Fun with Paper Folding

Over the last several years, I’ve been able to work with teachers from local pythag-foldedschool districts as part of a grant-funded project called “The Math and Science Partnership Program” (MSP). Phase II of this program focuses on “Improving Math & Science Teaching through School Outreach.” We offer free professional development workshops for teachers, held on Saturdays, several times a year. Teachers who are part of our MSP Partner Schools can earn a $150 stipend from attending each workshop. All workshops are accepted for re-certification credit in the Berkeley & Charleston County School districts. Descriptions of our workshops dating back to 2014 are available online.


Christel and Kate

Last weekend, together with my co-Leader Christel Wohlafka, I held a Workshop called “Mathematical Fun with Paper Folding.” I was inspired to create this workshop as a direct result of Patrick Honner‘s “Scalene Triangle One-Cut Challenge,” which I think I learned about because of a mention of it by Evelyn Lamb. The “scalene triangle” puzzle stuck with me for several hours one day and I was almost unable to function in any capacity until I figured it out.


Christel Wohlafka College of Charleston Department of Mathematics

Our agenda for our “Paper Folding Workshop” is available online. Many of our activities were inspired by great things I’ve learned about on Twitter, and many are available online at their original sources:

  1. The “Scalene Triangle” puzzle is part of @MrHonner’s blog series, “Fun with Folding”: The “One Cut Challenge” activities came from his “Fun with One Cut!” Workshop that he gave at the 2013 TIME conference. He blogged about it here: His templates are available online as a PDF file here:
  2. “Hole punch symmetry” was produced by Joel Hamkins (@JDHamkins). He wrote about it in a recent blog post: The template itself is available online: Joel has a whole set of blog posts devoted to “Math for Kids” —
  3. The “Fold & Cut Theorem – Numberphile” YouTube Video we watched is available here: The female mathematician featured in the video is Katie Steckles, who finished her Math Ph.D. in 2011 at the University of Manchester. Katie’s webpage: or you can find her on Twitter: @stecks
  4. Christel’s handout on “Dividing a Square into Thirds” came from an activity on Illustrative Mathematics
  5. Christel’s handout on “Paper Folding Proof of the Pythagorean Theorem” came from this “Teachers of India” resource.pythag1



Frank Monterisi Jr. folds paper.

I had a lot of fun at this Workshop and I hope we will offer it again next academic year. Between now and then, I need to order more and better-quality hole-punchers. With some of Joel’s “One Punch” activities, the paper ends up folded over itself five or six times, and some of the “well-loved” hole punchers we had with us weren’t up to the task.

E-Seminar on “Mathematics Teaching and Learning”

In a previous post, I wrote about finding an E-Seminar from the NCTM (National Council of Teachers of Mathematics). A full list of available topics can be found here. One of them I mentioned before is called “Mathematics Teaching and Student Learning: What Does the Research Say?” Check out the description on their webpage. Today was our first day in my summer SMFT course. Since the students are all in-service math teachers I thought they would benefit from watching the seminar. I hope that they got something out of it, especially considering that it took up around 75-minutes of our limited class time. Here are the top three take-home messages I got from the re-watch:

  1. The idea that teaching is a cultural activity. In other words, we all learn how to teach in a process of cultural immersion during our school years. We get some ideas about what a classroom is “supposed” to look like, what a teacher is “supposed” to be doing during class, and what students are expected to do. Many educators are not taught effective teaching methods and it is easy to revert to teaching how we were taught instead of how we would like to teach (or, how the research says we ought to teach).
  2. The idea that effective teaching is learned. It is not an “innate talent” and it requires a lot of “hard, relentless work.” This is a freeing idea since it allows us to ask questions like, “How do I learn to become a better teacher?” and “What is effective teaching, anyway?”
  3. The idea that improving teaching is a process instead of a goal. Instead of focusing on a large (unattainable?) goal of becoming an effective teacher, instead we can aim for a concrete, step-by-step process of making tiny changes in our classrooms over a long period of time. The seminar suggests to begin “by designing a few lessons with great care” — maybe even just one or two — and after implementation, then gather evidence on the lesson’s effectiveness. A lot of important work should take place after the lesson is introduced when we can consider how to improve it next time.
With these things in mind, one of the major assignments in my SMFT course this summer is for my students to engage in this third item: They are each required to create two lessons for use in their own classrooms. Although they teach for hundreds of hours per year, by focusing a lot of energy and attention on just one or two lessons I hope that they begin to make those small changes. In the meantime, I hope to change the culture of our classroom and move away from being the “Lecturing Professor” character.

Science and Math for Teachers

This week is the last week of our “Summer I” term and so my “Elementary Statistics” course is coming to an end. My next course begins on July 9th. It is part of a graduate here at CofC that offers a Master in Education in Science and Math for Teachers. My students will be participating in a professional development program called the Mathematics & Science Partnership.

The class itself is called “Applications of Algebra for Teachers.” The prefix for the course is “SMFT” since it’s part of the “Science and Math for Teachers” program. This is a new course, both under the SMFT prefix and in the summer Partnership program itself. I’ve been working on course development since late March, starting with the course description:

Applications of Algebra for Teachers (SMFT 697) – A course designed for middle-level and secondary teachers to investigate applications of algebra in science and technology. Topics will include numeration systems and number theory; linear, quadratic, exponential, and logarithmic functions; and matrix algebra with linear programming. Investigative labs, collaborative learning, and active learning approaches will be fundamental to the course structure.

(Other course descriptions for this summer’s program can be found here.) Our official textbook is “Reason and Sense Making in Algebra“, published by the NCTM. I have also used “Real-World Math with Vernier” for inspiration, since I hope at least some of our labs will use their LabQuest devices. We will also be using current and back issues of The Mathematics Teacher.