## 3 Methodology  
This study conducted a one-year PBL course at a university in Macau using a self-developed GAI-PBL online learning platform. Detailed records of students' learning behaviors were collected throughout the course. These records formed the basis for three in-depth analyses aimed at understanding the characteristics of students' learning behaviors, cognitive and thinking processes, and overall learning effectiveness in a GAI-assisted PBL environment. For the behavioral data collected, we adopted Lagged Sequential Analysis (LSA) for in-depth analysis and supplemented it with a variety of other research methods; the structure of this analytical framework is shown in Figure 1.  
From Figure 1, it can be seen that the study was completed in three stages: Data Collection and Processing, Pattern Discovery, and Analytical Perspective. At the Data Collection and Processing stage, we developed a GAI system integrated with the PBL process. The PBL-GAI platform, an online learning environment with an embedded GAI plug-in, served as the primary data source for this study. For data analysis, five sets of behavior recordings were randomly selected and independently reviewed by two experts to define and categorize student behaviors. A sequential behavior list was subsequently developed, and the behaviors were labeled at regular intervals using GSEQ 5.1 software. We then carried out the following three sets of data analyses in an attempt to  
Figure 1: Research framework. analyse the dynamic correlations, differences, and impact of students' behaviour during that learning process. * Behavioral Sequence Analysis: The first set of analyses employed Lag Sequential Analysis (LSA) to construct behavioral sequence diagrams that mapped learners' interactions during the GAI-PBL process. Using GSEQ 5.1 software, a frequency table of behavioral transitions and an adjusted residual table were generated. In this study, the Z-score was used as a key statistic to determine the significance of behavioural sequences in LSA. These tools identified significant behavioral sequences exceeding a Z-score threshold of 1.96, revealing non-random patterns and regularities in the learning process [32]. * Comparison of Behaviors: The second analysis compared behavioral patterns from the first and second semesters in three randomly selected groups. We evaluated the frequency of behavioral occurrences and identified the top five most frequent behaviors in each semester, providing insights into how learners' interactions evolved over time. * Performance-Based Behavioral Analysis: For the third analysis, learners were divided into high- and low-performance groups based on final semester grades. Grades were derived from evaluations of project completion, innovativeness, and process execution. Learning behaviors were further categorized based on their degree of GAI usage into four distinct types: \"Deep Use of GAI\", \"Functional Use of GAI\", \"Exploratory Use of GAI\", and \"No Use of GAI\". Behavioral distributions across three stages of the project (early, middle, and late) were analyzed. Additionally, a focused study of the interaction processes between GAI and learners during the final session was conducted for each performance group. These interactions were evaluated across five dimensions: \"Question Precision\", \"Keyword Effectiveness\", \"Dialogue Rounds\", \"Question Innovativeness\", and \"Question Complexity\". Meanwhile, in order to comprehensively assess the application value of GAI plug-ins in educational scenarios, we conducted a cost-benefit analysis of the collected data. * Cost-Benefit Analysis. We conducted a comprehensive cost analysis in three dimensions: learning cost, technology deployment cost and time cost, and correspondingly, a cost-benefit comparison in three dimensions, learning efficiency, learning quality, and innovation ability, in order to systematically assess the input-output relationship of GAI plug-ins in student learning.