I wonder, I notice | Freedom in Art
In the previous post, we were prepped and ready to dive into our first: “I wonder, I notice” art math project. I was a little nervous to say the least, but I am excited to say this project was wonderfully successful.
PLAY | Noticing and Wondering
There had been some interesting observations the day before, and the kids decided to work from there. First, they notice what all kids would notice that it looked like the empire state building or a huge rocket. Then they began to notice some patterns like the top two edges are mirrors of each other, and that each color rod was squared. They also noticed square shapes within the white figure.
My oldest is the creator of this art, and he said that he began by making a staircase train, that is a train with one color of ever rod, and then, beside that train, he built the same train as before minus the first rod of the previous train. He continued on with this pattern until there was no rods left. Then he repeated it as a mirror image. They noticed the curves, but it didn’t appear to be a favored feature or one that interested them. (Did I just dodge the curve bullet?) But my own personal wondering is if numbers have a natural curving effect? (I am not a mathematician if this seems a dumb question to you.)
Then I asked them what they wondered about. The biggest thing is “what does it all equal?” In fact, it seemed like a perfectly simple idea and an easy one. I could totally handle this, but I had no idea what was about to unfold.
DISCOVER | Patterns
Looking for the easiest way to add up all the rods, I encouraged them to build upon what they noticed. They had notice the squares at the top, so we built the first part of our equation with that information.
Then, we decided to break up all the white rods within the artwork, and that is when I noticed a pattern. So I paused for the cause and asked them if they saw a pattern.
(2 x 9) + (4 x 8) + (6 x 7) + (8 x 6) + ?
Do you see it? 2, 4, 6, 8 and 9, 8, 7, 6 ? I was so excited that the kids saw it too. It took all that was in me to sit back and wait for them to see it. Noticing the pattern, I asked, “I wonder what will come next?”
(10 x 5) + (12 x 4) + (14 x 3) + (16 x 2) + (18 x 1)!
Indeed, we double checked the prediction by looking at the picture and counting. If they had filled lower part with whites, this would have been clearly seen but my oldest had run out of white rods. Yes, I was very pleased so far, but to our joy the pattern finding continued.
We returned to the beginning of the equation to start working out the multiplication, and we decided to add later. This turned out to be an excellent idea because they found more patterns. As they figured out the worth of each rod squared times two, Hannah saw another pattern in the ones’ place.
2 + 8 + 18 + 32 + 50 + 72 + 98 + 128 + ? + ?
Hannah predicted that the one’s in the next two numbers would be 2 and then 0 following the 2,8,8,2,0 pattern. She saw sequential order of odd numbers in the ten’s place but it didn’t continue. It was a curious pattern that I think might reveal more if we continued squaring but fear of losing the my excited children, I kept focused on their goal.
Surprise! Another pattern. I think that anything that truly pleases the eye has a mathematical quality so it shouldn’t be a surprise to find all these patterns.
We finally came to the total and I didn’t realize so much time had passed. I know you have some clock watchers in your crew and you know they are just itching for math to be over especially after 30 minutes. A whole hour passed and they were saying math was awesome and could they do this everyday. Can we say today was a winner?
In fear of losing their enthusiasm, I was happy to end Math for today on such a high note. I thought it was going to be hard. That I would get stumped by a hard question from one of the kids or that we wouldn’t find anything so interesting. I had just as much fun noticing and wondering as the kids. I think for the rest of the week we will just build some more, notice and wonder.
Often, as parents we feel ill equipped to venture down this mathematical journey without a textbook in hand, but I am learning that I don’t have to have all the answers for my kids. In fact, it’s better that I don’t. I provide a safer environment for them to wonder and discover the beauty of math for themselves.
We could easily get wrapped up also in presenting our children’s ideas in correct mathematical notation. It was brought to my attention that I might not want to use the long bar for addition in such a manner that was done. This was a good point on what is better, the understanding of the necessary or the understanding of the arbitrary.
It might be in some eyes that a horror of misusing the long bar is poor teaching on my part. The long bar meaning equal is arbitrary information. My kids don’t understand the long bar means equal and that if using it, you must make sure both sides of the bar have the same amount. We were short on space and the children’s attentions are short. In fear of losing them on their quest to find the total of the artwork, I dispensed with the arbitrary and resorted to the chicken scratch of adding.
The kids understood the necessary and in time if they wanted to present their presentation formally, I would take the time to provide the arbitrary information of correct mathematical notation. This is a lesson though that if you fear not knowing the arbitrary information, you may commit the greater sin of not knowing the necessary information which ultimately gives context and understanding to the arbitrary.