The success of robotic agents in close proximity of humans depends on their capacity to engage in social interactions and maintain these interactions over periods of time that are suitable for learning. A critical requirement is the ability to modify the behavior of the robot contingently to the attentional and social cues signaled by the human. A benchmark challenge for an engaging social robot is that of storytelling. In this paper, we present an exploratory study to investigate dialogic storytelling—storytelling with contingent responses—using a child-friendly robot. The aim of the study was to develop an engaging storytelling robot and to develop metrics for evaluating engagement. Ten children listened to an illustrated story told by a social robot during a science fair. The responses of the robot were adapted during the interaction based on the children’s engagement and touches of the pictures displayed by the robot on a tablet embedded in its torso. During the interaction the robot responded contingently to the child, but only when the robot invited the child to interact. We describe the robot architecture used to implement dialogic storytelling and evaluate the quality of human–robot interaction based on temporal (patterns of touch, touch duration) and spatial (motions in the space surrounding the robot) metrics. We introduce a novel visualization that emphasizes the temporal dynamics of the interaction and analyze the motions of the children in the space surrounding the robot. The study demonstrates that the interaction through invited contingent responses succeeded in engaging children, although the robot missed some opportunities for contingent interaction and the children had to adapt to the task. We conclude that (i) the consideration of both temporal and spatial attributes is fundamental for establishing metrics to estimate levels of engagement in real-time, (ii) metrics for engagement are sensitive to both the group and individual, and (iii) a robot’s sequential mode of interaction can facilitate engagement, despite some social events being ignored by the robot.