# Analyzing Student Behavioral Patterns in MOOCs Using Hidden Markov Models in Distance Education
## 4 Discussion  
In this study, we propose a methodology that reveals the behavior patterns of students in a MOOC course. Analyzing student behavior is a challenging issue that enables tutors to design courses effectively. In recent years, many educational institutions have employed educational data mining. This occurs so that institutions to develop personalized learning tactics and improve learning outcomes based on learner profile modeling. For this purpose, we utilized HMMs to draw conclusions employing the R programming language. With this environment, we developed the Forward-Backward, Baum-Welch, and Viterbi algorithms in that order. In addition, charts have been constructed to visualize the information derived from our experiments. The dataset was found in Kaggle and it pertains to a MOOC involving 4037 students at the Technical University of Riga, Latvia. The scientist who deposited the dataset specializes in material science. We considered more interesting states from the log files as hidden states, forum_post_created, wiki_comment_created, quiz_attempt_submitted, among other relevant states.. The student IDs are enumerated from 1 to 4037 in ascending order, denoted as \(t\). With the Forward-Backward algorithm, the probability of a student ID belonging to a given state has been estimated. To make the computation feasible, the parameters \(\alpha\) and \(\beta\) were scaled. In the Baum-Welch step of the methodology, the magnitudes \(\gamma\) and \(\xi\) were calculated. This allows us to estimate the probability of the transitions from hidden states to the provided observed states. Moreover, the probability of two successive student IDs belonging to specific states is estimated. In addition, we calculated the transition and emission matrixes and plotted the transitions between states for some random students. Using the plots for the emission and transition matrixes, some estimations have been done. These are the achieved grades for each resource and the participation percentages across various resources of the course, respectively. Moreover, we applied the Viterbi algorithm to estimate the most likely sequence of consecutive states for the students. In comparison with [39], we consider the sequence of the students in ascending order rather than the time resolution to discover behavioral patterns by tracing the transitions of the students between states. In addition, the grades from the final exams are considered to be visible states, while the student transitions are considered to be observed states in [39]. We use the transition and emission matrixes to illustrate the transitions among states for the entire student population, and these transitions are visualized in charts. An application of the Baum-Welch algorithm and the Forward-Backward algorithms takes place to compute the posterior probabilities of transitioning from one state to another state. To find the most likely state sequence, we use the Viterbi algorithm. The transitions are depicted among states for some random users with directed graphs. Our approach differs because we consider the Markov property in a students' sequence rather than relying on the time resolution. We do not take into account other limitations like the [39] does. For example, we do not impose a time window based on active hours, nor do we perform any segmentation of the data, while in [39], the authors assume that each user is active within the same time window. The usefulness of the proposed methodology lies in its ability to help the instructors utilize its outcomes for a MOOC course. They become aware of the learners' behavior in the transitions among states in a clickstream dataset. Instructional designers, educators, and learning analytics practitioners can gain insights into the importance of resources, students' dedication, and their final achievements.