Monday, September 14, 2009
Exercises in Zero - Nothing and Placeholding - Part 1
Long time readers of this blog may remember my earlier post on the empty tray as a placeholder. In my training, we were told to have the child take the work tray from the shelf, remove all of the items onto an oil cloth or place mat and then return the tray to the shelf. The empty tray served as a placeholder preventing children from misplacing another tray in the spot.
This misplacement of trays is common in environments where the child keeps the tray at the table with them while doing the work. The empty place on the shelf seems so in need of something that a child places a different tray there and walks away. When the first child finishes his work and attempts to return it to the spot where he found it on the shelf, he sees that there is now another tray sitting there. So this first child stands there with a tray looking for somewhere to put it and yes there is a place. It is where the second child's tray should have gone and so the first child puts his tray there instead. Soon, either the lead teacher or the assistant comes by and notices that once again trays have been misplaced. This generally continues for most of the first several months of school.
Returning the empty tray to the shelf is an easy solution that indirectly presents placeholding. Later, when the child receives their first lesson on zero as a placeholder in the math area, they will recall this experience with the empty tray.
(Note: I am aware that many AMI environments limit the use of materials other than the Montessori materials. I, living on the East Coast, have most often worked in AMI/AMS environments. It is somewhat like that cuisine referred to as East/West Fusion. In AMI/AMS schools a collaborative relationship is maintained between teachers of both trainings. The classroom reflects this collaboration. Adding additional math materials to the shelf is up to the individual lead teacher and perhaps the head of the school)
My first placeholding exercise is for the younger students in the environment. This work is presented to a child who has had a lesson on using a hole puncher, has done that work many times (found on the shelf along side cutting work) and has had a lesson on how to use a glue stick. Also, the child has worked with both the spindle boxes and the cards and counters. Therefore, the child can recognize the symbols 0 - 5 and their quantities. Lastly, they may have played the zero game reinforcing that zero is nothing.
(See my post on musical chairs and zero: http://themoveablealphabet.blogspot.com/search/label/Zero) )
Setting up the tray:
In a beautiful box I placed a small bowl to collect punched circles, a glue stick and a few small pieces of colored paper to be used for hole punching. This box was placed on a slightly larger tray that held several half sheets of paper. Each sheet had six large boxes marked off and inside of and at the top center of each box was a single number from 0-5.
The work itself:
The child punches out several, construction paper circles and collects them in the small bowl. Next, they glue the correct amount of circles under the specific number in an individual box. They do not glue any circles in zero marked boxes. See the series of photos below of a child doing the work:
When she repeated the work, the second sheet did not have a zero included.
I have found that young children really enjoy this work and that the careful manipulation of the small, construction paper circles adds to their ability to later build a bead tower with the colored beads - also circles but three dimensional. Too, they are similar in size in regards to their circumference - the construction paper dot and the colored bead.
I have tried using small sticker dots but they stick on the children's clothing and they eliminate the hand strengthening and manipulation work that the hole punching provides.