This paper presents an approach for human activity recognition focusing on gestures in a teaching scenario, together with the setup and results of user studies on human gestures exhibited in unconstrained human-robot interaction (HRI). The user studies analyze several aspects: the distribution of gestures, relations, and characteristics of these gestures, and the acceptability of different gesture types in a human-robot teaching scenario. The results are then evaluated with regard to the activity recognition approach. The main effort is to bridge the gap between human activity recognition methods on the one hand and naturally occuring or at least acceptable gestures for HRI on the other. The goal is two-fold: to provide recognition methods with information and requirements on the characteristics and features of human activities in HRI, and to identify human preferences and requirements for the recognition of gestures in human-robot teaching scenarios