Hand-drawn graph problems in online education

Abstract

Machine-gradable assessments in online education platforms are currently limited to questions that require only keyboard or mouse input, and grading efforts generally focus only on final answers. Some types of problems in the science, technology, engineering, and math (STEM) domain, however, are most naturally answered through sketches drawn with a pen. We introduce a simple graph problem type that accepts solutions drawn using a stylus as a proof-of-concept extension to online education platforms. Simple graphs have a small number of components (vertices, arrows, and edges only), and we describe a three-step recognition process consisting of segmentation, symbol classication, and domain interpretation for converting users' pen strokes into a simple graph object representation. An experiment run on Mechanical Turk demonstrates the usability of our trained, recognition-driven drawing interface, and examples of simple graph problems illustrate how course developers can not only check students' final answers but also provide students with intermediate feedback.