Two conceptions of the linguistic system of bilinguals are in contention. The approach supports what we call a view, arguing that bilingualism and multilingualism, despite their importance as sociocultural concepts, have no correspondence in a dual or multiple linguistic system. In our view, the myriad lexical and structural features mastered by bilinguals occupy a cognitive terrain that is not fenced off into anything like the two areas suggested by the two socially named languages. But a strong critique of this view by Jeff MacSwan adopts the familiar position that, while allowing for some overlap, the competence of bilinguals involves language specific internal differentiation. According to this view, which we have called the , bilinguals possess two separate linguistic systems whose boundaries coincide with those of the two named languages. Several interdisciplinary considerations point to the lack of initial plausibility of the dual correspondence theory. And the main argument offered by MacSwan in defense of the theory, namely restrictions on code switching, lacks descriptive adequacy and theoretical coherence. The dual correspondence theory has had pernicious effects in educational practices. A much healthier educational climate is created by teachers who adopt the unitary view sponsored by translanguaging.