## 4 Experiments and Results
### Clustering
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\text{CWA}_{U}\)} & \multirow{2}{*}{**Features**} & **Cluster 0 (N = 249)** & **Cluster 1 (N = 286)** & **Cluster 2 (N = 109)** & **Cluster 3 (N = 19)** \\ \cline{3-6}  & & \(\mu\pm\sigma\) & \(\mu\pm\sigma\) & \(\mu\pm\sigma\) & \(\mu\pm\sigma\) \\ \hline \multirow{4}{*}{20\%} & mean\_multimedias\_time & \(10.37\pm 6.58\) & \(2.11\pm 4.64\) & \(9.78\pm 7.01\) & \(12.67\pm 6.02\) \\  & mean\_video\_time & \(13.89\pm 7.48\) & \(1.59\pm 4.22\) & \(10.33\pm 7.13\) & \(12.05\pm 6.22\) \\  & mean\_simulations\_time & \(14.30\pm 7.24\) & \(4.57\pm 5.96\) & \(0.00\pm 0.00\) & \(7.43\pm 8.99\) \\  & mean\_workshops\_time & \(9.82\pm 5.73\) & \(4.62\pm 5.09\) & \(26.06\pm 16.00\) & \(21.63\pm 12.83\) \\  & weighted\_average & \(3.40\pm 1.14\) & \(3.72\pm 1.18\) & \(4.00\pm 0.83\) & \(4.05\pm 0.82\) \\ \hline \multirow{4}{*}{40\%} & Cluster 0 (N = 224) & Cluster 1 (N = 136) & Cluster 2 (N = 290) & Cluster 3 (N = 13) \\ \hline \multirow{4}{*}{40\%} & mean\_multimedias\_time & \(12.23\pm 6.10\) & \(11.62\pm 5.08\) & \(2.32\pm 5.12\) & \(14.75\pm 3.93\) \\  & mean\_video\_time & \(13.05\pm 5.69\) & \(12.72\pm 4.94\) & \(1.43\pm 3.91\) & \(13.67\pm 2.76\) \\  & mean\_simulations\_time & \(26.13\pm 14.44\) & \(21.34\pm 14.75\) & \(7.43\pm 8.50\) & \(20.13\pm 11.81\) \\  & mean\_workshops\_time & \(27.61\pm 15.22\) & \(30.75\pm 19.03\) & \(9.22\pm 9.59\) & \(40.89\pm 18.65\) \\  & weighted\_average & \(3.35\pm 0.99\) & \(3.78\pm 0.97\) & \(4.03\pm 0.98\) & \(4.10\pm 0.54\) \\ \hline \multirow{4}{*}{60\%} & Cluster 0 (N = 234) & Cluster 1 (N = 114) & Cluster 2 (N = 15) & Cluster 3 (N = 300) \\ \cline{2-6}  & mean\_multimedias\_time & \(12.66\pm 5.49\) & \(12.37\pm 4.38\) & \(13.46\pm 4.92\) & \(2.47\pm 5.07\) \\ \cline{1-1}  & mean\_video\_time & \(12.91\pm 4.92\) & \(12.93\pm 4.54\) & \(14.65\pm 3.67\) & \(1.60\pm 3.91\) \\ \cline{1-1}  & mean\_simulations\_time & \(41.08\pm 20.21\) & \(35.39\pm 19.19\) & \(36.80\pm 16.76\) & \(11.02\pm 11.61\) \\ \cline{1-1}  & mean\_workshops\_time & \(37.18\pm 19.37\) & \(36.93\pm 20.38\) & \(44.04\pm 19.40\) & \(11.17\pm 12.23\) \\ \cline{1-1}  & weighted\_average & \(3.40\pm 0.97\) & \(3.83\pm 0.96\) & \(3.95\pm 0.60\) & \(4.11\pm 0.91\) \\ \hline \multicolumn{6}{c}{Cluster 0 (N = 215)} & Cluster 1 (N = 135) & Cluster 2 (N = 16) & Cluster 3 (N = 297) \\ \hline \multirow{4}{*}{80\%} & mean\_multimedias\_time & \(12.70\pm 5.73\) & \(12.59\pm 4.26\) & \(13.09\pm 4.80\) & \(2.24\pm 4.25\) \\  & mean\_video\_time & \(12.85\pm 5.12\) & \(12.93\pm 4.16\) & \(13.93\pm 3.38\) & \(1.59\pm 3.87\) \\ \cline{1-1}  & mean\_simulations\_time & \(52.25\pm 25.91\) & \(47.88\pm 25.18\) & \(53.82\pm 27.19\) & \(13.74\pm 14.48\) \\ \cline{1-1}  & mean\_workshops\_time & \(39.91\pm 21.32\) & \(41.64\pm 21.66\) & \(45.55\pm 18.48\) & \(12.08\pm 12.91\) \\ \cline{1-1}  & weighted\_average & \(3.33\pm 0.96\) & \(3.84\pm 0.97\) & \(3.97\pm 0.58\) & \(4.19\pm 0.86\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Number of students per group (N), feature average (\(\mu\)), standard deviation (\(\sigma\)) values per cluster, for the four different CWA\({}_{U}\) (20%, 40%, 60%, and 80%). high-performing clusters. Increased engagement with evaluative activities in these stages is associated with better performance, indicating the value of taking the necessary time to solve those evaluative activities. These findings suggest two potential interventions:  
1. Encouraging early and sustained engagement with multimedia and video materials may improve outcomes for lower-performing students. 2. Additional support for simulations and workshops at later stages could help students maximize their learning outcomes as they approach higher CWA\({}_{U}\) thresholds.