## 3 Proposed System
### Performance Evaluation and Expected Impact
The \"Calculation Error\" label achieved an F1 Score of 0.95, demonstrating the highest performance among all categories. This result indicates that the model accurately predicts data related to calculation errors and successfully detects most instances of this error type. The \"Concept Deficiency\" label recorded an F1 Score of 0.92, confirming that the model effectively classifies errors arising from a lack of understanding of mathematical concepts. For the \"Problem Comprehension Deficiency\" label, the model achieved an F1 Score of 0.90, indicating its ability to effectively classify cases where students struggled to comprehend problem conditions and contexts. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Label** & **Precision** & **Recall** & **F1 Score** \\ \hline Concept Deficiency & 0.93 & 0.92 & 0.92 \\ Calculation Error & 0.96 & 0.94 & 0.95 \\ Problem Comprehension Deficiency & 0.91 & 0.89 & 0.90 \\ Error in the Solution Process & 0.90 & 0.87 & 0.88 \\ Unit Conversion Error & 0.88 & 0.86 & 0.87 \\ Inequality Usage Error & 0.87 & 0.85 & 0.86 \\ Graph Interpretation Error & 0.86 & 0.84 & 0.85 \\ Condition Omission & 0.85 & 0.82 & 0.83 \\ Other & 0.82 & 0.78 & 0.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Precision, Recall, and F1 Score analysis for each error category. The \"Error in the Solution Process\", \"Unit Conversion Error\", \"Inequality Usage Error\", and \"Graph Interpretation Error\" labels recorded F1 Scores of 0.88, 0.87, 0.86, and 0.85, respectively. These results demonstrate that the model maintains stable performance even for categories with relatively low data frequency. The \"Condition Omission\" (0.83) and \"Others\" (0.80) labels also exhibited reliable classification performance despite their low occurrence frequency and the inherent ambiguity in label definitions. The F1 Score analysis confirms that the proposed system achieves high F1 Scores for major labels (e.g., Calculation Error, Concept Deficiency), effectively overcoming challenges associated with data imbalance. Notably, the model also achieved relatively high F1 Scores for low-frequency labels, demonstrating its capability to accurately classify various types of learning errors. These findings validate the proposed system as a practical and effective tool for real-world educational environments. 3. Real-time processing speed: The proposed system was designed to enable real-time analysis and feedback generation, and its real-time processing speed was evaluated accordingly. The processing speed was measured based on the entire workflow, which includes preprocessing, training, analysis, and result generation for the input diagnostic assessment data. Table 4 presents the average processing time, maximum processing time, minimum processing time, and the number of records processed per minute. The average processing time was recorded as 1.3 s, representing the total duration required to process a single diagnostic assessment record, including analysis and feedback generation. This result demonstrates that the proposed system provides sufficiently fast performance for real-time applications in educational environments. The maximum processing time was 2.8 s, observed in cases where the data were more complex or contained a larger number of labels. However, most records were processed within the average processing time. The minimum processing time was 1.0 s, achieved when processing simpler diagnostic data, allowing for faster analysis. The system was able to process 45 records per minute, indicating that it can efficiently handle bulk uploads of multiple student records without performance degradation. The real-time processing speed evaluation demonstrated that the proposed system is practically applicable in educational settings. In particular, the average processing time was measured at 1.3 s, confirming that the system operates stably even when handling large volumes of data.