An overview is given of three conceptual lessons that can be incorporated into any first-semester calculus class. These lessons were developed to help promote calculus students' ability to think conceptually, in particular with regard to the role that infinity plays in the subject. A theoretical basis for the value of these lessons is provided, and both indirect and direct evidence, that demonstrates that these lessons were successful in beginning to achieve their goal, is described. Ideas for how to incorporate these lessons into the standard calculus curriculum are presented as well as thoughts on how to further improve the lessons' ability to promote students' conceptual understanding. (Contains 1 table and 8 figures.)