This article is an extended version of a presentation made to the Drawing Research Network conference, Loughborough School of Art & Design, 5-6 September 2016. An original pedagogy of drawing is proposed for the art schools, based upon aspects of theories of visual perception and visual communication. It is argued that drawing practice facilitates an intelligence of seeing, bridging the gap between conceptual intrigue and perceptual intrigue. These terms are defined, and the gap between them in contemporary practices is blamed upon a historical resistance to theory influenced by Barnett Newman. Newman’s false logic is effectively debunked. A systemic-functional semiotic model for drawing is introduced, and related to five premises for applying the theoretical model to a teaching programme for drawing, illustrated with drawings by students and the author.