DAS3H stands for Difficulty, student Ability, Skill, Student Skill practice History. It extends the DASH model, which showed better results than the Bayesian version of Item Response Theory (IRT). The original DASH model did not handle multiple skills item tagging and 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. Handles multiple skill tagging: $h_{\theta}$ now takes into account multiple skills.
2. For each item and skill, easiness parameters are estimated.
3. Logistic regression is replaced with Knowledge Tracing Machines (KTMs).

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

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, the probability of correctness for student $s$ on item $j$ at time $t$ depends on student ability ($\alpha_s$), item difficulty ($\delta_j$), the sum of skill easiness parameters ($\beta_k$), and the temporal distribution and outcomes of 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 the student in the time window $w$ earlier, and $a_{s, k, w}$ is the total amount of encountering KC $k$ at time window $w$ earlier.