Learning to love math through the exploration of maypole patterns recounts to exploration of patterns in the ribbons after a maple dance. The students who took part in this mathematical exploration are students from non-math majors in university. After completing a dance, students came up with an inquiry idea: they wanted to be able to predict the pattern of any given dance (any numbers of ribbons, with any colours). First, to be able to do so, they had to find a way to represent their 3D patterning into a 2D figure, to not have to repeat the dance every time they wanted to investigate a new pattern. Then, they started using that representation to make conjectures about the patterns depending on the number of ribbons used. I noticed that their investigation was a rich mathematical task. Indeed, many aspects of thinking mathematically from Nrich (https://nrich.maths.org/) were present in this inquiry: exploring and noticing (what started the inquiry), working systematically (describing different patterns with their representation), conjecturing and generalising (the end goal of the inquiry), visualising and representing (they had to find a way to represent the patterns), explaining, convincing, and proving (students had to share their ideas and convince others of their veracity).
“This was one of the best parts of this class, no suggestion or conjecture was wrong necessarily, just one more step closer to a conjecture or major lead. […] We started by noticing how one ribbon wrapped around another, how each colour interacted, what kind of patterns and designs were left behind by different colour combinations (Campbell & von Renesse, 2019, p.139)”
It is amazing to see how passionate those students were about this problem. Analyzing the maple dance patterns led them to an inquiry requiring a rich mathematical investigation, much more complex than any of the task I ask my students to do. Like in Rosenfeld (2013) mentioned in her TedTalk, investigating the dance led them to do the type of mathematics mathematicians do. And the beauty of it was this desire to investigate those patterns came from them. Furthermore, the creativity those students used during this exploration was impressive. What also surprised me was the emotional control these students had during their inquiry. Some parts of it were certainly difficult and made them struggle, but it did not make them give up on the task. They were able to manage those emotions brilliantly. Isn’t that mathematics for human flourishing?
“I hated the first class, I had to sit in a group and talk about math (Campbell & von Renesse, 2019, p.134).”
As a student back then, I would have hated it too. Because math was easy for me, I hated having to work harder to try to explain my ideas to other people (the part where I struggled more). But I know after a while, I would have loved these tasks much more than completing worksheet because it would have challenged me. Last week, when I ask my students to create a graph representing where their feet rested without much more explanation, I became very quickly surround by students asking: “what do you want me to do?”
“I don’t understand”
“I don’t know what to do.”, etc.
They were confused and did not know how to get their graph ‘right’, which really triggered their anxiety. But after some encouragement and reinsurance, they all started their graphs and were engaged with the task. Below are some graphs created by them. (PS. The stick man walking up was made by my student with dyscalculia who is used to use stories to describe mathematical concepts. I loved it because it shows that he is now applying this strategy on his own to make sense of concepts. He was also one of the few to get the task started without being afraid of not getting the concept ‘right’.)
This activity and the reading reminded me of the concept of thinking classrooms from Peter Liljedahl. Building thinking classrooms is something I am working on this year, and my students are slowly getting used to tasks where they do not know what the ‘right answer’ is. When I brought this task up, it destabilized the students who are used and good at mimicking. Although, this showed me that by bringing physical activity into my task, I created the type of tasks that should be used in a thinking classroom. This task made them get stuck, having to think, and how to apply their graph knowledge to the position of their feet while climbing a stair, which is the definition of a good task (Liljedahl, 2021). Thus, bringing dance and/or physical activity in mathematical task may get our students frustrated at first, but after a while (Liljedahl (2021) mentions 3 tasks), it can engage our students much more and enhance their mathematics learning.
Questions
I do not enjoy dance; thus I have a hard time finding connections with dance and the mathematics curriculum I need to teach. Where would you go to find some ‘dancing’ inspiration? What is your process when you try to connect a dance to a curriculum topic?
References
Campbell, J., & von Renesse, C. (2019). Learning to love math through the exploration of maypole patterns. Journal of Mathematics and the Arts, 13(1-2), 131-151. https://doi.org/10.1080/17513472.2018.1513231
Liljedahl, P. (2021). Building thinking classrooms in mathematics: 14 teaching practices for enhancing learning, grades K-12. Corwin.
Rosenfeld, M. (2013, May 5th). Jump Into Math! [TEDx talks]. Youtube. https://www.youtube.com/watch?v=
I enjoyed reading your reflection, especially the way you connected the maypole inquiry to Liljedahl’s thinking classrooms. You highlighted something so important: when students generate the inquiry themselves, the mathematics becomes richer, more authentic, and more intellectually honest. The maypole example beautifully illustrates that full cycle of noticing, representing, conjecturing, and convincing. It’s exactly what Rosenfeld describes in her TED Talk: movement opening the door to the kind of mathematics mathematicians actually do.
ReplyDeleteI agree! It does sound like mathematics for human flourishing! As I read your description of the difficulties and the emotional control they had, I thought back to the chapter on “Struggle”. It is important to develop perseverance and it seems like these physical, embodied activities hit that sweet spot of flow – not too hard to give up easily and not too easy to not be engaged! Which is also a principle of Building Thinking Classrooms. I think we are more willing to persevere through hard problems when more than just our mind and a pencil is involved.
ReplyDeleteYou have asked a great question at the end of your post. I think I am learning that there are others out there doing this work; we are being introduced to them through this course. That is one source of inspiration. I now know that if there is something I want to try, I can search in the UBC library or Google scholar for papers and studies that just might inspire. I will also be keeping conferences like MACAS and Bridges in mind for future inspiration and learning. I wonder if another source of inspiration is to simply connect with other teachers. Is there a teacher in the building that might be experienced in dance? Maybe they do not have experience with mathematics but together we can find a connection that we wouldn’t find alone.
Finally, in Fiona’s post we were having a discussion that maybe dance doesn’t work for all topics and I want to add, it may not work for all teachers. What’s becoming clear to me is that we don’t have to create every connection ourselves. If a student learns mathematics through dance in grade 9, then encounters another teacher who connects math with weaving in grade 10, and another who uses music in grade 11, that student experiences a rich, varied mathematical landscape. We cannot bear the burden of bringing forth every connection for our students. I can continue to learn and grow myself, adding to my repertoire each year, but I am not going to be able to incorporate everything well. We share the load across our schools and communities. This means my role is to contribute my strength and to connect with others who can contribute their strengths. Together, the mathematics community grows more varied and diverse.
Yes, I agree, Katelyn! Not everyone is oriented towards every form of art (though of course, we can gradually learn new things). But if every math teacher makes connections to embodied arts and the living world, in a variety of ways, then kids will get a very rich and interesting experience!
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