Teaching Math with Clickers

Feb 13, 2009 by

Today’s guest blogger is Derek Bruff, Assistant Director for the Center for Teaching at Vanderbilt University. Derek writes a blog you may have stumbled across called Teaching with Classroom Response Systems.

Here’s a question I ask the students in my probability and statistics course:

Your sister-in-law calls to say that she’s having twins. Which of the following is more likely? (Assume that she’s not having identical twins.)

A. Twin boys
B. Twin girls
C. One boy and one girl
D. All are equally likely

Since I ask this question using a classroom response system, each of my students is able to submit his or her response to the question using a handheld device called a clicker. The clickers beam the students’ responses via radio frequencies to a receiver attached to my classroom computer. Software on the computer generates a histogram that shows the distribution of student responses.


I first ask my students to respond to the question individually, without discussing it. Usually, the histogram shows me that most of the students answered incorrectly, which tells me that the question is one worth asking. I then ask my students to discuss the question in pairs or small groups, then submit their (possibly different) answers again using their clickers. This generates a buzz in the classroom as students discuss and debate the answer choices with their peers.

After the second “vote,” the histogram usually shows me that there’s some convergence to the correct answer, choice C in this case. This sets the stage for a great classwide discussion. I usually ask a student who changed his or her mind to share their reasoning with the class. I then invite other students to defend or question particular answer choices. I usually wrap things up by drawing the appropriate tree diagram on the board, which helps to explain this question and introduces to the students a visual tool they can use to analyze similar probability questions.

Why use clickers to ask a question like this one? There are several reasons. The histogram generated by the classroom response system I use gives me useful information on my students’ learning. If the histogram shows me that the students understand the question, then I can quickly move on to the next topic. If the histogram shows me that the students are confused, then I can drill down on the question at hand, using the popular wrong answers to guide the discussion.

Asking for a show of hands might provide similar information, but students answering a question by raising their hands don’t answer independently. They look to their peers as they answer, which means that the distribution of hands I see doesn’t accurately reflect my students’ understanding. Using clickers allows my students to answer independently, yielding more useful information I can use to make teaching decisions.

While individual student responses are visible to the students, they are visible to me. This means that I can hold students accountable for their responses by counting clicker questions as part of the students’ participation grades. Clickers provide me a way to expect each and every student to engage with the questions I ask them during class, not just the students who are quick or bold enough to volunteer answers verbally.

Moreover, showing the students the distribution of responses can enhance the classroom dynamic. When students see that two or more answers are popular, they become more interested in the question. When it is obvious from the histogram and from what I tell my students that most students answered a question incorrectly, students are more ready to hear the reasoning for the correct answer.

Classroom response systems can be very effective tools for engaging students during class and for gathering information on student learning useful for making “on the fly” teaching choices. Resources you may find helpful for using clickers in your mathematics courses include the following.

Project Math QUEST – This NSF-funded project out of Carroll College has generated clicker question banks for linear algebra and differential equations. Their Web site also includes question banks for precalculus and calculus courses. Their resources page features links to over a dozen published articles on teaching math with clickers.

• “Clickers: A Classroom Innovation” – Here’s a longer article on teaching with clickers I wrote for the NEA’s higher education magazine, Advocate.

Teaching with Classroom Response Systems Blog – I use my blog to discuss research on teaching with clickers, case studies of clickers in the classroom, conference sessions on clickers, and other resources. The blog is a companion of sorts to my book, Teaching with Classroom Response Systems: Creating Active Learning Environments, available from Jossey-Bass on February 17th.

Thanks to Derek for the post! With any luck, I’ll be back in the USA this afternoon and we will resume our regularly scheduled programming.

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3-D Function Machine

Sep 22, 2008 by

Last spring break, I traveled to NKU and ICTCM. Andy Long, a mathematician at NKU, generously gave me a home for a few days while at NKU, and on the last night he confessed that he had a “Function Machine” in his basement. A what? A function machine.

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Math Provides Beauty and Truth in Physics

Feb 28, 2008 by

Murray Gell-Mann gives a TED Talk entitled Beauty and Truth in Physics.

The second part of his presentation is subtitled “Math Matters” (you can forward to this one)

Quote from Math Matters: “We express these things mathematically, and when the mathematics is very simple… when, in terms of some mathematical notation you can write the theory in a very brief space, without a lot of complication, that’s essentially what we mean by beauty or elegance.

The third part of his presentation is subtitled “Symmetry Matters” (again, you can forward to this)

As our notation improves and we are able to incorporate symmetry into equations, the equations become simpler and more elegant. Here is an example (from the talk) showing the progression in the equations for Relativity – I think that a multivariable calculus class would probably be able to appreciate it best:

This was a great little tidbit – a quote from Newton on why he was not mentioning his theory of gravity in one of his books:

Newton was worried that he would be labeled an “extravagant freak” and that readers would thus dismiss the rest of the book.

Best quip of the talk – Newton could have really written a great essay on “What I did on my Summer Vacation” (referring to the time that Newton spent away from school during the plague years – some of the most productive time of his life).

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Mathematical Visualizations for Multivariable Calculus

Dec 19, 2007 by

Jonathan Rogness (UMN) has a great collection of mathematical visualizations for multivariable calculus that run on Java. I don’t teach multivariable calculus (and hope never to have this experience), but I always love looking at the 3-D surfaces.
You may remember Rogness from the Mobius Transformations video I blogged about a while ago.

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Flash and Math

Nov 19, 2007 by

Barbara Kaskosz and Doug Ensley have put together a new site for learning to use Flash & Math with all their tutorials (beginning, intermediate, and advanced.

To see some of the Flash applications that have been built, go to the Math DL site and search for Flash/Shockwave resources (as shown in the image below).


Amongst other things, there is a nice collection of tools for multivariable calculus developed by Barbara.

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