The current work is the first article in a two-paper series exploring the role of explicit learning objectives in undergraduate mathematics instruction. A definition of student-learning objective (SLO) is introduced. We give examples of SLOs for topics from introductory college and university mathematics courses. We list potential advantages of a general program of grounding mathematics instruction in a set of such explicit SLOs. In the second paper in this series, an explicit, step-by-step algorithm for creating sets of student learning objectives will be described and its use illustrated. (Abstract)