This article explores why art education after modernism needs to engage with and assess two forms of knowledge. It distinguishes procedural knowledge or "knowing how" from declarative knowledge or 'knowing that", and argues that current classroom practice and more general thinking in art education in the UK confuses evidence of procedural knowledge with evidence for declarative knowledge. A corollary is that assessment evidence for "knowing how", which is shown or demonstrated, is confused with assessment evidence for "knowing that", which requires spoken or written forms of reporting. This conceptual confusion is currently embedded in the national, flagship examination known as the General Certificate of Secondary Education, taken by students at the age of 16, resulting in that examination requiring evidence of understanding the meaning of art in its socio-historical context while at the same time denying the necessity of written or spoken work to reveal such knowledge. The article advocates a Wittgensteinian, socio-cultural solution to the confusions of current practice.