Previous study developed a game-based learning environment, entitled My-Pet-My-Quest (MPMQ), for arithmetic practices. The purpose of this study is to understand the learning process of game-based learning in long-term real world. The study considered to define how the behavioral patterns be implemented and which coding scheme be used in the behavior analysis approach. For understanding students' behaviors in the environment, two processes were carried out. This study attempted to implement long-term intervention in an elementary after-school club as well as students' home, and then to analyze the learning process. Furthermore, this study adopted a sequential analysis approach, based on a designing framework, to help us examine and understand the each aspect of behaviors on students' learning and playing. These results can provide suggestions and references for the design of efficient learning environments in the future.