# Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics
## 5 Application Case: First Engineering Courses
In particular, those backpacks with an average duration of much less than one semester (A, AC, ACDQ, ADQ, CQ, Q), show that a significant proportion of students who fall into this situation dropout without even retaking such courses or attempting to pass them. 1. most frequent backpacks. The BPPM model also allows us to compare the backpack trajectories that include specific backpacks. For the three most frequent backpacks: Q (464 cases), ACQ (458 cases) and A (456 cases), Figure 6 shows the proportion of educational trajectories, according to the BPPM model, that ended either in RETENTION or in DROPOUT. While there are differences in the proportion of students who dropped out for each backpack, in all cases the majority of students remained. Following, a more fine-grained analysis is presented, to illustrate the differences in the educational trajectories that include each backpack. Figure 7 shows the 90% most frequent variants of the students who had backpack A, ACQ and Q. Figure 7a shows that the vast majority (94.56%) of the students had backpack A as the first and the only backpack in their trajectories. Figure 7b shows that the backpack ACQ was the first backpack for all of these students. Most of those who dropped out (62 over 88) had direct transitions from ACQ to DROPOUT. In contrast, the majority of students who remained emptied their backpack after several stages. The institution could then encourage those students who have the ACQ backpack not to take such failed courses simultaneously by suggesting a certain sequence. In this case, the vast majority of students who defer the Q course remain. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Statistics** & **No BP** & **BP \& Retention** & **BP \& Dropout** \\ \hline Number of cases & 2504 & 1723 & 239 \\ Number of variants & 1 & 51 & 40 \\ Average number of BP events & 0 & 1.27 & 1.37 \\ Std. dev number of BP events & 0 & 0.52 & 0.62 \\ Mean time BP (days) & 0 & 237.74 & 131.80 \\ Std. dev time BP (days) & 0 & 183.71 & 178.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics for BPPM trajectories. Figure 7c shows that most students did not have the backpack Q as the first backpack, but they had it after passing one or more courses they had previously failed. This behavior could show a sort of prioritization of students who have multiple courses in their backpacks, postponing taking course Q. Furthermore, only a small minority of the students who had this backpack, ended in DROPOUT. This reinforces the idea that students who remain, and have failed a course, have given higher priority to courses other than Q. The institution should then analyze the possibility of postponing this course in the study plan. * size of the backpack. The BPPM-S model allows us to compare the educational trajectories across different backpack sizes. This study illustrates the comparison between backpack trajectories for students who dropout and students who remain, as well as the comparison between those that start with different backpack sizes. Figure 8a shows that backpack trajectories for students who manage to empty it. They mostly start with a backpack size of 1 or 2 and most students who start with a larger backpack, reduce its size before emptying it, going through BP-1. In addition, the average time that students spend with a given backpack size is longer than one semester (150 days, approximately). Figure 8b shows that most backpack trajectories for dropout students start with a larger backpack size. Moreover, for backpack sizes larger than 1, there are mainly direct transitions from the nodes to dropout. Figure 9 shows the proportion of students who dropped out or remained, grouping them according to the initial backpack size. Most students whose initial backpack size is less than 4 (BP-1, BP-2 and BP-3), emptied their backpack and remained in their undergraduate programs. 96.57% of students who started in BP-1, 92.63% of students who started in BP-2 and 74.69% of students who started in BP-3, ended in RETENTION.