For this assignment, I explored Ali and Colin's concentric circle number representation activity inspired by the work of Wassily Kandinsky.

This week’s activity had me stretching my thinking in multiple ways. First, I found a sense of wonder in the way Sarah Chase’s brain worked–moving multiple parts of her body in a seemingly seamless choreography of dance. Thank goodness she broke down her ideas into moving ‘3 against 2’ because my body and brain could manage that activity. I marveled at how grounding the movement into thinking of mother, myself, father, summer, and winter made it all somehow more doable. I found myself enchanted with this activity, though I admit, I didn’t take it further to try to extend the activity. Mostly, because envisioning trying to have my grade 3s do such an activity made me feel instantly stressed. I could try this with a small group, but decided to look at Ali and Colin’s concentric circles instead as this seemed more in line with what my class would embrace and like to wrestle with.

The first thing I decided was that I needed to remind myself how base 3 worked. I instantly felt a pang of jealousy toward those that could whip out any base–something counting system like it was a breeze. I was briefly distracted by thinking about how I could use Kandinsky circles to round numbers to the nearest ten, but first wanted to try the activity as presented. I decided to try base five with the Kandinsky circles and realized how accessible base five felt. I suddenly felt like I could handle any base–well at least I knew if I didn’t get it, I just didn’t get it yet. Armed with four colours (white=0, purple=1, blue=2, red=3, green=4), I began trying to code my circles using base 5, and division was my friend. I also chatted with Claude AI and used the tool as a teacher of sorts, bouncing my ideas around and needing some reassurance that I was doing it correctly. Ah, the need for mathematical reassurance–sometimes I get bogged down by that need and am working on trusting my mathematical gut. I can, I must, I will!

I found creating this Kandinsky inspired art to be relaxing. I felt that the more time I could spend with it, the more it would make sense. I started with the numbers 1-16 and then wanted to know what would happen if I tried 77-80. Finally, I was getting to use the outer ring! As I was doing this activity, I realized that my students aren’t dividing yet and that this would be a difficult activity  for them. This is where the integration piece from our course readings became crucial-I didn’t want to just abandon the mathematical depth of the activity, but I needed to make it developmentally appropriate for my group of students.

Odd/even and rounding

Base 5 circles 1-16

Base 5 circles 77-80

This activity is spot on for addressing the course’s key question: how do we integrate embodied, arts-based activities with traditional mathematics teaching without trivializing either? The Kandinsky circles activity isn’t just fun art, it requires students to develop a systematic notation for representing numbers, to recognize patterns, and to translate between different representations. This feels like a low stakes way to start incorporating more arts-based, embodied mathematics into my practice–which, as this week’s course materials reminds us, is a multi-year journey with many baby steps along the way.

Extensions I explored and could use with students:

• Base 5 instead of base 3

• This would be more accessible to grade 3’s than base 2 or 3 as the numbers grow slower, patterns are clearer

• Adapted using circles for rounding to the nearest ten 

• Innermost ring = odd/even

• Middle ring = lower decade

• Outer ring = higher decade

• Adapted circles for use with place value

• Each circle represented ones, tens, hundreds and could go to thousands with four rings

• Floor circles using for embodied place value (explored in my mind)

• 3 concentric circles on the floor/draw on blacktop

• Students jump in each ring corresponding to place value

• Example-361: jump 3 times outer, 6 times in the middle, and once in the center

• Kinesthetic understanding of magnitude 

• Makes abstraction concrete

Curriculum Ideas:

Guiding Questions:

• How can numbers be represented in multiple ways? 

• Can visual and physical representations deepen our understanding of an idea?

• How do we create systematic notation?

Possible Learning Arc:

• See, think, wonder-Look at Kandinsky artwork and the Chamberlands’ mathematical version

• Explore creating circle for chosen numbers

• Discover patterns, compare with classmates

• Detective work-decode each other’s circles

• Innovate: can you invent your own system?

• How does this connect to our base 10 system?

Embodied Learning Ideas:

• Floor or blacktop concentric circles for jumping place value

• If group understands other bases, could also jump base n patterns

• Give students manipulative for grouping in new bases

• Create large scale outdoor version with sidewalk chalk or paint a mural on bulletin board paper

Art:

• Colour choice and design

• Variety of mediums

• Start a mathematical art gallery (I have started hanging up some of my work)

• Learn about Kandinsky (also connects to language arts and social studies)

Pencil Paper Math:

• Math journal reflections

• Problem solving

• Place value notation practice

• Many lessons on base system after exploration

More Possible Extensions:

• Students invent their own base/colour system

• Can students create a way for this to express skip counting by 10 or any other multiple

• Try adding/subtracting with circles

• Explore number properties through patterns (primes, multiples)

• Use larger numbers, needing more rings

• Challenge: create mathematical art with systematic rules

• Add to Math and Mingle night as a family activity

• Different colours for various decades

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