In this paper, several research topics are presented that provide productive avenues of exploration for students in an undergraduate cryptography course. The topics are intended for a variety of skill levels and interests. In some cases, a student might be inspired to try to solve the proposed problem or write computer code. Other topics might…

Using clickers in the statistics classroom can help students identify and understand common errors and misconceptions through a combination of surprise and discussion. Students are presented with multiple-choice questions that they discuss with each other and then vote on; a class-wide discussion follows. Questions for which many students vote for…

To identify clicker questions likely to provoke rich and engaging student discussions, we recorded the percentage of the class voting on each option on every clicker question used throughout each semester, encompassing nineteen sections of introductory statistics, taught by three instructors. Working from the hypothesis that seeing student votes…

We recorded the percentage of students voting on each option on every clicker question used in 19 introductory statistics classes. To identify the questions that provide the most useful feedback, we looked for those for which the percentage of students voting correctly varied the most from class to class, producing the largest standard deviations.…

This article presents a project that is meant to deepen student understanding of what it would mean for one preference voting method to be "better" than another. In the project we show the students how to rigorously compare the methods of plurality and plurality with elimination, and we then allow them to compare two other voting methods…

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…

Liberal arts mathematics courses can provide non-majors the opportunity to connect mathematical topics with areas of personal interest. This article describes two end-of-unit writing assignments (on voting and graph theory) that have been structured so that each student is able to synthesize course material in a unique way, while ensuring a…

Using technology to enhance the classroom environment can have a tremendous impact on student learning, as well as on an instructor's teaching. This paper describes one instructor's transition from traditional chalkboard lectures to a fully technological presentation of content. After carefully reviewing the literature, clicker technology was…

We describe a non-statistics, data-based activity developed by the author for an interdisciplinary course on mathematics and politics that uses actual ballot data from the City of San Francisco, California. The assignment is appropriate for a general education audience and develops students' ability to work with data, improves their understanding…

The combination of classroom voting system (clicker) questions and peer instruction has been shown to increase student learning. While implementations in large lectures have been around for a while, mathematics has been increasingly using clickers in classes of a smaller size. In Fall 2008, I conducted an experiment to measure the effect of…

One technique for identifying and addressing common student errors is 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, often using a hand-held electronic clicker. If a large number…

The purpose of this paper is to present results of a recent study in which students voted on multiple choice questions in mathematics courses of varying levels. Students used clickers to select the best answer among the choices given; in addition, they were also asked whether they were confident in their answer. In this paper we analyze data…

I present a unit on voting theory and social choice taught as the beginning of a liberal arts mathematics course for undergraduates. In this unit, students voted on the final grade calculation formula and topics to cover during the semester and then analyzed the results using various voting systems. I believe that by allowing my students to…

Clickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a…

We study how different sections voted on the same set of classroom voting questions in differential calculus, finding that voting patterns can be used to identify some of the questions that have the most pedagogic value. We use statistics to identify three types of especially useful questions: 1. To identify good discussion questions, we look for…