Properties and Applications of Wrong Answers in Online Educational Systems

In online educational systems we can easily collect and analyze extensive data about student learning. Current practice, however, focuses only on some aspects of these data, particularly on correctness of students answers. When a student answers incorrectly, the submitted wrong answer can give us valuable information. We provide an overview of possible applications of wrong answers and analyze wrong answers from three different educational systems (geography, anatomy, basic arithmetic). Using this cross-system comparison we illustrate some common properties of wrong answers. We also propose techniques for processing of wrong answers and their visualization, particularly an approach to item clustering based on community detection in a confusion graph.