The Internet of Things (IoT) enables the creation of Interactive Smart Spaces (ISSs) where different types of digital devices are integrated in the ambient or embedded in physical objects, and can sense human actions to control equipment, modify environmental parameters, or create multi-sensory effects. These IoT-enhanced interactive systems can support human activities in different contexts, e.g., education, entertainment, home assistance, rehabilitation, to name a few. This paper explores a human-centered perspective in the design of ISSs, which takes into account some salient characteristics of these systems and introduces new conceptual modeling issues going beyond representing hardware, software, and connectivity features of IoT devices. Interaction in particular emerges as a crucial modeling dimension, needed to capture the interplay occurring not only among multiple connected IoT devices but also among the users and the materials or the spaces embedding such devices. The paper presents a novel conceptual model for Interactive Smart Spaces and exemplifies the identified abstractions through a case study, modelling a complex ISS for children' play and learning that has been installed at two local schools and two therapeutic centers in our country.