This article critiques international assessment of adult literacy using research findings from students completing a Maori tourism certificate who achieved significant gains in assessment. It is argued that the focus of literacy assessments potentially forces educators to narrow their teaching and learning approaches, manoeuvring them into teaching toward singular or "convergent literacy." This leads to utilising teaching and learning strategies drawn from the cultural and social capital of the dominant culture, which is problematic for students without abundance of such capital. Blending Kaupapa Maori research theory with appreciative inquiry, research revealed that students made significant gains in assessment scores because their educators acknowledged and utilised ways in which they made sense and meaning of their world. Educators drew upon the social and cultural capital of students and engaged them as partners in culturally based teaching and learning processes. Relating to students' multiple literacies, and the contexts with which they bring meaning to their world in this way, is referred to as drawing from "divergent literacies." This study proposes a need to develop and research alternative ways for improving convergent literacy outcomes. It is suggested that multiple interventions using multi-modal and 360° approaches need to occur simultaneously for best outcomes.