Creating Discussions with Clickers and Classroom Voting
| Kelly Cline and Holly Zullo |
The following is an online extra from the June/July 2011 issue of MAA FOCUS. Read the entire issue here.
Classroom voting might be just the pedagogy for you if you want to get all of your students engaged in serious conversations about mathematics during every class period, working with peers to figure out new ideas. The new NSF-funded Project MathVote, with a collaboration of eight faculty at institutions across the United States, seeks to achieve these goals by developing materials and best practices for classroom voting with clickers.
Classroom voting is a teaching method where the instructor poses a multiple-choice question, gives the students a few minutes to work through the question and discuss it in small groups, then requires each student to vote on the answer, usually with an electronic clicker. The votes are instantly tabulated. Students and teachers see immediately whether the class understands the material.
Classroom voting has a strong record of success in collegiate mathematics, and research into this method shows that the key seems to be that voting motivates the students to regularly work through short problems and talk about math in small groups during class. Every student must choose individually which option to vote for. By listening to different perspectives, and explaining their own mathematical thinking to others, students learn to think critically, while investing themselves in the mathematical process. Then, when the answer is revealed, students are either excited to find that they were right, or interested and curious to find out why they were wrong.
Good Questions Are the Key
When classroom voting is used effectively, it enlivens the whole course and the students have more fun as they discover the key points of each lesson for themselves through voting and discussion. However, this requires the right voting questions used in the right ways. The questions must be well focused and lead the students through the lesson’s key goals. They must be an essential part of the instruction, rather than an optional enhancement; otherwise, the students will tune out.
Further, the best voting questions usually provoke genuine discussion, sometimes even heated debate, bringing up important issues and contrasting ideas. It helps if there is real depth to the incorrect answer choices, requiring the students to engage in serious thought to arrive at a strong mathematical conclusion.
Of course, it is very difficult for a busy instructor to write even a simple set of questions for every class period in the course of a term. To write a gem for every topic is almost impossible. Fortunately, more and more faculty are sharing their voting questions at places like our website (http://mathquest.carroll.edu), where extensive libraries of questions now exist for calculus, linear algebra, and differential equations. This makes it easier for faculty new to classroom voting to get started and allows faculty with lots of classroom voting experience to share their best questions.
How Do We Make It Work?
The Project MathVote team is developing voting questions for a variety of courses, including college algebra, precalculus, and statistics. But more importantly, we are studying classroom voting itself, trying to identify the types of questions and the teaching choices that produce the best discussions.
We have found that identifying good discussion questions is not easy. Before class, some questions look stimulating and intriguing, but in the classroom the discussion falls flat. Other times, a question appears to be a straight-forward practice question, and yet the classroom discussion becomes rich, with students bringing up a broad spectrum of ideas and perspectives.
To identify the best discussion questions, the Project MathVote team will be rating the quality of the discussion produced by each voting question that we use in our classes over the next few years. Of course, one question may work perfectly with one particular class on one particular day, but fail in other classrooms. That’s why we’re searching for questions that regularly produce quality discussions when used by different instructors, in different classes, at different institutions. If a specific question provokes good discussions when used by several different instructors in a wide variety of classroom settings, the question probably touches on something important.
Looking for Good Discussion Questions
What do good discussion questions have in common? How can we identify them more easily? How can we write multiple-choice classroom voting questions that are more likely to generate good discussions?
Our preliminary results suggest that if significant percentages of students vote for several different answers to a question, that question will likely create good discussions. Thus, past voting results from different classes can be a powerful way of identifying the most effective questions.
For example, we have asked the following question in three different integral calculus classes:
The derivative f' of a function f is plotted below. If we know that the maximum value of f on this range is 20, what is f(9.5)?
To warm up for this question we asked students to identify the value of x at which f reaches a maximum on this range. Eighty percent or more of each class voted correctly that this occurs at x = 4. Then we posed the question above, which requires the students to estimate the area between f' and the x-axis from x = 4 to x = 9.5 (about 14), and subtract this from 20, to get f (9.5) ≈ 6, and so (a) is the correct answer. The distributions of votes in these three classes were as follows:
|
a (correct) |
b |
c |
d |
Class 1 |
46% |
8% |
46% |
0% |
Class 2 |
33% |
40% |
20% |
7% |
Class 3 |
32% |
40% |
28% |
0% |
In all three classes, none of the options received a majority of the votes. Instead, significant numbers of students voted for (a), (b), and (c). Voting results like these tell us that we’ve got a good question here, which is worth the investment of class time. At this point in the course, students are challenged by this question: There are several options that appear reasonable, and it is likely that if this question is asked at the right time, it can provoke useful discussions.
We Need Your Help!
By gathering data from different instructors at different institutions, we plan to identify the most useful voting questions so that instructors can go into class armed with the best. To gather as much data as possible, we’re looking for external collaborators who are willing to give classroom voting a try, use some of the questions in our collections, and collect data. Data collection is easy and often involves no more than saving an extra file on your computer at the end of class. We will analyze the voting statistics to find questions that regularly produce good distributions and try to identify common features of the most effective voting questions. We plan to write several papers about this over the next few years, and anyone who can send us a significant amount of data, which is used in one of these papers, will be invited to join us as a coauthor. If you are interested in collaborating in our study, please contact Kelly Cline immediately.
The Project MathVote Team: Holly Zullo (Carroll College), Jean McGivney-Burelle (University of Hartford), Ann Stewart (Hood College), Derek Bruff (Vanderbilt University), Lahna VonEpps (Columbia College), Christopher Storm (Adelphi University), Kathy Shay (Middlesex County College), and Kelly Cline (Carroll College).