Peer Instruction-like resources for math (Module 2, ISTE-TS 2)

One of my most memorable college experiences as a student involved the use of clicker questions, but used in a little bit of a non-traditional way. The class was “baby quantum” as we called it. It was a prerequisite for the intro quantum mechanics sequence.

Typically, in my experience as a student, a multiple-choice question is presented on the projector, the students talk about it for 2ish minutes, we each submit our answer by pressing a button on our own clicker device, the final results are displayed as a histogram, and then we wrap up by talking about the answer options as a class.

On this day, however, we were not allowed to consult one another. Instead, we silently answered the question, we were not shown the final histogram, and we did not follow up by talking about the question/answer. We then switched gears and worked together on related a UW Tutorial. After we completed the tutorial, we were presented with the same clicker question again, giving us the opportunity to change our answer (I don’t remember if we were allowed to talk to each other this time – I would guess not). And again, we were not yet shown the results. But we could tell by the instructor’s reaction that something interesting had happened. She then revealed the histograms…

First she showed us the histogram from round one – I don’t remember the distribution off the top of my head, but it was more or less all over the place. Then she showed us the histogram from round two. The gasp was audible and there was a mild uproar – over 90% of us now chose the same answer! The right answer.

It’s hard to describe how exciting it was, and the story is also a success story about the tutorial we were working on (see here for a journal article on the tutorial, which includes the actual clicker question stats from this day). But we were elated. There was such a stark contrast between the histograms. The use of clicker questions really showcased the power of the tutorial. From an instructor’s perspective, the tutorial is probably main point of interest, but for me, the final reveal of the clicker question results is really what that made that day so memorable. Our jaws dropped to the floor.


For Module 2 we are looking at ISTE-TS 2: Design and develop digital age learning experiences and assessments – “teachers design, develop, and evaluate authentic learning experiences and assessments incorporating contemporary tools and resources to maximize content learning in context and to develop the knowledge, skills, and attitudes identified in the Standards•S.”

In particular, two indicators stood out to me as related to the use of clicker questions/classroom voting systems (CVS): Indicator 2a – “design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity,” and Indicator 2d – “provide students with multiple and varied formative and summative assessments aligned with content and technology standards, and use resulting data to inform learning and teaching.”

To go through the points in those indicators: Research has shown positive results on student learning with the use of CVS (Cline and Zullo, 2011; Crouch and Mazur, 2001). You can, but don’t have to, use digital tools to implement the questions. There is room to increase relevance by choosing questions that you feel your particular class needs to discuss. Discussing their answers with each other gives them more opportunity to think and reflect, and thus develop their own way of imaging the math (i.e., being mathematically creative). One of the main ideas behind CVS is to use the activity as a formative assessment. Additionally, students report that CVS are engaging, and from experience, I would agree.

I am familiar with physics related CVS resources. Peer Instruction (PI) by Eric Mazur (1997) details a particular methodology around the use of clicker questions and provides a set of physics clicker questions. In Henderson and Dancy’s (2009) study, they found that PI was the most commonly used research-based instructional strategies in college physics. So my question was (and has been for some time):

What are some PI-like resources for the college math class? Is there a bank of PI-like clicker questions for math?

To my surprise (although maybe I shouldn’t be surprised), I found exactly what I was looking for. The links below come from a Phoenix College page, Clicker Questions and Math, or from one of the pages it links.

What Are Clicker Questions?

For a more elaborate, yet still quick, overview of the process and benefits of using clickers, I will refer you to Derek Bruff’s guest blog post (2009), Teaching Math with Clickers, on busynessgirl’s blog. On his own site, Bruff’s posts (2009), Flexible Clicker Questions, details a particular time he asked a clicker question. The way Bruff describes using student-submitted “bucket questions” as clicker questions makes his clicker questions particularly relevant to his class. He also says that this gives him a better sense for how prevalent the confusion is, rather than just answering student-submitted questions at the start of class (i.e., it works as a relevant formative assessment).

For a lot of elaboration about CVS in math, check out editors Kelly Cline and Holly Zullo’s (2011) book, Teaching Mathematics with Classroom Voting: With and Without Clickers.

“This collection includes papers from faculty at institutions across the country, teaching a broad range of courses with classroom voting, including college algebra, precalculus, calculus, statistics, linear algebra, differential equations, and beyond. These faculty share their experiences and explain how they have used classroom voting to engage students, to provoke discussions, and to improve how they teach mathematics.

This volume should be of interest to anyone who wants to begin using classroom voting as well as people who are already using it but would like to know what others are doing. While the authors are primarily college-level faculty, many of the papers could also be of interest to high school mathematics teachers.” (Mathematical Association of America, 2017)

I haven’t read all of the book, but it seems valuable and I will likely purchase it. I thought chapter 2 offered an insightful breakdown of implementation options, addressing: clickers or non-electronic voting, one- or two-cycle voting, and to grade or not to grade the responses.

This book is generally geared toward college instruction, but I want to point out chapter 8, Using Clickers in Courses for Future K–8 Teachers, for my K-8 teacher friends.

Resources for Math Clicker Questions

So what about the CVS questions themselves? These two resources offer pages and pages of ready-to-use CVS questions for a variety of college math topics/courses. (Both projects were NSF funded.)

I worked through one of the Math QUEST question sets (The Fundamental Theorem and Interpretations set in the Integral Calculus question library) and I really liked it. I felt that the questions did a good job setting the stage for subsequent questions. Multiple times the next question touched on something I had just been thinking about. For example during question 7 I thought, “Well (a) would be right if it were |v(x)| instead of v(x),” and then question 8 asked about |v(x)|. So I was happy with the progression of the questions.

Last Thoughts

These resources are really exciting to me. Clickers are something that I really want to incorporate into my future teaching and it’s nice to finally tap into that vein of research. As easy to find as these resources were, I’m not quite sure why I haven’t found them already!


References

Bruff, D. (2009). Flexible clicker questions [Blog post]. Retrieved from http://derekbruff.org/?p=163

Bruff, D. (2009). Teaching math with clickers [Blog post]. Retrieved from http://busynessgirl.com/teaching-math-with-clickers/

Cline, K. S., & Zullo, H. (Eds.). (2011). Teaching mathematics with classroom voting: With and without clickers (No. 79). Mathematical Association of America (available here). Retrieved from http://ebookcentral.proquest.com/lib/spu/detail.action?docID=3330312

Crouch, C. H., & Mazur, E. (2001). Peer Instruction: Ten years of experience and results. American Journal of Physics, 69, 970-977.http://dx.doi.org/10.1119/1.1374249

Henderson, C., & Dancy, M. H. (2009). Impact of physics education research on the teaching of introductory quantitative physics in the United States. Physical Review ST Physics Education Research, 5(2), 1-9. https://doi.org/10.1103/PhysRevSTPER.5.020107

ISTE: International Society for Technology in Education. (2017). ISTE standards for teachers (2008). Retrieved from https://www.iste.org/standards/standards/standards-for-teachers

Mathematical Association of America. (2017). Teaching mathematics with classroom voting: With and without clickers. Retrieved from http://www.maa.org/press/ebooks/teaching-mathematics-with-classroom-voting-with-and-without-clickers

Mazur, E. (1997). Peer instruction: A user’s manual. New Jersey: Prentice Hall, Inc.

Novak, G. (2006). What is Just-in-Time Teaching? Retrieved from http://jittdl.physics.iupui.edu/jitt/what.html