Addressing common errors and misconceptions in integral calculus with clickers and classroom voting

Common student errors and misconceptions can be addressed through the method of classroom voting, in which the instructor presents a multiple-choice question to the class, and after a few minutes for consideration and small-group discussion, each student votes on the correct answer, using a clicker or a phone. If a large number of students have voted for one particular incorrect answer, the instructor can recognize and address the issue. In order to identify multiple-choice questions that are especially effective at provoking common errors and misconceptions, we recorded the percentages of students voting for each option on each question used in 25 sections of integral calculus, taught by 7 instructors, at 4 institutions, over the course of 12 years, on a collection of 172 questions. We restricted our analysis to the 115 questions which were voted on by at least 5 different classes. We present the six questions that caused the largest percentages of students to vote for a particular incorrect answer, discuss how we used these questions in the classroom, and examine the common features of these questions. Further, we look for correlations between question characteristics and the mean percentage of students voting for common errors on these questions, and we find that questions based on general cases have higher percentages of students voting for common errors.