Week 6 Activities + Connections

 

This week, we observed a handful of mathematical dancing and dancing mathematics videos. Many of them involved Dr. Karl Shaffer, a dancer and mathematician. Video links are at the end of the post. 

I was fascinated by the body calculator by Miranda Abbott through her program Dancing Digits. 
I wanted to learn this with my children and try to perform calculations of higher numbers to see if my 5 year old and 7 year old children could work out these more advanced concepts with me. 

I learned the movements and absolutely love the idea of using the body as a calculator!! I have been pondering how this was a possibility since watching Sarah Chase's video about dancing different numbers on the the body. 

Mathematical connections: As practice, I danced numbers 1-200 in a time lapse (below) and the repetition really demonstrates this base 10 counting system with 10 movements of the legs (10^0) creating one movement in the arms (10^1), and ten sets of arm movements creating one finger movement(10^2), and 10 sets of finger movements to generate one head movement (10^3). 

So, if leg movement = l 

arm movement = a

finger movement = f

and head movement = h

We could calculate our body number with: l(10^0) + a(10^1) + f(10^2) + h(10^3)

It would be really fun to make assumptions like let l,a,f, and h = s

Then have the students dance out s(10^0) + s(10^1) + s(10^2) + s(10^3) to see what kind of full body movements we would get rotating through 1111, 2222, 3333, 4444, 5555... etc. This might be a fun way to assess whether students understand the idea of substitution with an added embodied layer.

The clock really comes to mind with the cyclical motion of the second hand (12^0) generating one tiny movement in the minute hand (12^1). It also really reminds me of a reduction gear. 

A change to the system: If I were to teach this, I think I would try to use both my legs in the positions instead of a turn out of my feet. That way I could ensure a balanced use of the limbs that move the most. In addition, numbers 5-9 may get mis-read if my students and I don't turn out, or register that our support leg is turned out enough. This also helps if actually creating a piece from the movements as each time you put your support leg down (00, 05) you can move your body with it. 

With family: My children tried this experiment with me and my son really took off with it. He asked me to test him. My favourite part of this dancing activity while we practiced adding numbers is that he really had to think about carry over. At the beginning of the video, I asked him to add 10: he would cycle through the feet positions, and carry over to the arms. Then closer to the end of the video I asked him to add 30, he discovered that you could just move the arm positions independently. He was so proud of himself. 

Here's my general "sketch" for learning using this dancing digits idea:

1. First, I would teach the history of numbers at the beginning of the grade 9 curriculum as a foundational piece giving students perspective and appreciation for the symbols that we take for granted in communicating the concept of numbers.
   
   
2. History would lead to the number system: Natural, Whole, Integers, Rational, Irrational, Real, Imaginary and Complex.
   
   
3. Then, we would get into playing with/as integers. This is where I would introduce the dancing digits concept with call-backs to the history of numbers regarding various bases. In addition, I could ask the students to adapt this system (or invent a new system) for base 5, base 3, and base 2.
   
   When doing so, they should see a pattern: a progressive speed increase between the movements of the legs to arms, arms to fingers, fingers to head. It would also involve a placement calculation that may be trickier for them to mentally calculate: 5^0 + 5^1 + 5^2 + 5^3, for example
   
   
4. Then, I would ask them as a class to do addition or subtraction of 1-4 digit numbers (including negative integers) through the Dancing Digits technique. I would make sure to first use numbers that did not involve any carry over between body parts, so the students could get a feel for movements within the range 

• Examples to dance out:
• Easy level: 1 + 100 + 5 + 20 + 300 + 10 - 3 - 1 + 40 - 500 + 20 + 6 - 1 - 200 + 40. 
• Medium mode: 150 + 1037 + 2411 - 1066 + 23
  
  
• Then progressively, I would ask them to add and subtract numbers that would result in carry-over:  
• Hard mode: 232 + 567 + 9031 - 390 - 411
  
  
• Followed by a Journal Reflection:
• When doing arithmetic with your body, explain your patterns of thinking (or shortcuts) that are allowing you to get to the result efficiently. Provide examples. 

WONDERS that I'm working on: 

1. How can I adapt this using multiplication or division? 
2. Can I make this a two player game in which the coming together of individuals resembles a mathematical operation in which the result reveals itself rather than needing to be calculated?

Referenced Videos:

Viewing: (1) Karl Schaffer & Mr. Stern TedX  talk (2012) (10:18), 

(2) Karl Shaffer Math Buffet: Squishahedron and Tetrahedron (2021, Julia Robinson Math Festival) (2:32)

(3) Dances with math: Interviews with Karl Shaffer, Saki and Erik Stern (2021, Julia Robinson Math Festival) (12:51)

(4) Jump into Math! Malke Rosenfeld TedX talk (2013) (12:24)

(5) Keith Terry : Rhythm of Math -- Teaching Mathematics with the Body teaser (2015) (1:23)

(6) Keith Terry Rhythm of Math: Polyrhythms -- 3 against 4 (2015) (2:34)

(7) The geometry of longsword dance locks (Steel Phoenix) (2013) (4:47)

(8) George Hart: Mathematical Impressions: Longsword Dancing (2014) (5:46)

Optional viewing -- a bit of math theatre (two plays about women in math):
(a) Gerofsky, Witches of Agnesi musical math history play (2019/2021) Note: This link takes you to the National Math Festival (US) panel discussion and pre-recorded play. If you want to watch just the play, here is the link to it. (55:00)

(b) Moira Chas, The fictional letters of Alicia Boole (2021). (24:10)

Activity: (Note: Malke Rosenfeld’s website has just disappeared and been replaced by some ecommerce site! Here are some different and definitely worthwhile activities for you to try out and think about!)

Here are some math and movement activities from Karl Schaffer and company:

Making Stars (with Scott Kim) (1:38)


Mathematical Hellos (3:13)


Adrienne Clancy on dancing rotations (including the rotation of the earth on its 23.5º tilted axis..) (15:15)


MIranda Abbott’s In Constant Motion (5:02) (Miranda is a Canadian professional dancer who is now a Grade 2 teacher in Costa Rica, and teaches mathematics through dance…)