For gaining proficiency in physical human-robot interactions, it is crucial for engineering students to be provided with the opportunity to gain hands-on experience with robotic devices that feature kinesthetic feedback. In this article, we propose HandsOn-SEA, a low-cost, single degree-of-freedom, force-controlled educational robot with series elastic actuation and introduce educational modules for the use of the device to allow students to experience the fundamental performance trade-offs inherent in robotic systems. The novelty of the proposed robot is due to the deliberate introduction of a compliant element between the actuator and the handle, whose deflections are measured to perform closed-loop force control. As an admittance-type robot, HandsOn-SEA relies on force feedback to achieve the desired level of safety and transparency and complements the existing impedance-type educational robots. We present the integration of HandsOn-SEA into the robotics curriculum, by providing guidelines for its use in a senior level robotics course, to help students experience the challenges involved in the synergistic design and control of robotic devices. We systematically evaluate the efficacy of the device in a robotics course delivered for five semesters and provide evidence that HandsOn-SEA is effective in instilling fundamental concepts and trade-offs in the design and control of robotic devices.