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Student modeling is useful in educational research and technology development due to a capability to estimate latent student attributes. Widely used approaches, such as the Additive Factors Model (AFM), have shown satisfactory results, but they can only handle binary outcomes, which may yield potential information loss. In this work, we propose a new partial credit modeling approach, PC-AFM, to support multi-valued outcomes. We focus particularly on the amount of assistance, that is, the number of error feedback and hint messages, a student needs to get a problem step correct. Because errors and hint requests may not only derive from student ability, but also from non-cognitive factors (e.g., students may game the system), we first test PCAFM on synthetic data where this source of variation is not present. We confirm that PC-AFM is indeed better than AFM in recovering the true student and knowledge component (KC) parameters and even predicts student error rates better than a model fit to error rates. We then apply the approach to six real-world datasets and find that PC-AFM outperforms AFM in reliable estimation of KC parameters and produces better generalization to new students, which requires better KC estimates. However, consistent with the hypothesis that student assistance behavior is driven by motivational or meta-cognitive factors beyond their ability, we found that PC-AFM was not better in reliable estimation of student parameters nor in generalization across items, which requires accurate student estimates. We propose "cross-measure cross-validation" as a general method for comparing alternative measurement models for the same desired latent outcome. [For the full proceedings, see ED615472.]

Computational models of learning can be powerful tools to test educational technologies, automate the authoring of instructional software, and advance theories of learning. These mechanistic models of learning, which instantiate computational theories of the learning process, are capable of making predictions about learners' performance in instructional technologies given only the technology itself without fitting any parameters to existing learners' data. While these so call "zero-parameter" models have been successful in modeling student learning in intelligent tutoring systems they still show systematic deviation from human learning performance. One deviation stems from the computational models' lack of prior knowledge--all models start off as a blank slate--leading to substantial differences in performance at the first practice opportunity. In this paper, we explore three different strategies for accounting for prior knowledge within computational models of learning and the effect of these strategies on the predictive accuracy of these models. [For the full proceedings, see ED599096.]