# An Early Warning System to Detect At-Risk Students in Online Higher Education
## 6 Case Studies: Computer Fundamentals and Databases
### Performance of GAR Model  
CF course has four assessment activities starting during the semester timeline at 0% (AA1), 25% (AA2), 50% (AA3) and 75% (AA4) approximately. The formula to compute the final mark (FM) is:  
\[\begin{array}{c}FM=MAX(10\%\ Grade_{AA1}+10\%\ Grade_{AA2}+10\%\ Grade_{AA3}+35\%\ Grade_{AA4}+35\%\ Grade_{EXAM},\\ 50\%\ Grade_{AA4}+50\%\ Grade_{EXAM})\end{array} \tag{4}\]  
where \(\ Grade_{AAn}\) is the grade of the assessment activity AAn and \(\ Grade_{EXAM}\) is the grade of the final exam. The AA4 (which is a practical assessment activity) and the EXAM are mandatory, and they have a significant impact on the final score. Note that, the course can be even passed without performing the three first activities. However, the teachers know by experience that it is difficult to pass the course without the first three activities where fundamental topics are learnt. Thus, most of the students pass the course by completing the four activities.  
In the case of DB course, five assessment activities are delivered during the semester timeline at 0% (AA1), 20% (AA2), 40% (AA3), 60% (AA4), and 80% (AA5), approximately. AA2, AA3, and AA5 are practical activities that deal with SQL concepts (basic SQL statements, triggers, and storedprocedures, and JDBC, respectively). The final mark (FM) in the DB course is computed as follows. First, a global mark for the practical assessment activities (GradeP) is computed. In case the student delivers AA2, AA3, and AA5, the two best grades are selected, and GradeP is computed as the average of both grades. Otherwise, the average of the two submitted practical activities is the global mark for the practical assessment activities. Secondly, the final mark for the course (FM) is:  
\[\begin{array}{c}FM=MAX(32.5\%\ Grade_{EXAM}+32.5\%\ Grade_{P}+21\%\ Grade_{AA1}+14\%\ Grade_{AA2},\\ 50\%\ Grade_{EXAM}+50\%\ Grade_{P})\end{array} \tag{5}\]  
Students must perform at least two of three practical activities (AA2, AA3, and AA5) and the final exam (EXAM) in order to pass the course. Although AA1 and AA2 are optional, most of the students pass the course by completing these optional activities too, similarly to CF.  
Table 4 shows the performance of the GAR model for both courses. For each submodel, _TP, FP, TN, FN_, and the accuracy metrics _ACC, TNR, TPR_, and \(F_{1,5}\) are summarized. The table also shows the best algorithm (_Algorithm_) and the last semester for the training set (_Semester_) that was used to train each submodel (as detailed in Section 4.2). Although, in the case of CF the first submodel (which corresponds to the AA1) is considered a low-quality model for detecting non-at-risk students (i.e., TNR smaller than the threshold of 75%), the quality is good for the rest. In the case of DB, the accuracy is very good from the very beginning of the course in the detection of the students that are likely to pass the course (TNR begins at 89.53%). That means that the grade for AA1 is a very good indicator to predict success in DB. However, the submodel still does not predict correctly students that may fail the course (TPR is 68.18%). This fact is very different in the CF course, where the students at-risk are detected from the AA1 (TPR 82.83%).