Much computer-based learning is largely passive, based primarily on task-based, exercise-driven interactions. We argue that computers have greater potential for promoting more active forms of learning. In particular, the advent of wireless and pervasive technologies offers many opportunities for designing learning experiences that encourage children to explore, initiate and reflect. Novel forms of interactions can be developed, that exploit the `physical' and the `digital' in a diversity of ways that move beyond the constrained `desktop' genre of interactions. In this paper we describe how this can be achieved, focusing on the notion of digitally-augmented physical spaces. Our claim is that getting children to interact with the physical world, resulting in relevant augmented digital information appearing and which can subsequently be interacted with, is what can facilitate active learning. We describe three case studies where we developed such novel learning experiences...