## 3 Results
### Interpretable Modeling Approach
#### 3.3.3 Synergistic Effects of Key Digital Technologies on Student Classroom Engagement  
Given that digital technologies in classroom settings are typically used in combination rather than independently, we further examined the synergistic effects of paired combinations of digital technology tools on student classroom engagement. Figure 5a-f illustrates the interaction effects between subject-specific software, management software, websites, and mobile devices on classroom engagement. Figure 5a depicts the combined effects of subject-specific software and management software on classroom engagement, demonstrating a pronounced synergistic effect. Specifically, the simultaneous high-level application of both subject-specific software and management software resulted in optimal predicted classroom engagement. Moreover, management software alone was also found to substantially enhance engagement, even at relatively low levels of subject-specific software usage. Figure 5b shows the joint impact of subject-specific software and websites on student engagement. The results reveal that once the usage level of subject-specific software exceeds a critical threshold (approximately 4.0), classroom engagement rapidly increases even when website technology usage remains at a lower level. Thus, subject-specific software represents a primary driving factor in enhancing student classroom engagement, whereas website technology plays a secondary role, effectively amplifying engagement only when combined with a higher level of subject-specific software. Figure 5c indicates that increasing levels of subject-specific software significantly improve student classroom engagement. However, the standalone use of mobile devices at high levels (4.0-5.0) does not notably enhance classroom engagement unless coupled with similarly high usage of subject-specific software. Moreover, excessive reliance on mobile devices without sufficient subject-specific software usage could negatively affect predicted student engagement. Figure 5d reveals that classroom engagement gradually increases with higher management software usage levels, even when website usage remains moderate or low. When the usage level of management software surpasses a threshold (approximately 4.0 or higher), the positive influence of website becomes significantly magnified, substantially boosting student engagement. This indicates that the beneficial impact of websites strongly depends on the  
Figure 4: Partial dependence plots of digital technology variables on student engagement: **(a)** subject-specific software, **(b)** management software, **(c)** websites, **(d)** mobile devices. The upper blue boxplot illustrates the data distribution across various usage frequency intervals after logarithmic transformation, including the median, interquartile range, and extreme values, while the green bars indicate the corresponding sample size or frequency for each interval. The blue solid line in the lower section represents the trend of student classroom engagement as a function of usage frequency, derived from partial dependence analysis (PDP), with the blue shaded area denoting the associated confidence interval (or standard error).  
effective utilization of management software. Figure 5e illustrates that increasing mobile device usage alone does not lead to substantial improvements in classroom engagement. However, as management software usage increases, student engagement significantly improves, reaching its peak when both management software and mobile device usage are at high levels (4.0-5.0). Lastly, Figure 5f demonstrates that classroom engagement remains low when mobile device usage increases independently, particularly at low levels of website technology usage. Nevertheless, student engagement significantly improves as the usage of website technology increases. Notably, when both website technology and mobile device usage reach high levels, predicted classroom engagement achieves its highest value, underscoring a significant synergistic effect.