In this plenary I reflect on the research I have shared over the past many years of participating and presenting in PME and PME-NA conferences to identify three intellectual divides that continually challenge and motivate my scholarship. I discuss how these intellectual borders (mathematics/education; expert/novice; research/teaching) create adversarial relationships and unwarranted hierarchies in our field and among ourselves. Although these divides have been with us for a long time, I contend that these are far more dangerous than we might realize. These divides prevent us individually and collectively from imagining new and creative solutions to the perennial question about how to improve the quality and equity of mathematics education. I propose a reflexive and collaborative approach to identifying and problematizing the intellectual divides that challenge our goals and commitments to pursuing research that makes a difference in the very communities that we seek to serve. [The abstract is written in both English and Spanish. For the complete proceedings, see ED583608.]