## 5 Results  
This section presents the findings from three analyses conducted using the behavioral data collected on the GAI-PBL platform. The results provide a comprehensive overview of the impact of GAI on learners' behavioral patterns, cognitive processes, and learning effectiveness. 1. Behavioral Patterns Through LSA:  
Figure 5: Learning behavior classification diagram. The first analysis employed LSA to uncover the temporal dependencies and sequential relationships between learner behaviors. LSA, a robust tool for time series analysis, revealed significant regularities in students' actions throughout the experiment. The probability of one behavior immediately following another demonstrated clear patterns, indicating that the integration of GAI influenced the learners' approaches to task completion. These findings suggest that the use of GAI not only enhanced the structure of learning activities but also played a role in shaping students' learning styles and strategies over time. 2. Long-Term Impact on Behavioral Changes:  
To assess the sustained influence of GAI on learners, we compared the most prominent behavioral features exhibited during the first semester with those observed in the second semester. This longitudinal comparison highlighted significant changes in learners' behavioral dimensions, particularly in areas that reflect their cognitive engagement and problem-solving approaches. The GAI-assisted environment appeared to encourage more sophisticated thinking processes, as evidenced by the evolution of behavioral patterns. Moreover, a detailed examination of the most frequent behaviors in each semester further validated these observations. The shift in behavior frequencies between the two periods underscored GAI's role in enhancing learners' cognitive frameworks, reinforcing its impact on developing higher-order thinking skills. 3. Association Between GAI Utilization and Learning Effectiveness;  
The final set of analyses focused on the relationship between GAI utilization and learners' performance. Participants were stratified into performance groups based on their final grades, encompassing metrics such as project completion, innovation, and process evaluation. By analyzing the behavior distribution across different stages of learning (early, mid, and late), as well as the specific use of GAI tools during the final sessions, the study identified a strong correlation between the depth of GAI integration and learning effectiveness. Learners who exhibited frequent and advanced use of GAI--such as leveraging it for multi-round dialogues, critical reasoning, or innovative solutions--consistently outperformed their peers. 4. Cost-Benefit Comparison. The final set of analyses focused on assessing the cost-benefit relationship of GAI utilization within the PBL learning process. Participants were grouped based on their learning outcomes, which included metrics such as task completion efficiency, learning quality, and innovation performance. The results highlight that the manner in which learners engaged with GAI, the frequency of its use, and their mastery of its functions were crucial factors in determining their performance outcomes. These findings underscore GAI's transformative potential in enhancing learning effectiveness and emphasize the need for pedagogical strategies that promote deeper, more strategic use of AI tools. 5.1. GAI Impacts Learners' Learning Methods  
The impact of GAI on learners' approaches to PBL was examined through LSA, revealing distinct behavioral patterns. The analysis provided insights into how GAI influenced learners' interactions, critical thinking, and creative engagement during PBL tasks. Figures 6-9 illustrate the findings, emphasizing key behavioral tendencies. In the LSA diagram, the arrows indicate transitions from one behavior to the next, with the starting point of each arrow representing a specific behavior and the endpoint representing the subsequent behavior.