Robotics provides useful tools for educational purposes, allowing to engage students in learning within disparate domains, from computer science and artificial intelligence – traditionally the main domains for educational robotics – to general education, human and social sciences and arts. Robots can be used with different purposes, from being simple tools to be programmed with some specific behaviour, to being peers with whom to engage in a fruitful interaction for a collaborative learning purpose. In this sense, they can also foster learning of transversal skills such as communication and cooperation. In this article, we propose robot swarms as a novel educational tool to target exactly those transversal skills that are difficult to account otherwise. The usage of multiple robots interacting to solve a common problem can support the learning of concepts related to cooperation and collective actions and can make accessible notions about complex systems that are common in physical, biological, economic and social sciences. Additionally, the possibility to interact and participate in the collective behaviour displayed by the robot swarm can strongly increase the comprehension and engagement with the proposed concept. Motivated by this picture, we propose a roadmap for the utilization of swarm robotics for educational purposes, which is hinged on the Thymio robot, a simple but powerful educational robot that presents all the features required for swarm robotics experimentation. We propose two case studies and we substantiate the proposal with preliminary results from a demonstration of robot swarms performed during a recent robotics festival.