This interactive essay serves as a research companion to support the reader in thinking and talking about equity in research design, implementation, and reporting in post-secondary mathematics education. The terms equity, diversity, inclusion, and social justice have entered the mathematics education research lexicon. Yet, researchers continue to face significant challenges in gaining a nuanced understanding of the various ideas associated with these words and how those ideas are consequential for research. The authors describe and illustrate tools for making sense of (and making sense with) "equity" as an essential component of research. The tools focus on self-aware communication, an essential component of enhancing mathematics education research with an equity lens. The authors offer a set of reflective questions, outline the call for courageous conversations in mathematics education research, and provide a tool for engaging in such conversations. The piece closes with suggestions for further reading and prompts for related challenging conversations about equity in rigorous research in post-secondary mathematics education.