In this paper, the first of two, we analyse three widely-held conceptions of critical thinking: as one or more skills, as mental processes, and as sets of procedures. Each view is, we contend, wrong-headed, misleading or, at best, unhelpful. Some who write about critical thinking seem to muddle all three views in an unenlightening melange. Apart from the errors or inadequacies of the conceptions themselves, they promote or abet misconceived practices for teaching critical thinking. Together, they have led to the view that critical thinking is best taught by practising it. We offer alternative proposals for the teaching of critical thinking.