Mathematics education research over the past half century can be understood as operating in four distinct yet overlapping and simultaneously operating historical moments: the process–product moment (1970s–), the interpretivist–constructivist moment (1980s–), the social-turn moment (mid 1980s–), and the sociopolitical-turn moment (2000s–). Each moment embraces unique theoretical perspectives as it critiques or rejects others. Moreover, because methodology is inextricably linked to theory, each moment calls forth unique methodological perspectives. Using exemplars of research articles from each moment, the authors illustrate how each moment provides different possibilities for data collection, analysis, and representation.