The relationship between poverty and education is a longstanding issue for education policy, research, and practice. Through a policy as discourse approach, this article focuses on the work policy does to define education as a solution to poverty. Recent policy discourses in Aotearoa have positioned the teacher as the most important factor in raising student achievement irrespective of socio-economic factors like poverty. However, by linking student achievement to economic success, those policy discourses also position teachers as a remedy to poverty. This article considers the ways two Aotearoa education policies, Ka Hikitia and Investing in Educational Success, impossibly position teachers between needing to ignore and remedy poverty. The analyses show how both policies impossibly position teachers by reducing education to learning and students and teachers to learners. By positioning teachers as responsible for learning, policies are able to displace structural and historical conditions of poverty through a focus on the work teachers do to improve learning, culminating in a logic where one learns not to be poor. The article concludes with a coda seeking to reverse the impossible position of teachers by describing education as weak, whereby teachers can acknowledge poverty without having to remedy it.