In this study, I offer a critique of representational thought and the related concept of intentionality in the theory and practice of curriculum in arts education. I use the philosophies of Jacques Derrida and Gilles Deleuze alongside new materialist and posthumanist theory to interrogate three figures of representational thought in arts education: the art object, the curriculum as enclosure, and the transmission-acquisition theory of learning. My analysis of these figures reveals how the theory and practice of curriculum in arts education uses privileged forms of interiority—the work of art, human subjectivity, and intentional consciousness—to pre-judge difference(s) according to recognizable subject-object determinations and established values. I argue that in the guise of representational thought, such determinations often (re)produce divisions and hierarchies of the human and nonhuman that, while making differences visible and knowable, also encloses them in fixed images. In arts education, such representational enclosures produce exclusionary boundaries for participation and learning which subordinate difference to identity, matter to form, and creativity to already-given determinations of subject and object in the mind of the intending human subject. I suggest that thinking about curriculum and learning in terms of inclosure rather than enclosure may allow arts educators to create living curricular forms that respond to and affirm differences rather contain them under representational identities.