We hypothesize that the initiative of a robot during a collaborative task with a human can influence the pace of interaction, the human response to attention cues, and the perceived engagement. We propose an object learning experiment where the human interacts in a natural way with the humanoid iCub. Through a two-phases scenario, the human teaches the robot about the properties of some objects. We compare the effect of the initiator of the task in the teaching phase (human or robot) on the rhythm of the interaction in the verification phase. We measure the reaction time of the human gaze when responding to attention utterances of the robot. Our experiments show that when the robot is the initiator of the learning task, the pace of interaction is higher and the reaction to attention cues faster. Subjective evaluations suggest that the initiating role of the robot, however, does not affect the perceived engagement. Moreover, subjective and third-person evaluations of the interaction task suggest that the attentive mechanism we implemented in the humanoid robot iCub is able to arouse engagement and make the robot's behavior readable.