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Where does one enact boundaries for what can be known systematically? Is mathematics one branch of knowledge, separate from, say, social justice or chemistry, or is it possible to understand mathematics, justice, and the physical sciences within one system of knowing? Early Habermas provides a typology of human interests that constitute different knowledge types, beginning with the empirical or analytic, traversing the hermeneutic or historical, and terminating with critical or emancipatory knowledge. Brandom’s reconstruction of Hegel’s Phenomenology of Spirit describes three responsibilities that are the norms for systematicity as well as an “algebra of normativity,” which is a “mathematical” way of understanding recognitive communities. The stories that those recognitive communities tell and retell are curricula. Although Habermas is primarily understood as a sociologist, critical or emancipatory knowledge is very much about the unity of being and knowing that occurs within individuals as they act intentionally in the world, reflect on those actions, and become more through the process of self-actualization. This notion of criticality is more or less absent from mathematics education discourses but is a powerful organizing thread from Kant through Hegel, to Habermas. Instead, most mathematics educators are concerned with critical theory as it pertains to social critique, centering social justice through critical race theory, critical disabilities studies and other critical theories. The tension between understanding emancipation at the level of individuals compared with political emancipation of marginalized groups enforces an ambiguity about who is being emancipated, what they are being emancipated from, and what role mathematics plays as either liberating or oppressive. Moreover, this tension is related to deep epistemological questions about how people come to know and repeat anything at all.

The philosophy of mathematics education (PoME) is a field of inquiry that pursues questions arising from the long tradition of mathematics as a school subject. An integrated area of study, PoME draws on other established disciplines such as philosophy of mathematics and philosophy of education. However, propositions and theses within PoME also have implications for the theory and practice of mathematics education. Rather than actively blurring boundaries among contributory disciplines, PoME is a subdiscipline that reflects their inherent interdependence. Many of PoME’s core questions address the very nature of mathematics, how we come to learn it, and the historical and contemporary aims of mathematics education. Though not the first to address these individual lines of inquiry, Paul Ernest’s The Philosophy of Mathematics Education (1991) may be regarded as PoME’s inaugural text. His landmark publication also demonstrated how philosophical inquiry may guide critical analysis of educational practices and policies. Questions about what mathematics is are not disentangled from those about its teaching and learning. Thus, PoME demonstrates a kind of internal elasticity: how we answer one question has a bearing on how we might answer another. For example, is mathematics something “found” or “made”? The perception of mathematics—how we tend to characterize its nature—can underscore beliefs about mathematics pedagogy. The view of mathematics as a cultural construct (rather than an absolute body of knowledge and related skills) likely dovetails with a constructivist pedagogical approach. But at the same time, such a view of mathematics may encounter ideological tension, if not outright resistance, in sociopolitical arenas. Reconceptualizing mathematics and mathematics education may be considered philosophical endeavors that challenge dominant assumptions and build frameworks with the potential to make mathematics fundamentally more inclusive. The story of PoME is the story of its genesis, its role in imagining a more equitable and humanistic school math experience, and the need to make room for new, alternative approaches and viewpoints that honor the radical spirit in which PoME was developed.