## 5 Results
### The Effectiveness of PBL Influenced by Learners' Use of GAI
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Stage**} & \multirow{2}{*}{**Group**} & \multicolumn{6}{c}{**Behavioral Coding Categories**} \\ \cline{3-6}  & & **Deep** & **Functional** & **Exploratory** & **No Usage** & **Total** \\ \hline \multirow{3}{*}{Early Stage} & High-performance group & 11 & 3 & 12 & 28 & 54 \\  & Medium-performance group & 9 & 2 & 7 & 13 & 31 \\  & Low-performance group & 33 & 0 & 14 & 35 & 82 \\ \hline \multirow{3}{*}{Middle Stage} & High-performance group & 16 & 3 & 24 & 35 & 78 \\  & Medium-performance group & 7 & 3 & 9 & 12 & 30 \\  & Low-performance group & 11 & 3 & 6 & 25 & 55 \\ \hline \multirow{3}{*}{Late Stage} & High-performance group & 13 & 9 & 12 & 42 & 76 \\  & Medium-performance group & 10 & 2 & 4 & 13 & 29 \\ \cline{1-1}  & Low-performance group & 7 & 3 & 7 & 37 & 54 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Distribution of behaviors among different performance groups over time. * _Enhanced learning for high performers_: High-performing students benefited significantly from GAI by leveraging its advanced features for iterative problem-solving and deeper cognitive engagement;
* _Missed opportunities for low performers_: The low-performance group's declining engagement and inadequate problem-framing skills limited the effectiveness of GAI as a supportive tool. In order to more rigorously verify the validity of the experimental results, two experts were invited to meticulously score the behavioral performance of different performance groups during their interactions with the GAI (see Table 4 for details). This scoring process was designed to explore the potential correlation between the effectiveness of users' interactions with the GAI and their final performance through multi-dimensional and fine-grained analyses. The scoring basis encompasses the following aspects:  
* _Question Accuracy Score_: This assesses the accuracy and relevance of the questions posed by users, gauging their ability to articulate their needs or queries in a clear and precise manner;
* _Keyword Effectiveness Score_: The objective is to ascertain whether the keywords employed by the user in their questioning are appropriate and effective and whether these keywords assist the GAI in comprehending the user's intention with greater accuracy;
* _Conversation Round Score_: This evaluation assesses the efficiency and patience of the user's interaction with the GAI, based on the number of conversation rounds and the depth of dialogue between the two parties;
* _Innovative Questions Score_: This scoring system encourages users to pose innovative and exploratory questions, thereby measuring their flexibility and creativity;
* _Question Complexity Score_: This evaluation assesses the complexity of the questions posed by users, encompassing the structure, rationale, and scope of the questions, in order to reflect the users' capacity to engage in profound thinking and rigorous analysis. It can be concluded that there is a significant correlation between a user's level of mastery of the GAI and their behavior and performance in interacting with the GAI. In particular, users who are able to pose questions accurately and effectively, utilize appropriate keywords, and demonstrate innovative thinking and in-depth analysis in the dialogue tend to achieve higher scores. GAI significantly impacts the effectiveness of PBL by enhancing learners' ability to engage in exploratory and functional behaviors. However, the degree of benefit depends on the learner's skill in effectively leveraging GAI's capabilities. High-performing learners demonstrated consistent and strategic GAI use, translating to superior project outcomes, whereas low-performing learners faced challenges that limited their progress. This underscores the importance of guiding learners in developing effective GAI interaction strategies to optimize its benefits across diverse performance groups.