This morning, I was feeling lethargic, but I knew I had to be accountable to Carol (our classmate), who became my fitness buddy after we trekked the hilly neighborhoods of Nanaimo in December 2021. So today, I decided to make a change my exercise pattern. Instead of using a run app that sets 2-minute jogs/3 minutes walks intervals, I decided to use Susan’s math session as my interval timer. My speed stayed between 2.0 to 2.5 mph since I knew our class would approximately an hour and half in time, it had to be maintainable. As each person spoke, I would change the speed by 0.1 mph. Example 2.0 to 2.1 to 2.2 to 2.3 to 2.4 to 2.5 then back down to 2.4 and so forth. This week videos and readings is all about movement with math and for me when I exercise, not only do my hips wiggle to dance, but my mind is constantly counting, thinking that time would go faster when jogging at a higher speed. The unpredictable nature of using various peoples talking moments as target timers made this the treadmill, combined with the engaging topics of conversation, made this physical activity fun. I was shocked at how fast time flew. All in all, I thought this tied in nicely with this week’s videos, tying the ideas of movement and math and the ideas of looking for new ways or even breaking patterns to embody movement and math into our classes, practices, and in this case my life.
Dancing Mathematics and the Mathematics of Dance (Sarah-Marie Belcastro and Karl Schaffer)
As Susan mentioned in this morning’s session, Belcastro and Schaffer are both dancers and mathematicians for the past 20 years. The authors want readers to look beyond the “superficial connections” between math and dance for example “counting steps” or “noticing shape”, but to notice the “deeper connection” such as “math inspired dance” or “dance that naturally incorporates math concepts” or critical thinking involved in “solving choreographic problems” (p.16).
Belcastro et al. wrote about math within a dance, the importance of music and counts as cues to movement playing with the rhythm and the symmetry of dancer(s). This comment reminds me of the Saturday Box Fit classes, how my instructor uses movement, music and count to keep us in a rhythm and limited space (for social distancing of course), to motivate us to right jab, left jab, right cross, left uppercut, right leg kick, and back leg kick, giving us a great intense workout. People in the workout class are quick regiment and rigid in the movement, whereas I notice because I love music and dance, my body naturally like on the treadmill, starts to wiggle its hips and an extra hop in the moves making the box fit class more dance like and fun. Because of that, the workout itself is masked within the joy of the dance and makes exercising enjoyable.
Another stop for me in this article was “How
does math sound?” in this case they were referencing tap dance and clogging. The Figure 9 below showed how the beats of 3
and 8 with sound can reach the LCM of 24 (p.19).
Which inspired me to use this grid count and math sound as part of my
clapping activity in the next section. I
also want to give credit to Jen W. week 5 video with her son and how she used
a clapping pattern with her son to find different LCMs. You should go check it out if you have time.
Belcastro and Schaffer ends off with the idea of a third space, letting “dance take its own life” being able to “interplay these elements with math” which “engages us as artists (p.20). Which Susan and Sandra commented in this week’s group session. In my previous school, a portion of students at Windermere had a passion for hip hop dancing. It amazes me the ability and the intensity these students had with memorizing a 3 minute highly choreographed routine. I have had these students, in my Workplace Math 10 class, that lived and breathed dance. If I had used methods of embodied math involving movement and music and spoke to them in mathematical language using dance terms, these students would have probably understood the math better in an embodied way.
Found a YouTube clip of my ex-students competing in a dance competition back in 2019. Enjoy!
MAINUHVENT - The Release Dance Competition 2019 - Junior Division
“Clapping Hands” (The Activity)
As a starter before we did the Clapping Hands game, students were provided with grid paper and asked to fill in the 12 by 12 multiplication table. I would fill the 12 by 12 multiplication table on my tablet for students to check their products. Then they were given 10 minutes to study the table before we played a clapping game, I recalled from my French teacher during my high school days called “Zing”. Zing was a game where students would say the sequential numbers verbally in French when the teacher pointed at them with a meter stick. When students got called upon multiples of 7 then they we say the word “Zing”. Any student who makes a mistake either saying the number in French or saying “Zing” on a multiple of 7, they would be seated a removed from the game. Last person standing wins the game.
How did I modify this French “Zing” game in a math class? I asked my students to stand around in a circle, and practice just saying the numbers in sequential order clockwise but told then when a “Multiples of 5” happens they are to clap their hands. So, a rhythm naturally happens with the count and with the clap that the game flowed (1, 2, 3, 4, clap, 6, 7, 8, 9, clap ……) until a student makes a mistake and is removed from the game. I would change the multiples from “5” to “3” then to “8” and so forth. By the time two students were left standing I decided to increase the difficulty and threw in two multiples ex. “2” and “3”. The students had fun, recalling their multiples in this game, with smiles and laughter. They also felt the intensity of the game when they were focused on the count making the game a friendly competition.
Once the clapping game was complete, we continued to use the grid paper incorporating the multiples embodying the math with the clapping game relating it to equivalent fractions. They were able to visually see the multiples of from the counts in each bar to determine the equivalent fraction. This idea of using the grid paper was like Figure 9. Clapping on every third beat against an eight-beat count produces a single clap on each of the eight beats before repeating. My old way of teaching would be just showing the fractions and ask what you multiply to get to the equivalent fraction. Now, incorporating the clapping game and the grid as a visual, the ideas of math, showing the sets off, enhances the concept.
Every week, I am surprised with the results from each activity. I see the positive affects it has on my students in my math classes. How can I share and open the minds of my colleagues, whom are traditional teachers, to see and experience the things I am seeing, unfolding with my math students? What is funny is that I send photos to my math coworkers, and I have a feeling, they think I am nuts. But I am fortunate to have an administration team that always provides me with positive feedback and support, encouraging me to continue to explore these ideas from Susan's course in my math classes.
April, what I love most about the thinking you shared in your post, is how you have taken the ideas presented this week and personalized them. You didn’t just complete an activity, you considered the purpose of the activity and made it fit your circumstances and who you are. Bravo! I think this is a great step toward answering your question about opening minds. Your personal stories are inspiring. When you share what you are seeing unfold with your students, you will inspire others. It might start slow… but it might catch on too. When we offer others the opportunity to take an idea (like embodying mathematics to increase student understanding) and translate it in a way that makes sense in their lives, we increase capacity in others and ourselves. I think this is also a step to moving beyond the superficial connections that Belcastro and Schaffer are refering to and closer to critical thinking. I saw evidence of this in the reading I did this week as well. Students were building deep understanding of patterns, theorems and proofs through dancing with ribbons around a pole. Through the movements of the dance, the students were able to see the patterns developing.
ReplyDeleteYou commiserated that “If I had used methods of embodied math involving movement and music and spoke to them (students) in mathematical language using dance terms, these students would have probably understood the math better in an embodied way”. The great news is, now you can! It might be a new group of students with new passions, but isn’t it great that your students now can benefit from your wisdom?
I love that you were working out during our meeting this morning, and not just working out, working out purposefully connected to mathematics!
One last thing – MAINUHVENT… amazing. Thanks for sharing.
Morning Joy,
DeleteThank you for noticing how I embodied the theme of the week in my blog. I like to really dive into each week's like how an actor/actress learn a new role in a movie.
I guess, just like the students, people in general want to see the instantaneous results from an action that is imposed. But your reminder of patience is what I will work on.
With the students on Mainuvent, that was from my previous school, who love to hip hop dance, but in my current school, the students love to act and film. So the school culture changed now. But finding was to adapt to each school is what I will take from it.
Hello April,
ReplyDeleteI appreciate your explanation of the clapping exercise. It sounds that your students were having fun. This activity will be applicable to the work I would like to do with older adults and seniors. I am thinking that depending on the age of the seniors we can do the clapping in odd numbers for example.
I tried to follow the activities done in the video by Keith Terry : Rhythm of Math -- Teaching Mathematics with the Body teaser (2015) (https://www.youtube.com/watch?v=1DAyUaS23lo) but it was too complex for me. Your explanation is much easier to understand. :)
I am wondering how to work with students that are shy and may feel nervous to follow the game. I am thinking the activity in the grid paper will help them to feel more comfortable with the activity.
I saw the video of your students and it is amazing, but it is intimidating. I am not sure if I would be able to work on activities relating to movement with them. I will not be able to show by example. However, I am assuming I would need to guide and show videos done by other teachers. It reminds me of discussions for my class EDCP542 (Theorizing Pedagogy). Would it be possible to teach without knowing the content? Can you take the role of student/learner while you are the teacher? I will be learning from my students how to dance. I will provide the choreography (steps or algorithm) and they will execute the dance.
Morning Lida,
ReplyDeleteI have discovered from working with shy students is you have to build a safe supportive environment for them to come out of their shell. I love to share short vignettes of obstacles in my own life and how I overcome them. The open genuine honesty, and the time I take to take to each students individually, combined with their collaboration working in pairs/groups or playing games in pods, has gotten my students to become comfortable working, playing and exploring together. I was at one school, during Pi day, where I gave them time for each student to memorize as much digits as they can so that we can have a game reciting the digits of pi. I kid you not, all the kids participated, did their best, were a tad competitive, but engaged with that activity. As a reward, I gave all the students a slice of pie.
The mainuhvent video to showcase the students' what they do in their other classes. I definitely did not teach them dance and I can see how it can be intimidating. A handful of these dancers, were weak math students, and although they could memorize a dance routine, the confidence did not translate to math class. But I always teach the fundamentals first, find strategies to support them, and then ask them to explore the ideas further through an activity or exercise individually or collaboratively dependent on the task. I think it was in my week 3 post, where my student said "Ms.A.Jung, you need to trust us, we know what we are doing.", which reminded me that sometimes, once the set up is done with the fundamentals, we as teacher need to give students the time and space to create and explore the math on their own.
Last comment that I learn from all the schools I've taught at is when you watch students in a non-academic course, such as choir, band, dance or students who participate in extra-curricular activities such business groups, student council or leadership, the amazing things they can do, where math is most likely embedded in it without them knowing. Some of these students excel and take lead in these roles outside the classroom so now I am thinking how can I take what they enjoy to do, and give math that same spark.
Hey April…
ReplyDeleteRight off – treadmill workout and breaking patterns – how about “disrupting patterns”? I think your treadmill workout disruption is like what you have been doing with your teaching – disrupting patterns and finding all sorts of cool results for you and your students. I think this is also related to what Malke Rosenfeld said in the TedxBloomington talk Jump into Math – how the work of mathematicians is having a question with no answer yet and then using the math you know to explore. You had a question about what it would be like to change your workout tempo based on the turn taking of our class meeting, or you have questions about exploring art/movement/etc with your students, and you apply math to see what happens.
A major “stop” for me in your post was when you talk about Belcastro and Schaffer’s idea of the third space of interplay of dance and mathematics. As I said (thanks for the reference!) in the Zoom meeting, I really like that idea because it allows it not to be dance helping math or math helping dance but both are being explored in conjunction with one another, living together as they seem to naturally occur. In the paper I read (Vogelstein et al., 2019), the authors speak of a hybrid space which might be similar to the ’third space’. They write, “…an important aspect of the hybrid space: the knowledge that can be built there is neither the ‘mathematics’ of mathematicians (or schools) nor the ‘dance’ of dancers” (Vogelstein et al, 2019, p. 344). In the margin I wrote “hybrid space the dwelling?” and I was referencing the dwelling space we considered in Tim’s class. I think the third space/hybrid space are like the dwelling space in that they can be set up in ways that support exploration of math and dance so that deeper understanding of each is achieved. I find it interesting that there is no citation of Karl Schaffer,Erik Stern, nor sarah-marie Belcastro in the Vogelstein work (but Susan is cited – twice!). I wonder how theses authors’ work might have been shaped with some exploration of the work of these mathematical dancers/dancing mathematicicans.
Thanks for an engaging and fun post April, and for contributing to the conversation taking a life of its own everybody. A kind of “dwelling place” as Sandra says, quoting Vogelstein. How does this dance of words and worlds happen? With one hap or movement, number word then two, three …?
ReplyDeleteI join the group in complimenting you April for adapting the clapping activity to your circumstances and strengths in ways that inspire this conversation and our practices. Not least for working out a math and dance sequence during the online class and provoking everybody to explore further ways in which dance and math might be understood in conjunction. I wonder what might happen next?!
Interesting question Sandra about how author’s writings may be shaped by words cited and not cited. I wonder about the influences of words, people, and places on a person’s mind, body, emotions, perception, spirit, soul in relation to exploring math-dancing?
ReplyDelete