The purpose of this research review is to open dialog about quantitative, qualitative, and mixed research methods in engineering education research. Our position is that no particular method is privileged over any other. Rather, the choice must be driven by the research questions. For each approach we offer a definition, aims, appropriate research questions, evaluation criteria, and examples from the Journal of Engineering Education. Then, we present empirical results from a prestigious international conference on engineering education research. Participants expressed disappointment in the low representation of qualitative studies; nonetheless, there appeared to be a strong preference for quantitative methods, particularly classroom-based experiments. Given the wide variety of issues still to be explored within engineering education, we expect that quantitative, qualitative, and mixed approaches will be essential in the future. We encourage readers to further investigate alternate research methods by accessing some of our sources and collaborating across education/social science and engineering disciplinary boundaries.