# Tracing Student Activity Patterns in E-Learning Environments: Insights into Academic Performance
## 2 Theoretical Background  
While autonomous and self-directed learning (SDL) seems to have early roots [18; 19], it was [PERSON] who brought it to the forefront of educational research in 1971 [20]. Following [PERSON], researchers such as [PERSON] [21], [PERSON] [22], and [PERSON] [23] defined autonomous and SDL as the process where the learners determine the pace and the path of their learning procedure and are responsible for their progress in a course. In the 1990s, efforts to define autonomy in learning revealed two distinct dimensions: the first dimension involves the process in which the learners are the leaders in executing and evaluating their educational path, with the educational institution possibly playing a facilitating role; the second dimension, refers to the autonomous learners' profile and focuses on their desire to take responsibility for their learning [18; 24]. A literature review has suggested that the degree of autonomy and the effectiveness of the students' SDL path is directly influenced by the characteristics of the educational framework to which they belong. In the year 2000, [PERSON] introduced the social cognitive model, which is the most widely embraced theoretical framework for assessing self-regulated learning [25; 26]. This model suggests that learners' motivation, cognitive functions, and strategies for self-regulated learning may vary based on the contextual features of the learning environment and the characteristics of the learning tasks. Consequently, external factors, such as course designs and Learning Management System (LMS) layout, have the potential to either facilitate or impede self-directed learning processes [27], subsequently influencing academic performance [26]. Researchers in learning analytics frequently gather and analyze trace data to comprehend students' learning behaviors by observing their navigation through courses, accessing resources, attempting quizzes, and completing assignments in their LMS [28]. The trace data collected from the learners' navigations are often associated with the learners' performance [29]. Studies indicate that learners who consistently engage with the learning environment often demonstrate higher academic achievement and stronger self-regulation [30]. Based on established research in online learning, there are advantages to integrating trace data from LMS logs for learner profiling [31; 32]. In the field of learning analytics, many studies have employed prediction techniques to establish learner profiles, correlate them with academic performance, and subsequently apply modern pedagogical strategies to support or address learner requirements. Markov model-based techniques prove to be valuable for analyzing data where sequence plays a crucial role. Extensive research has explored Markov Chain Models in various contexts, including predicting enrollments in education systems, forecasting students' performance in laboratory courses, modeling teachers' decision-making processes, and analyzing genetic algorithms [16; 17]. [PERSON] and [PERSON] [33] investigated the application of Markov chains in creating user profiles on eLearning-oriented web platforms in Portugal. They identified common patterns students follow when navigating through virtual learning environments containing educational resources. Their findings suggested that by analyzing user navigation patterns, coordinators and tutors can tailor platforms to better meet students' preferences and behaviors, thereby enhancing navigation and responsiveness to their needs. Similarly, [34] examined e-book reading patterns among students using Markov Chains, indicating potential for intervention systems for at-risk students through transition data and visualizations to evaluate content utilization. Moreover, [PERSON] and [PERSON] compared the standard six-year graduation rate method with a Markov Chain Model for estimating graduation rates in American universities [35].