scores that yield statistically driven classifications of students. Using data from a newly developed diagnostic arithmetic assessment that was administered to 2032 fourth-grade students in Germany, we evaluated whether the multidimensional proficiency scores from the best-fitting DCM have an added value, over and above the unidimensional proficiency score from a simpler unidimensional item response theory model, in explaining variance in external (a) school grades in mathematics and (b) unidimensional proficiency scores from a standards-based large-scale assessment of mathematics. Results revealed high classification reliabilities as well as interpretable parameter estimates for items and students for the best-fitting DCM. However, while DCM scores were moderately correlated with both external criteria, only a negligible incremental validity of the multivariate attribute scores was found.