# Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics
## 4 The Backpack Process Model (BPPM) Approach  
This section proposes the Backpack Process Model (BPPM) approach, in order to systematize the analysis of curricular trajectories using PM techniques, based on the backpack metaphor. This model represents the curricular trajectories of the students as a sequence of failed courses that they must retake; that is to say, as a sequence of backpacks. This sequence of backpacks is represented as a Directly Follows Graph (DFG), one of the most popular and widespread process modeling notations [31]. A DFG is a graph with nodes and transitions (directed edges) that corresponds to directly follows relationships (see Figure 1) [31]. In the BPPM, each node represents the group of failed courses that the student must retake and each edge represents the transition between a given backpack and the next one. Table 1 shows the backpack trajectories for two students, namely 23 and 24. In this example, student 23 failed algebra (A) and chemistry (Q) in the first semester, beginning the following semester with both courses in his/her backpack. This situation is labeled \"AQ\" in Table 1. The second semester, this student passed chemistry (Q) but failed algebra (A) again, keeping it in his/her backpack. Finally, this student passed algebra (A) and continued studying with an empty backpack. This situation is tagged with \"RETENTION\" in the event log. On the contrary, student 24 failed chemistry (Q), maintained it in the backpack for one semester and the next semester dropped out. This situation is tagged with \"DROPOUT\" in the event log. Figure 1 represents the DFG for the backpack trajectories illustrated in Table 1.  
Additionally, our analysis considers a derivation of this model, called BPPM-S (BPPM, grouped by size), where curricular trajectories are represented as a sequence of backpack sizes for each academic period. Figure 1 represents the DFG for the backpack trajectories included in Table 1, according to the BPPM-S. In Figure 1, BP-1 and BP-2 represent the backpack size at the end of a semester; that is, the number of courses students failed and have not yet passed. BP-1 indicates a backpack size of 1, while BP-2 indicates a backpack size of 2. More details on the meaning of nodes and transitions shown in Figure 1 are explained later, in the event log generation subsection.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Student ID** & **Backpack** & **Starting Date** & **Ending Date** \\ \hline
23 & AQ & 1 July 2013 & 1 December 2013 \\
23 & A & 1 December 2013 & 1 February 2014 \\
23 & RETENTION & 1 February 2014 & 1 February 2014 \\
24 & Q & 1 July 2013 & 1 December 2013 \\
24 & DROPOUT & 1 December 2013 & 1 December 2013 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Example of event log for BPPM.  
In order to develop the previously proposed analysis models from the curricular records of a HEI, it is necessary to apply a PM methodology. An appropriate methodology, such as the one presented below, allows to apply PM techniques and to understand the results [33]. This methodology, as can be seen in Figure 2, defines the following four stages: Data extraction, event log generation, discovery and analysis.