# Analyzing Student Behavioral Patterns in MOOCs Using Hidden Markov Models in Distance Education
## 1 Introduction
To achieve this, we formulate the following research questions:  
1 st Research Question: Is it possible to identify a behavior model for a student or group of students given some observed and some hidden sequences? This question is addressed using the Forward-Backward, Baum-Welch, and Viterbi algorithms. 2 nd Research Question: Is it possible to determine the most likely sequence of transitions among Moodle states for a large number of students? We address this question by employing the Viterbi algorithm and utilizing the outcomes of Baum-Welch and Forward-Backward algorithms for a sample of 4037 students. We also propose two hypotheses in our methodology:  
**Hypothesis 1**. : _Students who achieve Grades 5 to 6 are treated similarly to those who pass the exams. As shown in Table 1 and Figure 1, the number of students who achieve Grades 4 to 6 is negligible._  
**Hypothesis 2**. : _Each student ID depends only on the previous student ID. This hypothesis allows us to apply the Markov property, enabling us to correlate a state with preceding states and a symbol with the preceding symbols (the symbol is the observed state, i.e., the grades)._  
The Markov processes, and specifically the Markov chains, assume that all states are fully observable, allowing us to know the sequence of the states. Markov chains use the Markov property in order to correlate a state with the preceding states in the sequence. This means that the value of a symbol depends on the value of the previous symbol, not on the complete entire sequence. When the data of the state sequence accessed by the process is unknown and can only be inferred by a sequence of observations, these partially observable Markov processes are referred to as Hidden Markov Models (HMMs). In the following paragraphs, we report some related work that pertains to MOOCs and the Hidden Markov Models. The authors of [7] simulate MOOC students before performing a large-scale experiment on real students. They use Markov chains to model student activities and the Expectation Maximization algorithm to fit the model. Moreover, the k-means algorithm with the elbow method is employed to cluster MOOC students into different groups. In [8], the authors build knowledge during a MOOC, examining activities and weekly progress to explore learning paths and adapt the course accordingly. An application exists in [9] that concerns methodologies like HMMs to analyze student behaviors and associate these behaviors with students' final performance, utilizing data from log files. In [10], there is a presentation of various behavioral patterns in the problem-solving domain, applying automated clustering to detect patterns and comparing these patterns with those from previous studies in the literature. The authors of [11] consider student engagement and active participation as critical success factors. To this end, they propose a flipped MOOC, which provides a personalized,interactive, and engaging learning environment. The MOOCs can be further enhanced with gamification and learning analytics. The high attrition rate in MOOCs is examined in [12]. Pedagogy and learning design are identified as the main factors influencing learner engagement patterns. Some students work intensively for one week, while others study at a steady pace. Additionally, some students briefly visit the course to sample content, while others fully complete it. The authors have used clustering techniques to analyze these engagement patterns. According to [13], student behavior patterns are discovered using a tutoring system. The authors categorize, interpret, and bin the student actions during the sessions with symbols. This approach allows the authors to discover recurring patterns and describe frequent tutor events using a motif-discovery algorithm. The resulting motifs are characterized and sorted as student behaviors. In [14], a method is proposed to characterize MOOC sessions through habitual behavior pattern mining. These behaviors are related to the level of success in the course, whether higher or lower.