We describe the pedagogy behind the MIT Beaver Works Summer Institute Robotics Program, a new high-school STEM program in robotics. The program utilizes state-of-the-art sensors and embedded computers for mobile robotics. These components are carried on an exciting 1/10-scale race-car platform. The program has three salient, distinguishing features: (i) it focuses on robotics software systems: the students design and build robotics software towards real-world applications, without being distracted by hardware issues; (ii) it champions project-based learning: the students learn through weekly project assignments and a final course challenge; (iii) the learning is implemented in a collaborative fashion: the students learn the basics of collaboration and technical communication in lectures, and they work in teams to design and implement their software systems. The program was offered as a four-week residential program at MIT in the summer of 2016. In this paper, we provide the details of this new program, its teaching objectives, and its results. We also briefly discuss future directions and opportunities.