Reprinted from the San Antonio Register
By Lori Colavito
In kindergarten, children learn about addition and subtraction using friendly, colorful objects: unifix cubes, small plastic teddy bears, wooden cusinaire rods. We learned that in addition different things, sometimes numbers, are brought together to make something that is more than any of the others are separately—such as one teddy bear plus one teddy bear equals two teddy bears. The children liked this very much.
I have learned from Aesthetic Realism that adding and subtracting are opposites and they are everywhere, including in ourselves. So we come to subtraction. Like many teachers, I have seen that this is a subject that children have a particularly hard time with; they often see addition as good and subtraction as bad. I wanted my students to see that both are present all the time and together make for something beautiful. I began by telling the class: "Today we are going to learn how to subtract for the same reason we learned how to add: to know the world." In subtracting, we take a part of something away--say, one teddy bear from a number of teddy bears. We saw how when we add things together, the outcome is that something gets bigger; when we subtract things, the outcome is that something gets smaller.
We had a wonderful time looking to see if these opposites—addition and subtraction—are together in the world, and in things we had already studied: how a tree grows, the water cycle, and an ant colony. I asked: "Does a tree need to add things to itself so it can grow big?" Nadia said, "A tree needs water." Armen said, "It adds sun." I asked, "Does it also subtract things from itself?" Kazuo said, "Trees subtract apples and give us food." Selasi explained, "The leaves fall off and give the dirt vitamins." Roger added, "And after the leaves fall, they also warm the animals who live underneath." Jovanna said, "The trees subtract seeds and help make new trees!" I asked, "Is it good for the world the way trees add and subtract?" With much excitement, many children shouted "yes!"
"And do addition and subtraction work together in making rain?" I asked. Max described how water vapor rises up from the ocean, saying: "The steam drops of water connect and make a cloud." I asked, "What happens when those many, many drops of water add themselves together?" Eddie said, "They get too heavy and fall down as rain!" Yes, we saw, water is subtracted from the cloud when it falls. I asked: "From this subtraction, do good things happen? How does rain help the world?" Brett said, "We can take a bath and get a drink of water." Katy commented, "We can clean our plates and cups." With a big smile, Michelle said, "Rain helps flowers and trees grow." And with excitement Joey said, "We can go swimming!" We were seeing this exciting fact: we need subtraction because it's good for the world for some things to be less, and other things to be more!
This is so different from the way a child can feel he or she is adding to oneself by lessening, wrongly subtracting from the feelings of another child—just because, maybe, that child has a different skin color or eyes shaped differently from ours. It is the Aesthetic Realism method that makes this relation.
I now asked, "Who is ready to see how numbers can be subtracted from each other?" There were enthusiastic shouts of "ME!" I see this as a tremendous victory, since, as I mentioned, so often subtracting numbers is a source of dread—and the reason has not been understood. Today, there are so many workshops on how to teach math—some of which I have attended—trying to have the subject seen as friendly to children.
The teachers of the workshop for educators that I attend described a discussion on this very subject that took place in an Aesthetic Realism class taught by Ellen Reiss. In it, trouble about subtraction was described as having to do with a great debate within a child between the desire to lessen things and a beautiful fear of doing so. Children can not want to subtract because it means doing with exactitude something they have wanted to do any way they pleased: make less. And also they are afraid of the thing in them that wants to lessen the world. The inner tumult about wanting to lessen things and the deep, good fear of doing so can make for great discomfort when they meet the subject of taking away, or subtraction, in a mathematical unit. I feel this understanding is so kind and respectful of what goes on inside a child.
As the lesson continued, we sat in a circle and I gave each child a basket filled with 10 unifix cubes. Using a clave, I tapped a number for the children to "build"— 5. After they put together 5 unifix cubes, I wrote "5" on chart paper for them to see. Then, I introduced the subtraction symbol ( - ) and wrote it next to the 5. I asked them to listen for the smaller number we were going to subtract, take away, from 5, called the subtrahend. I tapped a 3, and after giving the children time to count, and to take away three cubes, I asked, "How many cubes are left when you subtract 3 from 5?" The children said 2; and as I wrote the number they were thrilled to see and read the completed equation with me "5-3=2". They liked seeing how subtraction works, and were also excited to see this wonderful thing—that as they were subtracting, they were also adding as they first "built" the larger number, called the minuend! We solved many equations together, including 7-4=3, 8-7=1, 6-4=2, 9-3=6, 10-1=9. After doing this, I asked the children, "Can you think of how adding and subtracting which are in numbers and the world, are in ourselves, and in things we do every day?" Alexander said, "We lose baby teeth and grow new ones." Raiza commented, "When we are a baby, we don't have hair, then we grow it, and then cut it!" Armen said, "Every time we go to sleep, we subtract our shoes and clothes and add our pajamas." Madeline said, "We subtract dirt from our faces when we take a bath." Kate said, "When we play outside, we subtract ourselves from the classroom and we add ourselves to the playground."
Throughout the lesson many children said, "This is fun. I like this." I asked them, is this fun different from the way we can make fun of other people, make less of them to make ourselves bigger? The children were very thoughtful. Yes, they said.
My Students Loved Learning!
The children in my class learned to add and subtract with ease, and exactitude. They also had great pleasure learning how to spell each others' names and drew pictures of each other. They loved this.
It affected me very much to see throughout the term what Aesthetic Realism explains about the relation of accurate knowledge and ethics: when a child sees reality's opposites in a subject, he or she learns, and also becomes kinder to people standing for reality—so prejudice is defeated. That is why as Rishi from Nepal, who used to push the other children, began to see them as related to himself, he changed, and made many friends, who encouraged him by teaching him new words during lunch. By the end of the term he was not only speaking English, but was also reading and writing it! Jovanna and Laura who had snubbed other students, and the early kindergarten clique Nadia, Alexander, Kate, and Daniel stopped being exclusive, and worked well with the other children during lessons. Suki Yamata from Japan, who had hated and looked down on her new school, and the children whom she saw as different from herself, also learned to speak and read English, and made friends with her classmates. Mrs. Yamata, who had to sit by her daughter's side in September, gratefully wrote to me: "Thank you very much for everything you did for Suki. She enjoys her school life!"
I love the kind, comprehensive principles of the Aesthetic Realism Teaching Method which understand and meet the hopes of children everywhere, and can make education in America a true success: there will be an intelligence and kindness brought forth in children new in the history of education!