Bridging Engagement and Difficulty in Math Education Data: A Novel Adjusted Performance Metric and Predictive Modeling

Student engagement and performance are key indicators of learning success, but traditional measures often ignore contextual factors like question difficulty. This study proposes a novel difficulty-adjusted performance metric that integrates raw scores with item difficulty to better evaluate outcomes. Using a dataset of 9,546 math question attempts (372 students, 833 questions) with features such as performance, engagement, and difficulty, we compute the new metric and incorporate it into predictive modeling. Multiple classifiers—including logistic regression, decision tree, random forest, and neural network—are trained and compared. Results show that incorporating the adjusted metric improves model performance, with a decision tree achieving 96.0% accuracy (precision=0.88, recall=0.90 for the "Advanced" class) in classifying question difficulty. Feature importance analysis highlights difficulty index and engagement as strong predictors. These findings demonstrate the value of blending engagement and difficulty factors to enhance educational data mining and support more equitable evaluation of learning outcomes.