The Elements of Item Response Theory and its Framework in Analyzing   Introductory Astronomy College Student Misconceptions. I. Galaxies
  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. 
Andrej Favia, Neil F. Comins, Geoffrey L. Thorpe
physics.ed-ph