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In the United States (US) and elsewhere across the world, undergraduate mathematics instructors are increasingly aware of the value of inquiry-based instruction. In this research commentary, we describe the intellectual origins and development of two major strands of inquiry in US higher education, offer an explanation for apparent differences in these strands, and argue that they be united under a common vision of Inquiry-Based Mathematics Education (IBME). Central to this common vision are four pillars of IBME: student engagement in meaningful mathematics, student collaboration for sensemaking, instructor inquiry into student thinking, and equitable instructional practice to include all in rigorous mathematical learning and mathematical identity building. We conclude this commentary with a call for a four-pronged agenda for research and practice focused on learning trajectories, transferable skills, equity, and a systems approach. 

Concerns over the quality and diversity of the future workforce in science, technology, engineering and mathematics (STEM) in the United States have led to repeated calls to reform undergraduate education. This paper focuses on the efforts of one mathematics education reform movement in higher education to frame itself and its inquiry-based learning (IBL) teaching methods. Since its inception, members of this IBL movement struggled to negotiate their historical connection to the legacy of the late mathematician R. L. Moore and their need to modernize to recruit new mathematics instructors. A strong initial connection to Moore and his now-troubling racial and sexist views led to intense disputes over the framing, or branding, of the movement that at first inhibited its growth, but over time led to an understanding of IBL that embraces a broader range of methods and people.