Current strong emphasis on literacy and numeracy in New Zealand educational policy, as elsewhere, reverberates in different ways in institutions charged with children's and adults' learning. A common response is to locate literacy and numeracy centrally in programmes aimed at preparing children for and enhancing adult participation in 21st century life and work. These agendas overlap in preservice teacher education. Preservice teachers enter Initial Teacher Education (ITE) programmes as adult learners engaged in building literacy and numeracy capability for teaching across the curriculum, working with student achievement data and administrative tasks, aspects of which may also be useful in their wider lives. These activities involve making judgements that require critical thinking, another key policy focus in New Zealand and internationally for children's and adults' learning. This article explores meanings of "critical" in the context of mathematical thinking in ITE programmes. Given that mathematically based arguments can have both helpful and harmful consequences for humanity, we propose that development in preservice teachers' capacity for critical mathematical thinking is crucial. In these times of significant global change we advocate for development of the kind of critical mathematical thinking that facilitates teachers working actively in pursuit of a socially just and sustainable world.