In this paper, we will discuss the way various features of consciousness interact with each other and with cognition, specifically, the cognition of mathematical reasoning and problem solving. Thus we are interested in how consciousness and cognition "work," in a somewhat mechanistic way, rather than in larger philosophical questions about consciousness. Our goal is ultimately to answer questions like: Where does one's "next" idea come from? Answers to such smaller questions may eventually help in understanding the nature of consciousness itself. We will discuss the relationship between consciousness and cognition in terms of two illustrations, and recall and extend some features of consciousness pointed out by Mangan (1993, 2001), following William James. The resulting framework will then be used do analyze three situations from mathematics: students (I) evaluating proofs, (II) writing equations, and (III) failing to use "adequate" knowledge to solve problems. A bibliography is included.