Measuring ``how much the human is in the interaction'' -- the level of engagement -- is instrumental in building effective interactive robots. Engagement, however, is a complex, multi-faceted cognitive mechanism that is only indirectly observable. This article formalizes with-me-ness as one of such indirect measures. With-me-ness, a concept borrowed from the field of Computer-Supported Collaborative Learning, measures in a well-defined way to what extent the human is with the robot over the course of an interactive task. As such, it is a meaningful precursor of engagement. We expose in this paper the full methodology, from real-time estimation of the human's focus of attention (relying on a novel, open-source, vision-based head pose estimator), to on-line computation of with-me-ness. We report as well on the experimental validation of this approach, using a naturalistic setup involving children during a complex robot-teaching task.
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