To develop engineered systems with enhanced functionality, improving their design is essential. Robots and humans each have specialized competence advantageous to design. Robots excel in terms of fabrication reliability and observation of trends in data whereas humans have prior knowledge and experience to inform decision making. By enabling robots and humans to collaborate on design problems, we may be able to achieve the best of both worlds. We explore this concept for the design problem of paper airplanes with an objective to reach a target distance and present various collaboration mechanisms for iterative design, test, and evaluation processes. We demonstrate that with the optimal collaboration technique where the robot provides initial design exploration followed by human exploitation, a target-reaching design is found quicker than other collaborative or non-collaborative methods. This work presents an initial exploration of collaborative human-robot design methods which could inform future methodologies for increasingly complex design problems.