## 4 Results and Analysis  
### Performance Comparison: TF-IDF + XGBoost vs. Baseline Models  
This study aims to demonstrate the superiority of the proposed TF-IDF + XGBoost model by comparing its performance with widely used text classification models. For this purpose, models such as TF-IDF + Logistic Regression, TF-IDF + SVM, LightGBM, BERT, and DistilBERT were selected as benchmarks. The evaluation was conducted using key \begin{table}
\begin{tabular}{l l l} \hline \hline
**Evaluation Metrics** & **Description** & **Result** \\ \hline Accuracy & Average accuracy for key labels & 91.75 \% \\ F1 Score & Average F1 Score recorded in class imbalance scenarios & 0.87 \\ Real-Time Processing Speed & Average processing time per instance & 1.3 s \\ Processable Data Volume & Number of cases processed per minute & 45 cases \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comprehensive performance evaluation of the proposed system. performance metrics, including Accuracy, F1 Score, Precision, and Recall. The training and testing of all models were performed under the same dataset and conditions to ensure a fair comparison. Detailed information regarding dataset composition, preprocessing, and experimental setup can be found in Section 3.3 (Dataset) and Section 3.1 (System Architecture). Table 6 summarizes the comparative performance results between the proposed TF-IDF + XGBoost model and other models. Experimental results show that the proposed TF-IDF + XGBoost model outperformed all benchmark models in every evaluation metric. The proposed model achieved the highest Accuracy of 0.9885, along with exceptional Precision (0.9867), Recall (0.9854), and F1 Score (0.9860). Particularly, it effectively classified key labels such as \"Calculation Errors\" and \"Conceptual Deficiencies\", demonstrating its practicality in analyzing students' learning status and generating personalized feedback. These results confirm that the proposed model can accurately learn and classify critical patterns in text-based educational data. The TF-IDF + Logistic Regression and TF-IDF + SVM models recorded Accuracy scores of 0.9677 and 0.9656, respectively, indicating strong performance. While both models are efficient for text classification, their performance was slightly inferior to XGBoost, particularly in multi-class classification and handling complex data patterns. Additionally, minor differences in Precision and Recall resulted in lower F1 Scores than XGBoost. The LightGBM model exhibited significantly lower performance, with an Accuracy of 0.0038. This suggests that LightGBM is not well-suited for processing sparse matrices, such as text-based datasets, as it is primarily optimized for continuous numerical data rather than high-dimensional sparse vectors generated by TF-IDF. Additionally, LightGBM relies heavily on structured input features, which limits its effectiveness in unstructured text classification tasks. Similarly, BERT and DistilBERT recorded Accuracy scores of 0.0 and 0.0017, respectively, reflecting suboptimal performance across all evaluation metrics. This result may stem from the dataset size (30,000 instances) being insufficient for effective fine-tuning of transformer-based models. Unlike simpler models, BERT and DistilBERT require significantly larger labeled datasets to fully capture contextual dependencies. Furthermore, hyperparameter tuning and pre-training strategies are essential for optimizing transformer performance, which was not the primary focus of this study. These results highlight a key insight: TF-based models, particularly TF-IDF + XGBoost, are highly effective for classifying learning errors in mathematical diagnostics. Unlike transformer-based models, which emphasize contextual meaning, TF-IDF focuses on explicit Term Frequency and categorical representation. Mathematical learning errors often involve structured terminology with distinct, repetitive patterns (e.g., 'addition mistake','miscalulated fraction').