"Look at zero and you see nothing, but look through it and you will see the world," Robert Kaplan "The Nothing That Is: A Natural History of Zero."
Zero is a poet's puzzle. It is the single stroke of a Zen artist.
It is the circumference of a circle recalling the rim of a favorite bowl or the thin band of gold or silver that we wear on our ring finger. It is the celebrated symbol of mathematicians, young and old. As the wonderful title of Robert Kaplan book states, it is "the nothing that is."
The Memory Game:
The Montessori math exercise titled the Memory Game is a celebration of nothingness. It confirms for the teacher that the child understands zero as without quantity. It also reveals to the teacher whether or not the child is mature enough to move forward with the math materials.
Maturity in a child is not always that easy to recognize in regards to the stability of the maturity. One of my trainers, Mrs. Fernando, stated that a child who continues to use metal inset work to make rainbow pictures and to use as many colors as possible drawing hearts inside their ellipsoid outline is an immature child. She said that it did not mater how many times we asked a child not to draw butterflies and flowers all over their metal inset work if the child was too immature to resist the wonderful display of colors before them at the metal inset shelf. "Too immature to resist the colors," is a statement that still speaks to me. Instead of observing the behavior as not listening and a misuse of the materials, note that the child remains too immature to not include colorful drawings in their metal inset work.
This is the same in regards to the Memory Game. It is this game/activity that assists the teacher in determining a child's maturity while simultaneously demonstrating whether the child has or has not grasped that zero is nothing.
I have seen some very lovely Memory Games with the wooden numbers placed in hand sewn envelopes. I have also seen store bought numbers placed in small store bought envelopes. I made some for a younger class where I just used glitter paint on the underside of pre-cut pieces of felt to write the numbers. The children flipped over the felt piece, saw the number and then flipped it back over. See below:
Both worked well. What is important is that the game be done.
In eleven small (ex. 2" x 2") envelopes place one of the numbers 0-10. Place these in a lovely box or basket. Ask several(no more than eleven) children to come to the rug and make a circle. If six children are in a circle, remove five of the envelopes from the basket but make sure that the envelope with the zero is included.
Next, hand an envelope to each child. Ask them to carefully look at their number but not to show the other children. Then instruct them to either put their number back in its envelope and leave it at their spot in the circle or carry it with them as they go and gather a number of items equal to the number in their envelope. A child who gets two might go and get two flowers from a vase or if they get ten bring ten pairs of scissors to the circle.
Even if a child has not had a lesson on the hierarchical materials or chains, they may select 8 golden beads or 4 short chains (example) for this activity.
(Note: children will hide their items under their shirt (as in the first photo above), behind their backs, etc in an attempt not to let the other children see what they have chosen before their turn)
This provides them with a rare opportunity to touch materials that they have wanted lessons on but maybe aren't ready for. Too, if a child repeatedly picks the same materials that they haven't had a lesson on for this game, it reveals the child's interest in that work. This is also an excellent game to help the children become more familiar where materials are kept and to actively look at the shelves in all areas of the classroom.
The child that gets zero is to go into the environment and act like they are looking around for a specific material that they want a quantity of. They can be very clever about this. I have seen children cup their hands and then close them as if they were holding something. The mature child loves to get zero and acts like they got ten. They come to the rug with their hands cupped together. When it is their turn to show their quantity, and to see if they correctly matched it to the card in their envelope, they look each of their peers in the eye and then dramatically and happily announce, "I have zero! I have nothing!" They open their hands slowly and reveal the empty space between their palms. It can be quite a performance.
The immature child generally does not like to get zero. When the do they (a) throw it down, cross their arms and declare that they want to pick another envelope (b) cry (C) get up and go to a shelf where they get as many of a single item they can, like 15 crayons. Then when they come to the rug with their 15 crayons and reveal that they had actually got the zero, the other children then call out, "Zero is nothing." The immature is not often pleased at the declaration of their peers.
It is an important step that the child counts out the quantity of their objects in front of the other children in the circle. They then re-remove their number from their envelope and check to see if the quantity and symbol match (or in the case below, turn the number over.)
This is Cards and Counters as a movement and group activity. If the quantity does not match the number, the child immediately returns to the environment to get more or to return the extra of the specific items that they chose.
Children love this game and I am always fascinated by what some children chose. I have seen children bring flags, cotton balls, scissors, spindles and so many other objects. All of the objects in the first photo below are used in flower arranging:
Again, reinforcing where things are in the environment, the children return all of their items to the correct places on the shelves before playing again. I often play the game 5 or 6 times.
Concept of Zero:
Have several or all of the children gather in a circle. Tell them that you are going to ask each of them to do something a certain amount of times such as touch your toes four times. As the game continues and you have asked individual children to do a variety of things like jumping like a frog, spinning like a ballerina and hopping like a kangaroo, ask the next child to (ex.) do zero somersaults. When they look at you and say, "I can't. Zero is nothing," use all of your inner acting abilities and respond, "I am your teacher and I have asked that you do zero somersaults, so please do them."
(above image - jenniferwigmore.com)
The child and perhaps others will again repeat, "Zero is nothing." Then maybe cover your eyes with your hands and act like your crying and repeat the request, "Please do zero somersaults, please for me." By now the children are rolling with laughter and they will again deny your request. Then move on to the next student and ask something that can be done ex. Blow 5 kisses.
As with the first Memory game/activity, have the child count as they do the action. So they would say out loud, "One, two, three, four, five kisses." This is very important as often a child will not count out the correct amount and will have to repeat their counting and the action. (Or not, if the child is very young...its an individual call.) All the children, 2.8 through 6 love this game. Love it!!!!