Vertical and Stationary Scales for Progress Maps

Students and instructors would bene t from a graphical dis-play of student pro ciency throughout a course. However,valid and reliable pro ciency estimates based on modern sta-tistical techniques require data that are not usually collectedin traditional instruction. For example, problems that stu-dents solve on tests and homeworks may not be properlyequated to a vertical scale; building a true vertical scale re-quires that overlapping anchor items be administered in waythat supports the estimation of student growth between as-signments. This paper suggests an alternative, a stationaryscale in which the expected student growth is subtractedout so that a student making normal progress remains at thezero point in the scale. We de ne the stationary scale modeland validate it on a real-world data set of student answersto homework items. We further produce a Progress Map, avisualization of student pro ciency throughout a course.

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