# Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## Featured Application

**In this work, Process Mining techniques are used with a curricular analytics approach, to model the educational trajectories of engineering students during their first courses.**

## Abstract

## 1. Introduction

## 2. The Backpack Metaphor

## 3. Related Work in Process Mining

^{2}[33]. Both methodologies have a broad scope, covering the entire process management cycle [34]. Different authors have proposed domain-specific methodologies that take into account the particularities of each domain. For education, Maldonado-Mahauad et al. [35] adapted PM

^{2}, narrowing its scope from data extraction to model analysis. Johnson et al. [36] extended PM

^{2}to include domain-specific requirements in healthcare, in terms of ethics and participation of domain experts, among other things. Martin et al. [29] established that a process mining methodology in healthcare should highlight usability, in the building of domain-specific event logs and in the management of unstructured data. In manufacturing, Lorenz et al. [37] proposed a methodology with a scope that included the improvement of the processes.

^{2}, which is widely used, and its scope goes only from data extraction to model analysis. The main contribution of this work is not the sequence of stages in the methodology, but the approach used to understand the curricular trajectories through the backpack metaphor.

## 4. The Backpack Process Model (BPPM) Approach

#### 4.1. Data Extraction

- -
- s indicates the ID of the student who took the course
- -
- p the academic period when the course was taken
- -
- c the identifier of the course taken
- -
- g the final grade obtained
- -
- d the end date of the academic period.

#### 4.2. Event Log Generation

_{1}, b

_{2}, … b

_{n}>; and (2) a b

_{i}event is defined as the record of the group of failed courses that the student must retake at the end of academic period i. For example, for the student identified with s = 23 in Table 2, <AQ, Q, -> represents their backpack trajectory and graphically it can be seen in Figure 3. In his/her first academic period (for example, semester), this student had failed algebra (A) and chemistry (Q) and therefore must retake them. In their second period the student must still retake chemistry (either because the student took it and failed it again or because the student decided not to take the course in the second period) and finally, after the third academic period, the student does not have courses that should be retaken.

_{i}; b

_{i+1}; …; b

_{i+n}; …> where b

_{i}= b

_{i+1}= … = b

_{i+n}, will result in a case <… b

_{i:i+n}…>, where backpack b

_{i:i+n}ranges from period i to period i + n.

_{i:i+n}event was labeled with BP-j, where j represents the size of the backpack. For example, the case represented by <AQ, Q, RETENTION>, was replaced by <BP-2, BP-1, RETENTION> in the BPPM-S event log.

#### 4.3. Discovery

#### 4.4. Analysis

## 5. Application Case: First Engineering Courses

- (P1)
- BPPM trajectories ending either in retention or in dropout

- (P2)
- most frequent backpacks.

- (P3)
- size of the backpack.

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Example of educational trajectories, according to the BPPM and BPPM-S models. (

**a**) Shows an example of BPPM. (

**b**) Shows an example of BPPM-S. The darker color of the nodes represents a higher percentage of students who went through each state. The thickness of the arrows represents the percentage of students who had transitions between both states. All values are percentages in relation to the total number of students included in each model.

**Figure 2.**Stages for the generation of the process model, based on an adapted version of PM

^{2}methodology [35].

**Figure 3.**Graphical representation of the sequence of backpacks for the student with s = 23, shown as an example in Table 2, according to the BPPM model.

**Figure 4.**Percentage of educational trajectories, according to the BPPM model, that started with each backpack. The graph considers only the most frequent variants for each model, corresponding to 80% of the students. The RETENTION column considers only students who had a backpack and emptied it (1383 cases, seven more frequent variants). The DROPOUT columns consider only students who had a backpack, were not able to empty it and finally dropped out (199 cases, 13 more frequent variants).

**Figure 5.**Average time (in days) that the students stay in each backpack. The graph considers only the most frequent variants for each model, corresponding to 80% of the students. The RETENTION columns consider only students who had a backpack and emptied it. The DROPOUT columns consider only students who had a backpack, were not able to empty it and finally dropped out.

**Figure 6.**Proportion of educational trajectories, according to the BPPM model, that includes each one of the three most frequent backpacks (Q, ACQ and A) and end either in RETENTION or in DROPOUT.

**Figure 7.**Educational trajectories, according to the BPPM model, which includes the three most frequent backpacks, showing only the most frequent variants, which correspond to 90% of the students in each case. (

**a**) Shows backpack trajectories that include the A backpack. (

**b**) Shows backpack trajectories that include the ACQ backpack. (

**c**) Shows backpack trajectories that include the Q backpack. The darker color of the nodes represents a higher percentage of students who went through a state. The thickness of the arrows represents the percentage of students who had transitions between both states. All values are percentages in relation to the total number of students included in each model.

**Figure 8.**Educational trajectories, according to the BPPM-S model. (

**a**) Shows only students who had a backpack and emptied it. (

**b**) Shows only students who had a backpack, were not able to empty it and finally dropped out. The darker color of the nodes represents a higher percentage of students who went through a state. The thickness of the arrows represents the percentage of students who had transitions between both states. All values are percentages in relation to the total number of students included in each model.

**Figure 9.**Number and proportion of students who, according to the BPPM-S model, either finished in RETENTION or in DROPOUT, grouped according to the initial backpack size.

**Figure 10.**Educational trajectories that ended in DROPOUT, according to the BPPM-S model. (

**a**) Shows only students who started with only one course in the backpack. (

**b**) Shows only students who started with two courses in the backpack. (

**c**) Shows only students who started with three courses in the backpack. (

**d**) Shows only students who started with four courses in the backpack. The darker color of the nodes represents a higher percentage of students who went through a state. The thickness of the arrows represents the percentage of students who had transitions between both states. All values are percentages in relation to the total number of students included in each model.

Student ID | Backpack | Starting Date | Ending Date |
---|---|---|---|

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 |

Student ID (s) | Period (p) | Course (c) | Grade (g) | Ending Date (d) |
---|---|---|---|---|

23 | 2013-1 | Algebra (A) | 2.0 | 1 July 2013 |

23 | 2013-1 | Chemistry (Q) | 3.5 | 1 July 2013 |

23 | 2013-1 | Calculus (C) | 4.5 | 1 July 2013 |

23 | 2013-1 | Innovation (D) | 5.5 | 1 July 2013 |

23 | 2013-2 | Algebra (A) | 3.4 | 1 December 2013 |

23 | 2013-2 | Chemistry (Q) | 5.0 | 1 December 2013 |

23 | 2013-3 | Algebra (A) | 6.5 | 1 February 2014 |

24 | 2013-1 | Algebra (A) | 5.5 | 1 July 2013 |

24 | 2013-1 | Chemistry (Q) | 3.5 | 1 July 2013 |

24 | 2013-1 | Calculus (C) | 4.5 | 1 July 2013 |

24 | 2013-1 | Innovation (D) | 6.0 | 1 July 2013 |

24 | 2013-2 | Chemistry (Q) | 3.8 | 1 December 2013 |

Model | Perspective | Node Type | Transition Type | Filters | Figure |
---|---|---|---|---|---|

BPPM | (P1) Final event (DROPOUT or RETENTION) | Number of students | Number of students | Final state: RETENTION; DROPOUT Does not include initial state RETENTION More frequent variants: 80% | Figure 4 |

average time | Number of students | Final state: RETENTION; DROPOUT Does not include initial state RETENTION More frequent variants: 80% | Figure 5 | ||

(P2) Most frequent backpacks | Number of students; % students | Number of students | Does include state A; ACQ; Q Final state: RETENTION; DROPOUT | Figure 6 | |

Number of students | Number of students; % students | Does include state A More frequent variants: 90% | Figure 7a | ||

Number of students; average time | Number of students; % students | Does include state ACQ More frequent variants: 90% | Figure 7b | ||

Number of students; average time | Number of students; % students | Does include state Q More frequent variants: 90% | Figure 7c | ||

BPPM-S | (P3) Size of the backpack | Number of students; average time | Number of students; % students | Final state: RETENTIONDoes not include initial state RETENTION | Figure 8a |

Number of students; average time | Number of students; % students | Final state: DROPOUT | Figure 8b | ||

Number of students; % students | Number of students | Initial state: BP-1; BP-2; BP-3; BP-4Final state: RETENTION; DROPOUT | Figure 9 | ||

Number of students; average time | Number of students; % students | Initial state: BP-1 Final state: DROPOUT | Figure 10a | ||

Number of students; average time | Number of students; % students | Initial state: BP-2 Final state: DROPOUT | Figure 10b | ||

Number of students; average time | Number of students; % students | Initial state: BP-3 Final state: DROPOUT | Figure 10c | ||

Number of students; average time | Number of students; % students | Initial state: BP-4 Final state: DROPOUT | Figure 10d |

Statistics | No BP | BP & Retention | BP & Dropout |
---|---|---|---|

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 |

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**MDPI and ACS Style**

Salazar-Fernandez, J.P.; Munoz-Gama, J.; Maldonado-Mahauad, J.; Bustamante, D.; Sepúlveda, M.
Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics. *Appl. Sci.* **2021**, *11*, 4265.
https://doi.org/10.3390/app11094265

**AMA Style**

Salazar-Fernandez JP, Munoz-Gama J, Maldonado-Mahauad J, Bustamante D, Sepúlveda M.
Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics. *Applied Sciences*. 2021; 11(9):4265.
https://doi.org/10.3390/app11094265

**Chicago/Turabian Style**

Salazar-Fernandez, Juan Pablo, Jorge Munoz-Gama, Jorge Maldonado-Mahauad, Diego Bustamante, and Marcos Sepúlveda.
2021. "Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics" *Applied Sciences* 11, no. 9: 4265.
https://doi.org/10.3390/app11094265