The difficulty in maintaining attention can interfere with the acquisition of critical academic skills. Recently, researchers have used embodied and game-based learning to support skill acquisition for children with learning difficulties. In this context, robots can be an interesting asset to foster engagement and investigate game dynamics. However, it is still an open question of how to develop adaptive learning environments for children with learning difficulties. Before one can provide effective adaptation, a first step is needed to understand the differentiating behaviors during the activity for children with attention difficulties. Three such differentiating behaviors are how a child divides his or her attention during the learning activity, the child's level of cognitive load, and the child's physiological fatigue, which are the focus of our study Using a robot assisted, gamified activity, we conducted a user study with 18 children having difficulty in maintaining attention. Using process mining techniques and eye-tracking data, we found the importance of integrating the autonomous robots into the attention patterns to successfully complete a game and the influence their behaviors can have on the participant's attention. This importance was supported by the cognitive load of participants decreasing the more they focused on the autonomous robots in successful games. This work contributes to the understanding of children's behaviors during tangible game-based activities and can be used to build effective adaptation for children with attention difficulties.