# A Scoring Algorithm for the Early Prediction of Academic Risk in STEM Courses
## 4 Overview of the Variables Used in the Analysis
The first midterm takes place in week 5, the second in week 11, and the third in week 16. The results of the third midterm were not included in the analysis, as they were obtained at the very end of the semester and are therefore not relevant for the development of an early identification system. In addition to the midterms, students take four short bonus tests throughout the semester. These tests provide the opportunity to earn up to 5 additional points, helping students improve their midterm results. The bonus tests are administered at weeks 4, 7, 10, and 13. The variables _Colloquium 1_ and _Colloquium 2_ denote the percentage of points obtained in the first and second midterm exams, respectively. The variables _Test 1_, _Test 2_, _Test 3_, and _Test 4_ record the percentage of points earned in the corresponding bonus tests. Descriptive statistical indicators for these variables are presented in Table 4.  
The results in Table 4 show that students performed significantly better on the first midterm exam (Mean = 0.72, Median = 0.80) compared to the second midterm exam (Mean = 0.44, Median = 0.38), indicating a decrease in performance as the semester progressed. Furthermore, while the first and last tests had relatively higher mean and median scores, intermediate tests show notably lower averages, suggesting that many students either did not attempt these tests or struggled to achieve points. Data on previous mathematical knowledge, collected through a questionnaire, together with the corresponding variables, are presented in Table 5. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Week** & **Variable** & **Mean (Std Dev)** &
\begin{tabular}{c} **Median** \\ **(Min-Max)** \\ \end{tabular} \\ \hline Week 4 & _Test 1_ & 0.46 (0.38) & 0.55 (0.00–1.00) \\ Week 5 & _Colloquium 1_ & 0.72 (0.24) & 0.80 (0.00–1.00) \\ Week 7 & _Test 2_ & 0.11 (0.25) & 0.00 (0.00–1.00) \\ Week 10 & _Test 3_ & 0.11 (0.25) & 0.00 (0.00–1.00) \\ Week 11 & _Colloquium 2_ & 0.44 (0.25) & 0.38 (0.00–0.94) \\ Week 13 & _Test 4_ & 0.61 (0.45) & 0.90 (0.00–1.00) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistical indicators for the variables _Colloquium 1_, _Colloquium 2_, _Test 1_, _Test 2_, _Test 3_, and _Test 4_. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Week** & **Mean (Std Dev)** & **Median (Min–Max)** \\ \hline Week 1 & 0.00 (0.00) & 0 (0–0) \\ Week 2 & 0.00 (0.00) & 0 (0–0) \\ Week 3 & 4.33 (11.24) & 0 (0–51) \\ Week 4 & 23.92 (40.35) & 4 (0–203) \\ Week 5 & 7.61 (21.33) & 0 (0–152) \\ Week 6 & 3.75 (14.21) & 0 (0–95) \\ Week 7 & 7.43 (17.19) & 0 (0–96) \\ Week 8 & 2.18 (14.26) & 0 (0–122) \\ Week 9 & 3.96 (22.42) & 0 (0–193) \\ Week 10 & **24.51** (45.22) & **0 (0–200)** \\ Week 11 & 17.75 (46.06) & 0 (0–342) \\ Week 12 & 8.50 (33.79) & 0 (0–255) \\ Week 13 & 3.38 (12.17) & 0 (0–72) \\ Week 14 & 8.57 (20.11) & 0 (0–119) \\ Week 15 & 149.5 (227.67) & 53 (0–1318) \\ \hline \hline \end{tabular} Note: The weeks preceding midterm exams are highlighted in light blue.  
\end{table} 
Table 3: Descriptive statistical indicators for the variable _Video_ by week. Table 6 shows that students exhibit the highest levels of motivation in external regulation (Mean = 5.62, Median = 6.00) and introjected motivation (Mean = 5.50, Median = 6.00), indicating that external pressures and internalized expectations significantly influence their academic engagement. In contrast, motivation to experience stimulation (Mean = 3.88, Median = 3.75) and identified motivation (Mean = 3.76, Median = 3.50) received the lowest scores, implying that fewer students are driven by personal identification with learning goals or the enjoyment of studying itself. The relatively high variability in responses, particularly in identified motivation (Std Dev = 1.84), suggests notable differences in how students perceive their reasons for academic effort.