Vertical and Stationary Scales for Progress Maps

Students and instructors would benefit from a graphical display of student proficiency throughout a course. However, valid and reliable proficiency estimates based on modern statistical techniques require data that are not usually collected in traditional instruction. For example, problems that students solve on tests and homeworks may not be properly equated to a vertical scale; building a true vertical scale requires that overlapping anchor items be administered in way that supports the estimation of student growth between assignments. This paper suggests an alternative, a stationary scale in which the expected student growth is subtracted out so that a student making normal progress remains at the zero point in the scale. We define the stationary scale model and validate it on a real-world data set of student answers to homework items. We further produce a Progress Map, a visualization of student proficiency throughout a course.