In this theoretical paper, the authors provide an overview of mathematics education as a research domain, identifying and briefly discussing four transitions or historical moments in mathematics education research. Using the "Instructional Triangle" as a point of reference for the dynamics of mathematics instruction, they illustrate how mathematics education researchers working in different moments explore different questions and use different theoretical perspectives. The authors then provide brief summaries of critical theory and postmodern theory, and suggest critical postmodern theory (CPT) as a hybrid theory that offers new possibilities for conceptualizing and conducting mathematics education research. [For the complete proceedings, see ED584829.]