# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 1 Introduction  
Smart Learning Environments (SLEs) [1] combine educational technologies, ubiquitous learning, and learning analytics, among others. One of the objectives of SLEs is to provide more information (e.g., through dashboards [2]) about students' behaviors and performance, such as their progress in the course. With this information, it is possible to develop systems that can provide adaptative and personalized learning experiences (e.g., provide adaptable materials or scaffolding questions if needed, as in Intelligent Tutoring Systems [3]) and feedback/support [4, 5]. Another possible use of SLEs is to detect situations in which to intervene (e.g., to detect students with difficulties, such as risk of dropout, failure, lack of engagement or motivation, etc.) [6]. Online and blended learning can also benefit from SLEs, as digital platforms can collect many information about students' performance, behaviors and possible difficulties. Among the possible student difficulties, low persistence can be an issue to pay attention to. Persistence is a personality feature [7], but it can be defined in different manners in different contexts even in the educational area. In the educational context, several articles consider persistence as the fact of staying/continuing a degree to complete it (e.g., [8; 9]), thus close to be the opposite for the concept of dropout. For example, [PERSON] et al. [10] considered students were persistent when they enrolled in the following spring semester. [PERSON] et al. [11], in contrast, analyzed persistence at course level in an online context and they considered that students were persistent when they interacted with the course at least once a week. Similarly, [PERSON] et al. [12] defined three levels of persistence (low, medium and high) depending on how many weeks students had worked in the course. Regardless of the scope of this definition of persistence (at the course or degree level), this definition of persistence aims to capture to what extent a student keeps on doing an activity in a long period (e.g., course/degree). This type of definition of persistence is related to activities that last for a long time and it does not explicitly consider the difficulties during the learning process (e.g., specific difficulties that occur throughout the course or degree). As this definition of persistence comprises a long period that can be subdivided for analyzing persistence (degrees can be subdivided in semesters and courses in weeks), we will refer to this definition as \"global persistence\". However, for many other authors (e.g., [13; 14]), persistence is considered as a synonym of perseverance so that a student is considered persistent when s/he keeps on working on a task (e.g., an exercise) after trying to solve it incorrectly [13]. In this case, persistence can be measured using data from individual exercises. Because of that, we will refer to this type of persistence as \"local persistence\". However, local persistence is not computed for each individual exercise, but an overall value of student persistence is computed for a set of exercises. Local persistence has not been addressed as many times as the \"global persistence\", but it can also be relevant as some researchers have shown that being persistent at the local level can lead to better performance. For example, [PERSON] et al. [7] found that local persistence could be useful to predict grades, although self-regulated learning, which can also be related to local persistence [7], and engagement variables achieved higher predictive power. However, high values of local persistence are not necessarily good because if there is no reflection after trying to do a task incorrectly, learning might be only superficial [15]. Nevertheless, from an analytical point, a low local persistence can also be negative since it shows that students lack the ability to face the problems associated with the tasks they have to do.