in three downstream tasks: knowledge mapping, difficulty estimation, and score prediction.

Assessment Modeling
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Formal Definition of Assessment Modeling
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![The relationship of features predicted in general AIEd tasks, knowledge tracing and assessment modeling. Assessment modeling predicts the distribution of assessments, the subset of interactive features which can act as pedagogical evaluation criteria. Note that predicting an exam score (`exam_score`), a grade (`grade`) and whether a student will pass to get a certificate (`certification`) are tasks outside knowledge tracing.[]{data-label="fig:am_def"}](assessment_def.pdf){width="50.00000%"}

Recall that knowledge tracing is the task of modeling a student’s knowledge state based on his/her learning activities over time. Although the task is considered as fundamental and studied extensively over time, it has not been defined formally and explicitly in existing literature. In this subsection, we first define knowledge tracing in a form that is quantifiable and objective from a particular IES design. Subsequently, we introduce the definition of assessment modeling that addresses the educational values of the label being predicted.

A learning session in IES consists of a series of interactions $[I_{1}, \dots, I_{T}]$ between a student and the system, where each interaction $I_{i} = \{f_{i}^{1}, \dots, f_{i}^{n}\}$ is represented as a set of features $f_{i}^{k}$ automatically collected by 