Within the school of thought known as Critical Thinking, identifying or finding missing assumptions is viewed as one of the principal thinking skills. Within the new subject in schools and colleges, usually called Critical Thinking, the skill of finding missing assumptions is similarly prominent, as it is in that subject's public examinations. In this article we examine how school- and college-focused texts explain and teach "this very important skill". The same texts also deal with the nature of assumptions, validity and the role of stated reasons in arguments, and the way these matters are tackled will also be examined in our inquiry. In addition we explore what respected contributors to the critical thinking movement have had to say about some of these issues.