File this under “Better Late Than Never.”  Back in January 2010, I coordinated (with Kelly Cline and Kien Lim) a contributed paper session on teaching with clickers at the Joint Mathematics Meetings in San Francisco.  Shortly after the conference, I blogged about some clickers talks that didn’t fall in our session, but I never got around to blogging about the talks in our session!  Five months later, I’m finally getting around to sharing my notes from those talks…

“The Evolution of Classroom Voting in Contemporary Mathematics,” Jean McGivney-Burelle, University of Hartford [PowerPoint Slides]

Jean teaches a “math for the liberal arts” course called Contemporary Mathematics taken by music and arts majors among others.  She finds her students come to the course with relatively little interest or self-reported ability in mathematics, so it’s a tough crowd to teach.  A few years ago, she started teaching with clickers in order to appeal to what she calls the “thumb generation”–students used to spending a lot of time sending text messages.

Jean interspersed some clicker questions throughout her lectures and encouraged students to discuss them in small groups before voting.  She and the students liked this, but she found that most of her questions were answered correctly by most of her students  and that the small group discussions didn’t involve much debate among students.  The next year, Jean decided to ask tougher questions.  She calls them QEDs–Questions to Encourage Discussion.  She aimed for the analysis, synthesis, and evaluation levels of Bloom’s Taxonomy.

For example, in Jean’s first year using clickers she gave her students a preference schedule–a list of how each voter in an electorate (only four of them to keep things simple) ranked all of the candidates.  She then asked her students to determine which candidate would win the election using the instant run-off voting scheme.  This is a straight-forward application of a particular algorithm.

The next year, Jean asked another question in which she shared a preference schedule with her students and asked them to analyze it.  However, this time, she asked the question at the beginning of the unit on voting schemes and asked her students to indicate which of the candidates had the best case for winning the election.  There’s no single correct answer to this question since winner of an election (well, one involving at least three candidates) depends on what scheme you use to count the votes.  This is a great example of a one-best-answer question (since students are asked to select the one answer they think is best among multiple reasonable answers) used to create a time for telling (since it’s used to make the point that which voting scheme you use matters).

Jean found that these more challenging and ambiguous questions generated longer and more engaged small group discussions as well as more “horizontal” bar graphs–ones indicating significant disagreement among the students.  Looking ahead, she plans to build on this success by writing questions designed to develop mathematical habits of mind–an important goal of this course.  For example, here’s a sample question she shared aimed at pointing students towards the notions of proof and counterexamples:

Suppose there is a majority winner in an election. Will all of the voting methods we have studied thus far always pick that winner?  Yes or no?  If you answer yes, prepare to defend your answer. If you answer no, have a counterexample ready.

I really like this question.  It has a degree of ambiguity that students often find disconcerting, but it also reminds students of how they’ll need to defend their answers, which should help put their minds at ease.  As Jean noted in her talk, in a course like this one, it’s more important students develop mathematical habits of minds (like the ones surfaced by this question) than learn particular math content areas.  I hope this kind of question helps with this objective.

Stay tuned to the blog for more notes on these talks over the coming days…

Image: “Deep Down Inside, We All Love Math” by Flickr user Network Osaka / Creative Commons licensed

A couple of weeks ago, Stephanie Chasteen shared a series of blog posts on teaching with clickers in upper-division physics courses: Part 1, Part 2, Part 3, and Part 4.  I’m often asked if clickers work well in upper-division courses, yet I’ve not met many faculty members who use them in such courses.  So I was glad to see this series by Stephanie.  It’s adapted from a talk she gave at the American Association of Physics Teachers conference a few months ago, and it includes videos that feature interviews with faculty and students about teaching and learning with clickers.  Here are some highlights from Stephanie’s posts…

One of the students interviewed in the video in Part 1 of the series says that she likes clicker questions because they allow her to take a concept and metaphorically put in her pocket.  I like that metaphor.  It indicates that the clicker question allows her to confirm that she understands a concept, which is useful during class since it helps prepare her for what follows.  This idea that clicker questions allow students to test themselves on concepts during class is one that shows up often in student surveys as a positive aspect of using clickers.  This self-testing is a type of formative assessment, and Stephanie notes it’s important to include even in small classes.

Another type of formative assessment is also mentioned in the same video.  Steven Pollock, whom I interviewed for my book, mentions that prior to using clickers he found himself making assumptions about what his students did and did not understand.  He notes that clickers provide him actual data on his students’ learning so he doesn’t have to rely on his assumptions.  I wonder if this aspect of using clickers is even more important in upper-level courses since common student misconceptions in these courses may not be as well known as in lower-level courses.

Several different types of clicker questions are mentioned in Stephanie’s series: conceptual questions, application questions, review questions used at the start of class, procedural questions asking students to identify the next correct step in a derivation.  I like the conceptual question Steven shared that distinguishes between students approaching physics from a classical mechanics point of view and those using a quantum mechanics approach.  I can imagine this kind of question is particularly useful for students making the transition to an upper-level course like quantum mechanics.

One of the arguments against using clickers in upper-level courses that Stephanie says she hears is that students in these courses are sophisticated learners.  They don’t need the structure of clicker-facilitated peer instruction to help them learn.  Stephanie presents a strong counter-argument, that since these students are more sophisticated learners, they actually get more out of the peer instruction method, more seriously engaging in small-group and classwide discussions.

Stephanie also shares some interesting data on student perceptions of clickers in upper-level courses.  Students who took a non-clicker upper-level course were asked how they would feel if they had taken the course with clickers.  They were resistant, arguing that clickers were for lower-level courses.  However, students who actually went through a clicker-enhanced upper-level course were extremely enthusiastic about their use.  Stephanie points out that students aren’t always able to predict how they’ll respond to a particular teaching approach, which is an important point to remember when trying out new approach in one’s teaching.

Take a look at Stephanie’s blog posts for more thoughts on using clickers in upper-level courses, including thoughts on their role in creating “times for telling.”  Stephanie also contributes to the clickers efforts at the Carl Wieman Science Education Initiative at the University of British Columbia, where they’ve put together a 36-page guide to using clickers in the sciences.

I picked up a few ideas on teaching with classroom response systems at the Joint Mathematics Meetings in Washington, DC, last week.  Rick Clearly of Bently University spoke about test construction as part of a panel on creative assessment of student learning.  He didn’t mention clickers at all, but he described two kinds of exam questions he uses that are similar to clicker questions I’ve heard other faculty describe.

Dr. Clearly sometimes asks his students to circle responses to multiple-choice and true-false exam questions in which they are confident.  Circled responses get +3 points when correct, but -1 points when incorrect.  Responses that aren’t circled get +2 points when correct, but earn 0 points when incorrect.

I’ve spoken with instructors who use similar schemes for in-class clicker questions, having students rate their confidence level (high, medium, low) in their answers to content questions.  Some instructors modify the amount of points students earn based on their confidence level as Rick does on his exam questions.

I’m not sure how I feel about assigning exam points in this way, but for instructors using confidence-level clicker questions, there’s something to be said about using exam questions that align well with in-class clicker questions.  This means that clicker questions help students prepare for exams, which students generally appreciate according to surveys.  Also, if an instructor has a particular learning goal, it’s only appropriate that this class time be spent helping students move toward that goal and exams be used to assess the extent to which the goal has been met by students.

As another example, Dr. Clearly mentioned that on his exams, he sometimes presents a worked problem to his students, asking them to determine if the solution is correct.  This is a great idea for an exam questions, since it allows Dr. Clearly to assess his students’ problem-solving skills (particularly their error-detection skills) without requiring students to spend a lot of exam time working through a complete problem on their own.  This kind of question also works well as an in-class clicker question.  On the exam, an instructor might ask students to write why the sample solution is incorrect.  In class, those arguments could come out in the discussion.