We propose a new vision of normative multi-agent systems for computer-supported collaboration in the framework of socio-physical computing. An example application to the RISK game, in the context of the TangiSense distributed tangible environment, is provided to support the proposed design. Our work is driven under three complementary views: (i) a systemic view, to integrate in a single modelling a wide range of levels, from the very physical infrastructure level to the higher social level of human coordination, (ii) a normative view, in which norms are introduced to mediate human activity, in accordance with the principles of activity theory, and (iii) a trace-based view, in which traces, left in the information space by an action, are made to evolve under the application of norms. In this way, norms do not act as a prerequisite, or as a way to apply a priori constraints on action. Rather, they are meant to situate action, by evaluating norm-dependent properties that may then be considered by other agents, in proper contexts. We further distinguish between application-dependent and communication-dependent norms, which respectively check the correctness of action and delimitate proper viewpoints in the information space. We show through simple examples the potential richness of the proposed concept.