## 3 Methodology
### Data Collection and Description
For 2016-2 and 2017-1, most of the interaction happens on Week 7. The 2017-2 semester has the highest number of interactions, where the peak is found on Week 8. From the interactions, we generated thirteen datasets with different sets of derived attributes to compare the performances of the models. Table 2 shows the description of the attributes generated. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Semester** & \begin{tabular}{c} **Interaction** \\ **Count** \\ \end{tabular} & \begin{tabular}{c} **Average of** \\ **Interaction** \\ \end{tabular} & \begin{tabular}{c} **Students Approved** \\ \end{tabular} & \
\begin{tabular}{c} **Students Reproved** \\ \end{tabular} &
\begin{tabular}{c} **Total of Students** \\ \end{tabular} \\ \hline
2016-1 & 10,395 & 547.10 & 6 & 13 & 19 \\
2016-2 & 11,512 & 605.89 & 6 & 13 & 19 \\
2017-1 & 23,457 & 902.19 & 9 & 17 & 26 \\
2017-2 & 33,727 & 1,349.08 & 12 & 13 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of data. It is important to point out that each attribute in Table 2 is gathered at student level, that is, every calculation in based on data collected for each student. _Cognitive Count_, _Teaching Count_ and _Social Count_ are the counting of the Cognitive, Teaching and Social Presences presented in Swan [23]. \"Other count\" is a category created by us for all the other interactions that do not fit the three previously mentioned categories. In other words, the sum of these four types of interactions result in \(Count_{i}\) (Equation (1)). Table 3 presents how different interactions inside Moodle fall into the three types of presence evaluated in our work. \begin{table}
\begin{tabular}{c c} \hline
**Attribute** & **Description** \\ \hline Count & Interaction count for each week \\ \hline Average & Average of interactions on the week \\ \hline Median & Median of interactions on the week \\ \hline Zeroed weeks [50] & Number of weeks with zero interactions until the moment \\ \hline Average of the difference [50] & Average of the difference between interactions on week \(i\) and week \(i\)\(+\)\(1\) \\ \hline Commitment factor [50] & Ratio between the student’s week interactions and the average class interaction for that week \\ \hline Cognitive count [23] & Number of cognitive interaction on the week \\ \hline Teaching count [23] & Number of teaching interaction on the week \\ \hline Social count [23] & Number of social interaction on the week \\ \hline Other count & Number of other types of interaction on the week \\ \hline \end{tabular}
\end{table} 
Table 2: Description of the attributes. Figure 3: Interaction frequency distribution in each week for every semester. Students interactions are normally highly correlated to engagement in distance learning settings, reflecting the behaviour students have in relation the their course. According to [PERSON] [51], the interaction with content (cognitive presence), interaction with instructors (teaching presence) and interaction among peers (social presence) are the three kinds of interactivity that affect the learning process. Each of these interaction types supports learning and in practice, none of them works independently [23]. The idea of using these types of interaction is to better discriminate each type of interaction aiming to help on the generation of better predictive models, that better capture students behaviour in those learning settings. The implicit idea is that students who fail present different interactions in the different types of presence than students who succeed and that difference helps to generate better models. Following, we formalize every attribute contained in the datasets. \[Count_{i}=\sum_{j=1}^{7}x_{j}. \tag{1}\]  
Equation (1) represents the sum of interactions on every day \(j\) in each week \(i\).