3G: Evaluating evidence of student understanding

Abstract

Consider two exercises you might find in an introductory statistics course: “What is the standard deviation of the set {-1, 2, -4, 7, 11, 5}?” vs “Draw four rectangles for which the standard deviation of the 4 rectangles’ heights would be greater than the standard deviation of the 4 rectangles’ widths.” Which exercise would give you more evidence to evaluate how students understand standard deviation? The first question is closed -- it has a single correct solution while the second is open to many. Open-ended questions give instructors much more information on how students are understanding (or misunderstanding) statistical concepts. This session explores the nature of open questions and the tools instructors can use to ‘open-up’ closed questions they’re already using in their classrooms.