This paper addresses a call for teachers to promote students' knowledge of criteria and standards within curriculum domains for self-monitoring and improvement purposes. We present the case for students to develop, as part of their learning in content areas, the evaluative knowledge and expertise of the type that teachers bring to the classroom. The aim is to reduce trial-and-error learning by introducing approaches to systematically lessen student dependence on the teacher as the sole or primary source of feedback. In making the case, we draw on a range of salient, empirical projects conducted from 2005-2016 to illustrate key ideas for embedding criteria and standards into practice using what we refer to as 'an inquiry mindset' for teachers and students. Four enabling conditions to develop students' evaluative expertise are proposed: (1) teachers' assessment identities--dispositions; (2); students' assessment identities; (3) the role of artefacts; and (4) social moderation. While learning and assessment are structured within the curriculum, taken-for-granted institutional practices, and policy fields, 'assessment as critical inquiry' recognises that teacher and student assessment identities, the associated assessment artefacts and opportunities for focussed discussion on the meaning of criteria and standards can work to either support or inhibit teaching and learning.