In this article, the authors describe critical issues related to the pursuit of rigorous and innovative research in the fields of mathematics and science education. The paper is framed to help researchers consider aspects of both their research project and their research proposal. The authors describe features of high-quality and fundable research projects and whether the research is intended to support descriptive, design-oriented, or causal interpretation. They discuss the critical role of grounding proposed research in existing literatures; attending to relevant research from associated fields; and posing research questions that are clear, specific, and feasibly addressable. The goals of the research should cohere with the methodological and analytic design proposed. The authors also discuss the multidisciplinary nature of research that has implications for practice in general and for educational practice more specifically. The authors touch on the characteristics of more and less successful interdisciplinary research teams, especially those that draw from education, cognitive science, methodology, educational psychology, the learning sciences, and relevant STEM disciplinary fields. Examples of STEM education research questions from different genres of research are considered and the authors describe how the questions themselves give rise to specific design choices, methodologies, measures, study samples, and analytical models as well as how they can reflect the disciplinary orientations of the researchers. Implications of these issues for successful educational research grant proposal writing are discussed.