We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification (local) and prediction of further performance (global). The inference algorithm has been employed in a student model for spelling with a detailed set of letter and phoneme based mal-rules. The local and global information about the student allows for appropriate remediation actions to adapt to their needs. The error classification, student model prediction and the efficacy of the adapted remediation actions have been validated on the data of two large-scale user studies. The enhancement of the spelling training based on the novel student model resulted a significant increase in the student learning performance. (Contains 6 tables and 17 figures.)