# Predicting Student Grades Based on Their Usage of LMS Moodle Using Petri Nets

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### The Basic Concept of Petri Nets

- P = {p
_{1},p_{2},…,p_{m}} is a finite set of places. A place represents a circle, such as p_{1},p_{2}and p_{3}in Figure 1. - T = {t
_{1},t_{2},…,t_{n}} is a finite set of transitions. A transition represents a bar, such as t_{1}in Figure 1. The intersection of P and T is an empty set, while the union of P and T is not an empty set, i.e., P∩T = ∅ and T∪P ≠ ∅. - A⊆(PxT)∪(TxP) is a set of arcs connecting places and transitions, such as the arrowhead from p
_{1}to t_{1}depicted in Figure 1. - W:A→{1,2,3,…} is a weight function, whose weight value is positive integers. Arcs, i.e., arrowhead, are labeled with weights. For example, in Figure 1, the arrowhead from t
_{1}to p_{3}, which is labeled with “2”, is denoted as W(t_{1},p_{3}) = 2. When the weight is unity and/or “1”, the label of arc is usually omitted, e.g., W(p_{1},t_{1}) = 1 is omitted in Figure 1. - M
_{0}:P→{0,1,2,3,…} is the initial marking. If there are k tokens inside place p_{i}, it is said that p_{i}is marked with k tokens. For example, in Figure 1a, p_{1}is marked with one token, which is denoted as M(p_{1}) = 1. p_{2}is marked with two tokens, which is denoted as M(p_{2}) = 2. If Figure 1a is the initial status, the initial marking is denoted as M_{0}(p_{1},p_{2},p_{3}) = {1,2,0}.

_{i}are marked with at least W(p

_{i},t) tokens, where W(p

_{i},t) is called the firing condition of transition t. For example, in Figure 1, the firing conditions of t

_{1}are W(p

_{1},t

_{1}) = 1 and W(p

_{2},t

_{1}) = 2.

_{i},t) tokens from each input place p

_{i}and adds W(t,p

_{j}) tokens to each output place p

_{j}. For instance, since M(p

_{1}) = 1 and M(p

_{2}) = 2 have satisfied the firing conditions of t

_{1}in Figure 1a, t

_{1}is fired. After t

_{1}is fired as Figure 1b depicts, t

_{1}has removed W(p

_{1},t

_{1}) = 1 token from input place p

_{1}of t

_{1}and W(p

_{2},t

_{1}) = 2 tokens from input place p

_{2}of t

_{1}, respectively, and then added W(t

_{1},p

_{3}) = 2 tokens to output place p

_{3}of t

_{1}[16].

## 3. Materials and Methods

- A design of student behavior models in a virtual learning environment, i.e., study of materials in individual parts of the course, models of logical functions, loop models, condition models, deadlocks, etc. that could simulate the student behavior in the virtual education system and its subsequent rating.
- After creating the appropriate educational models, it was possible to create a new e-course and test it with the models created for the e-course.
- A creation of an e-course from the proposed Petri Network models.
- After result evaluation of the real e-course using models designed for the e-course, it was possible to find out which parts of the e-course were most used for study and especially which parts contributed the most to the better grades of the students.

#### 3.1. Modeling Uncertainty with Petri Nets

_{0}was the weight of the firing transition and, w

_{i}was the weight of the i-th active transition. In the case of the parallel models of Figure 5, the probability of the final state depended on the combination of the final state probabilities of all concurrent models.

_{0}was the weight of the first transition, and w

_{3}was the weight of the second transition, where both could fire simultaneously without deactivating each other. w

_{0i}and w

_{3j}were the weights of the i-th and j-th group of active transition, where the firing of one deactivated others. The transitions for which firing of one deactivated the others were called the group of transitions of transition T. The weight of this transition was called w and the weights of transitions from the group were called w

_{s}. Therefore, the previous formula could be generalized to:

_{i}was the transition weight of the transition group that fired during this step, and w

_{ij}was the transition weight from the transition group Ti. The formula only worked where the models were concurrent and independent. If models were linked, other formulas needed to be used. In this case, the problem was the increasing number of possible combinations of active transitions. For the example in Figure 6, it was necessary to use two different types of formulas for two different activation options.

_{n}was the weight of the dependent transition, w

_{ij}was the weight of the independent transition, and w

_{ik}was the weights of the transition from group Ti.

_{i}was the weight of the i-th independent transition, w

_{ij}was the weight of all independent transitions from transition group Ti, and w

_{k}was the weight of the dependent transitions.

_{i}was the number of transitions that were active for each state acquired from the state [29].

#### 3.2. Observing Student Movement in LMS

- Time
- User name
- Affected user
- Event context
- Component
- Event name
- Description
- Source
- IP

_{0}and the user’s current URL was t, then this page was considered as one session if the inequality t − t

_{0}≤ θ was true. While for the next page, it was inequality t

_{0}+ θ > t.

## 4. Results and Discussion

#### 4.1. Model of the Final Exam in Petri Nets

#### 4.2. Model of Grade Prediction

_{a}was the weight of the fired transition, w

_{i}was the weight of the i-th transition, n was the number of active transitions, and p was the final probability.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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Visits | 0..4 | 5..12 | 13 | 14..17 | 18..29 | 30..56 |

Students | 22 | 18 | 6 | 2 | 6 | 4 |

A | 0 | 5 | 2 | 0 | 2 | 4 |

B | 2 | 1 | 2 | 0 | 4 | 0 |

C | 6 | 4 | 1 | 2 | 0 | 0 |

D | 4 | 1 | 1 | 0 | 0 | 0 |

E | 6 | 1 | 0 | 0 | 0 | 0 |

FX | 4 | 0 | 0 | 0 | 0 | 0 |

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**MDPI and ACS Style**

Balogh, Z.; Kuchárik, M.
Predicting Student Grades Based on Their Usage of LMS Moodle Using Petri Nets. *Appl. Sci.* **2019**, *9*, 4211.
https://doi.org/10.3390/app9204211

**AMA Style**

Balogh Z, Kuchárik M.
Predicting Student Grades Based on Their Usage of LMS Moodle Using Petri Nets. *Applied Sciences*. 2019; 9(20):4211.
https://doi.org/10.3390/app9204211

**Chicago/Turabian Style**

Balogh, Zoltán, and Michal Kuchárik.
2019. "Predicting Student Grades Based on Their Usage of LMS Moodle Using Petri Nets" *Applied Sciences* 9, no. 20: 4211.
https://doi.org/10.3390/app9204211