Christopher Storm

Student Surveys: What Do They Think?

Many individual faculty have surveyed their students about classroom voting, and they generally report positive results. How robust are these results across a wide variety of students, campuses, instructors, and courses? In this study, a total of 513 students in 26 classes were surveyed regarding the use of classroom voting in their classes. (See Appendix A for the survey form.) Fourteen instructors from ten different schools participated. The classes surveyed were primarily freshman and sophomore level courses in calculus, multivariable calculus, linear algebra, and differential equations. While several questions show the variation in response that one might expect, other questions generate consistent results, showing that student opinion in these areas is uniform across many variables.

An iterative construction of isospectral digraphs

Recently, Storm used generating functions to provide a proof that an infinite family of graphs constructed by Cooper have the same Ihara zeta function. Here, we generalize the construction of that infinite family of graphs to a directed graph construction. A similar generating function proof technique applies, and we exhibit conditions under which our digraphs have the same spectra with respect to the adjacency matrix.

Classroom Voting Questions to Stimulate Discussions in Precalculus.

Abstract Classroom voting can be an effective way to stimulate student discussions. In this pedagogy, the instructor poses a multiple-choice question to the class, and then allows a few minutes for consideration and small-group discussion before students vote, either with clickers, cell phones, or a non-electronic method. After the vote the instructor guides a class-wide discussion. Here we report on a study of precalculus voting questions that includes data from 25 classes taught by eight instructors at five institutions over the course of 7 years. The goal of this study is to explore ways of identifying the questions most likely to provoke good student discussions. We recorded the percentage of each class voting for each option on each question posed, a total of 851 votes. We have 60 questions on which we recorded the results from at least five classes. We identified the five questions with the most widely dispersed votes, a method that has a history of being helpful in identifying good discussion questions. We present these five questions here, four of which we found to be examples of questions which are particularly good at stimulating student discussions. We include notes about how we used the questions in class.