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.
A critical examination of acculturation theories
