Sunday, October 19, 2008
A Tray Returned to the Shelf, Musical Chairs and Zero - Exercises in Understanding Placeholding
The following post is an extension of my earlier post dated September 8th titled, "What Does An Empty Tray on the Shelf Tell?"
"A place for everything and everything in its place" is a cornerstone element of the Montessori method. Placement is prioritized. To create a more independent environment, methods of placement and placeholding are maintained by both the adults and the children in a Montessori Primary classroom. Yet, again and again, I have listened to frustrated lead teachers and assistants talk about how children repeatedly returned trays to the wrong shelves or even piled them up on top of one another. These teachers/assistants are not requiring that the tray be immediately returned to the correct place on the shelf after the removal of the materials on to a table by a child. Instead, they have the child work with the materials while they are still on a tray or they have the child place the trays under their chairs or tables. In the mean time, other children desperately looking for a place to return their trays see an open spot on the shelf and place their finished work there. This can be easily solved.
Children should return the emptied tray to the shelf immediately before doing the work. The tray, as I stated in my earlier post, becomes a placeholder. There is nothing on the tray but the tray holds the place. This is exactly like zero. Zero is nothing in terms of quantity but it holds a place. It's significance can not be exaggerated as it is that important to math.
I wanted to extend this understanding of placeholding beyond the tray and link it more specifically with zero itself. I also wanted a presentation or an activity that all of the children could participate in. I decided, with the help of an MIT visiting professor friend of mine, Barry Kort, to have the children play musical chairs. To extend the concept of zero as a placeholder, I told the children that in the beginning there would be a place for everyone and everyone would be in their place - referring to seating rather than specifically placement. When they all sat down in chairs arranged in rows back to back, I added one more chair and placed on it a sheet of paper with zero drawn on it.
Next, I told the children that they were to march around the arranged chairs when the music was on, but as soon as it stopped they were to find a place to sit down. I also told them that I would occassionally remove a chair or two and/or zero would be placed on the seat of a chair. This would limit the seating. There would not be enough places for everyone to sit. I asked them why they could not sit in a chair with zero on it. One child instantly answered, "Because it is like the trays in Practical Life, it is holding a place." Great answer.
I also told them that only one child could sit in one chair. I said it was like math; you never put two numbers in one place. Before I put on the music, I had the children practice walking around the chairs and sitting down on the chairs. I then divided the class selecting one group to go first, followed by the second. All of the children looked eager to start.
I put on the music and they began walking around the chairs. I carefully removed one chair while they walked and I placed the sheet of paper with zero on it on another chair seat.
They walked around and around.
I stopped the music and they sat down. There was no pushing or shoving. They just waited for the music to start again, which it soon did. More and more chairs were removed and the zero was placed on one chair and then another.
When there was only one chair left, I placed the zero on it. The children still walked around it to the sound of music. When the music stopped, they circled the chair and just stared. Not one attempted to sit on the seat. I started the music again and quickly replaced all of the chairs including one for zero. I stopped the music and everyone had a seat.
It was a great exercise.
My friend at MIT even suggested that elementary children play this game as a means to understanding homelessness. When there is no place for you, you feel you are displaced, left outside. I can see his point. For my purposes, it seemed to really impress on the children that zero is a placeholder.
The next day, I prepared the snack table while Cristina watched the children on the playground. I drew on the snack chalkboard the word zero and the image of zero itself. When the children came in, they stood looking at the zero. They looked a litte concerned. "I am hungry for snack," one of the younger children said to me. I said, "Well, go ahead and have a piece of pumpkin bread." The child looked at me and said, "But zero is nothing. I can not have nothing snack." I walked over to the small chalkboard and said you are right. I then said that I would change it.
Instead of erasing the zero - which might lead to a child erasing a zero in a math equation - I flipped the chalkboard to reveal a 2 - for two pieces of bread. The childrens' faces flushed with joy. One was so relieved that he pointed at the two and just smiled.
Again, it was a very successful lesson. I continue to seek out new ways to teach zero as a placeholder and will share any that I find.