DAS3H stands for Difficulty, student Ability, Skill, Student Skill practice History. DASH is the model which they extend and it showed better results than the Bayesian version of IRT (Item Response Theory). This model didn't handle multiple skills item tagging. and additionally, it is assumed that "the impact of past practice on the probability of correctness does not vary across the skills." In DAS3H DASH is extended in the following ways:

1. Handle multiple skill tagging: $h_{\theta}$ now takes into account multiple skills.
2. For each item and skill easiness of the parameters are estimated.
3. Logistic regression is replaced with KTMs (Knowledge Tracing Machines)

DAS3H is formulated as (when embedding dimesion is 0): (1)$P (Y_{s, j, t} = 1) = \sigma (\alpha_s - \delta_j + \sum_{k \in KC(j)} \beta_k + h_{\theta} (t_{s, j, 1: l}, y_{s, j, 1: l-1} )$

The formula for $h_{\theta}$ is: (2)$h_{\theta}(t_{s, j, 1:l}, y_{s, j, 1: l-1}) = \sum_{k\in KC(j)} \sum_{w=0}^{W-1}\theta_{k, 2w + 1} \log (1 + c_{s,k, w}) - \theta_{k, 2w + 2} \log (1 + a_{s,k,w})$

In the first formula probability of correctness for student s,on item j at time t, depends on student ability ($\alpha_2$), item difficulty ($\delta_j$), sum of easiness $\beta_j$ and on the temporal distribution and the outcomes of the past practice which is expressed using $h_{\theta}$.

In the second formula, w is the index of the time window, $c_{s, k, w}$ is the amount of correctly remembered Knowledge Component (KC) k by student in the time window w earlier and $a_{s, k, w}$ is for the total amount of encountering Knowledge Component (KC) k at time window w earlier.