Faculty in business and engineering schools are increasingly focused on teaching the fundamentals of the innovation process to students at all levels. There has been a recent embrace of teaching the innovation process through a user-centered "design thinking" methodology and on experiential "making" activities within interdisciplinary teams. Although valuable as part of an innovation curriculum, a focus on only one set of tools and methods such as design thinking may detract from other valuable approaches, thereby limiting the full range of incremental to radical innovation outcomes that students need to learn to be effective innovation leaders. In this essay we review pedagogy related to teaching innovation processes, and we categorize approaches into four modes depending on teaching method (experiential or analytical) and participant context (disciplinary or interdisciplinary). We propose that in order to teach innovation effectively, students need to be exposed to all four modes, where learning opportunities differ. We illustrate our points drawing from courses among multiple settings, and we provide implications for curriculum design that will help faculty to innovate how they teach innovation.