Kelly Cline

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.

Classroom Voting Patterns in Differential Calculus

Abstract 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 those that produce the greatest diversity of responses, indicating that several answers are regularly plausible to students. 2. We identify questions that consistently provoke a common misconception, causing a majority of students to vote for one particular incorrect answer. When this is revealed to the students, they are usually quite surprised that the majority is wrong, and they are very curious to learn what they missed, resulting in a powerfully teachable moment. 3. By looking for questions where the percentage of correct votes varies the most between classes, we can find checkpoint questions that provide effective formative assessment as to whether a class has mastered a particular concept.

Addressing Common Student Errors With Classroom Voting in Multivariable Calculus

Abstract 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 of students have voted for one particular incorrect answer, the instructor can recognize and address the issue. In order to identify multiple-choice questions which are especially effective at provoking common errors, we recorded the percentages of students voting for each option on each question used in 11 sections of multivariable calculus, taught by four instructors, at two small liberal arts institutions, all drawing from the same collection of 317 classroom voting questions, over the course of 5 years, during which we recorded the results of 1,038 class votes. We found six questions in which, on average, more than 50% of each class voted for the same incorrect answer. Here we present these six questions and we discuss how we used them in the classroom in order to promote discussion and student learning.

Creating discussions with classroom voting in linear algebra

We present a study of classroom voting in linear algebra, in which the instructors posed multiple-choice questions to the class and then allowed a few minutes for consideration and small-group discussion. After each student in the class voted on the correct answer using a classroom response system, a set of clickers, the instructor then guided a class-wide discussion of the results. We recorded the percentage of students voting for each option on each question used in 18 sections of linear algebra, taught by 10 instructors, at 8 institutions, over the course of 5 years, together recording the results of 781 votes on a collection of 311 questions. To find the questions most likely to provoke significant discussions, we identify the six questions for which votes were most broadly distributed. Here we present these questions, we discuss how we used them to advance student learning, and we discuss the common features of these questions, to identify why they were so good at stimulating discussions.

NUMERICAL METHODS THROUGH OPEN-ENDED PROJECTS

ABSTRACT We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible approaches, each with their own advantages and disadvantages. Because these open-ended problems lacked the normal cues that tell students how to get started, they were very effective at revealing student misconceptions, and illuminating weaknesses in their understanding. Further, they were very effective at challenging the strongest students, without leaving the weaker students behind. All students were required to write up their work on each project into a formal paper. This not only taught the valuable skill of mathematical writing, but was also an important step in teaching more organized thinking skills. Over the course of the semester, the students developed impressive abilities at dealing with these sorts of realistic problems. The students became more systematic in their explorations, and more aware of the different methods that they were forced to choose from at each stage in the project.

A Writing-Intensive Statistics Course.

Abstract We discuss an upper division applied statistics course that has been structured to satisfy our colleges writing intensive requirements within the mathematics major. In this course, students complete two projects, performing both a statistical survey and a controlled experiment, and then write up their work on each project in a formal paper. After each paper, the students read a group of papers written by their peers and then critique and rank these papers. Next, the students meet in groups, having read the same papers, and together they must form a consensus about their group rankings. Finally, after analyzing and discussing several papers from their peers, the students revise their own papers.

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.