  This is the first in a series of papers that analyze college student beliefs
in realms where common astronomy misconceptions are prevalent. Data was
collected through administration of an inventory distributed at the end of an
introductory college astronomy course. In this paper, we present the basic
mathematics of item response theory (IRT), and then we use it to explore
concepts related to galaxies. We show how IRT determines the difficulty of each
galaxy topic under consideration. We find that the concept of galaxy spatial
distribution presents the greatest challenge to students of all the galaxy
topics. We also find and present the most logical sequence to teach galaxy
topics as a function of the audience's age.
