JUNE 2017 UPDATE TO THIS POST IS FOUND AT THE BOTTOM – SCROLL DOWN.
This summer I asked 10+ math teachers in my district to write a guest blog for my site. I did this because I know I work with the most amazing math teachers and most of you out there will never know them because they do not have blogs (yet). One of the people I asked, Annie Perkins, promised me a post but after attending Twitter Math Camp she went and started her own blog. She is amazing. Check her out.
Another person I asked was Stephanie Woldum who teaches at the same school as I do – in fact last year we shared a room. Stephanie has both an Art and Math Education degree. She is a social justice expert – she incorporates her students community throughout the year in her tasks with students. Stephanie and another peer (who has also promised to do a guest post for me) Morgan Fierst speak on Social Justice and its place in the math classroom often. (Here is an article that our Minneapolis newspaper did on the two of them this last school year) Stephanie and Morgan are also the current finalists (the only 2) for the Minnesota Presidential award for Excellence in Math & Science teaching. I am lucky to work and learn from both of these teachers.
As I shared above, I shared a room with Stephanie this year. Almost everyone that walked into our classroom said the same thing, “Who made these beautiful math sculptures?” (most hanging from our ceiling) The answer was Stephanie along with students in her Geometry classes. Everything beautiful in the room was hers. This post is on one of those sculptures (my favorite one) , what inspired her and how she created it. I love the intersection of math and art. We all know we have students in our classes that need us to do more artful things. Enjoy.
WELCOME Stephanie! You are my very first guest blogger.
How 2500 popsicle sticks and 100 shades of glitter created real conversations about math in my classroom.
Stephanie Woldum, Minneapolis South High
The mere mention of the word is enough to make most Geometry students groan or eye-roll or both, simultaneously. The setting: A 10th grade Geometry class, the last weeks of the 4th quarter. The trig unit was meant as an introduction to topics that students would master later. Read the students: This is extra work!
Upon teaching this unit for the third time I was desperate to bring some interest and, dare I say, excitement to students who could only hope that summer would hurry up! Too often my best trig lessons had been destroyed with exclamations of “Why should I care about this? Trigonometry is Boring/Scary/Too hard/___________ !”. (Insert your own negative adjective here.) Difficult thing was, I empathized with my students. I didn’t much like the unit either.
A few weeks before embarking on the tumultuous journey that is the Trig unit, I was watching TV and happened to catch a video that inspired me.
The video is short (10 min) and it documents the working process of an amazing kinetic artist named Reuben Margolin. So much of this video I loved but I particularly loved that the video showed him doing math; being active in designing and creating using mathematics. I also liked that the video inadvertently acknowledged a misconception about mathematics that my students often hold. I think this misconception can sometimes grow from situations in which we, as instructors, force mathematics into our real-world problems or vice versa.
Here was the problem: I often would tell the students that math was created to describe the patterns we see in the world but rarely gave them access to examples where this held true. I loved that Reuben talked of this… He wondered, “How could I re-create the caterpillar?”. Mathematics as mimicry. Mathematics as a bridge from perception to creation. Perhaps creating a sculpture of our own held the key to unlocking my students’ appreciation and understanding of trigonometry.
Motivation for learning more deeply about trig became readily available to students after I shared the video with them. Still, most students assumed that the mathematics being done by Mr. Margolin was outside our reach. Most students were perplexed by the video’s use of the term sine “wave”. Most could not make a connection to our understanding of sine as opp/hyp and an oscillating graph. We took these wonderings and did a great mini unit featuring the unit circle and Geometer Sketchpad with some major “aha” moments as a result. Students discovered that they could create and wonder and theorize just like “real” mathematicians.
So, great. I was inspired and the kids were too. We had lots of questions and lots of mathematics to guide us. Exactly, though, how I was going to design a sine wave sculpture was a little beyond my expertise. I had to push myself to learn something new too!
So here’s what I did: I bought a roll of garden fencing, string, 2500 popsicle sticks and 100 colors of glitter. I stapled the fencing to a wood support to create a grid and labeled each row with degrees up to 2 full rotations. Every student was responsible for using a series of transformed equations to create a row of popsicle sticks for a particular degree measure. The neat thing I decided to do was to shift each equation by 10 degrees as students moved in their rows…. Here’s an example of what the student work looked like:
The calculation performed by each student gave the string length needed for each grid location. What I thought was cool about this is that students received instant feedback about the accuracy of their calculations. It was immediately apparent when calculations were done wrong as the glitter stick would not hang correctly.
Here’s what the sculpture looked like after the first day:
Here’s what I thought: “Oh, Crap! It doesn’t really look like anything…. This might be a big crash and burn!” I didn’t hide these thoughts from the students. I told them (and myself), “We are creating this sculpture together and the mathematics is telling us that it will look cool. Trust in each other to do good work and trust mathematics to lead the way!” I told them I didn’t know exactly what the sculpture would look like finished and tried to play it cool but, honestly, I was freaking out a bit. “Deep breath, trust the math.” I told myself.
Given the next day’s work, the pattern began to emerge and our excitement and contentment with the project started to grow. We were in it together!
During the year this sculpture was made I had 2 sections with about 55 students between them. It took us 3 days to construct the sculpture. Along the way we had great discussions about the interconnectedness of Geometry, the trig functions, the unit circle and transformations of functions. Students connected their work from Algebra I, Geometry and extended their thinking to connect with the next course, Alg II.
The sculpture allowed my students an opportunity to delve deeply into a mathematics. It gave them motivation to find insights and to collectively create something that continues to inspire and engage anyone who walks into my room in a conversation about math. It’s a great entry point to a math conversation with a math phobic parent or student! Pretty cool.
This year I’ll be teaching Geometry again and I am already excited about the formerly dreaded trig unit. Of course, there will be glitter, art and mathematics. There will also be plenty of new opportunities for me to engage students creatively with mathematics. I most look forward to this opportunity… the continued experiment called teaching. How we build access, appreciation and connection between mathematics is every bit as important as the content of the course.
Perhaps, in these waning days of summer, you can join me in seizing this opportunity. Think about your least favorite unit/topic to teach. Think about it deeply and seek inspiration! Find and share the beauty in math.
After all, if we’re not excited about what we’re teaching, how can we ask the students to be? I’ll admit, it can be daunting to try something new but I know from experience that the greatest “Ahas!” often come from the biggest “Oh Craps!”
You know, as my Math Coach often says, “It’s always darkest just before the glitter”.
Side note (From Sara VDW): Stephanie and I had a room next to another math teacher who was NOT a fan of glitter. One of my favorite moments this school year is when Stephanie had her student aide glue glitter to circular stickers about an inch in diameter. Stephanie would stick 1 of these glitter stickers to the ceiling above our colleagues desk. Slowly the glitter would rain down over the course of days/weeks. It drove our colleague nuts to find glitter on his desk (just a piece or two) day after day after day. Pranks on colleagues is what keeps us all doing what we do at some level.
Thank you to Stephanie. If you are not following her on twitter yet, click HERE and follow her. Let us know if you’d love to hear more from her. She is amazing.
JUNE 2017 UPDATE!
Stephanie taught Geometry again this year and during the last few weeks of school her classes made another amazing sculpture based on trig ratios. Check out the photos below (from her twitter account) and a video I made of it where she talks a bit about how she made it. LOVE IT!
4 sine waves each shifted 90 degrees + approx 500 fishing lures = the beauty of mathematics! The equations used to create this years sculpture are:
Check out my video here:
You can also check out short videos Stephanie made on her twitter account HERE.