Academic journal article Phi Delta Kappan

# A Constructivist Perspective on Teaching and Learning Mathematics

Academic journal article Phi Delta Kappan

# A Constructivist Perspective on Teaching and Learning Mathematics

## Article excerpt

Teachers who begin to base their practice on principles of constructivism should not expect to develop a finished repertoire of behaviors that, once achieved, will become routine, Ms. Schifter warns. There is no point of arrival, but rather a path that leads on to further growth and change.

Anne Hendry is a veteran first-grade teacher in rural western Massachusetts. She describes the way she began a unit on measurement fore Thanksgiving in 1990.

Before school, moving desks and chairs and using masking tape, I outlined the shape of a boat on the classroom floor, 16 by 6 feet. This was to represent the Mayflower. I also prepared a scroll for a child to read to the class and then to post on the bulletin board with our initial problem involving measurement on it. I selected one child, instructing him that at math time he would be a messenger from the King bringing an "Edict" to the Pilgrims.

When math time arrived, Zeb, the child who was appointed to be the messenger, read the "Edict," which said, "This ship cannot sail until you tell me how big it is." The children were puzzled.

"Well, what should we do? Who has an idea?" I asked. Thus our discussion of measurement began. Or I thought it would begin. But there was a period of silence - a long period of silence.

What do young children know about measurement? Is there anything already present in their life experiences to which they could relate this problem? I watched as they looked from one to another, and I could see that they had no idea where to begin. Surely, I thought, there must be something they could use as a point of reference to expand on. Someone always has an idea. But the silence was long as the children looked again from one to another, to Zeb, and to me.(1)

To most educators, Hendry's intention to connect her mathematics lesson with the upcoming holiday would appear unexceptionable. They would surely wonder, however, at a veteran teacher's choosing to endure so long and painful a silence from a roomful of confused students. Why had she given her first-graders a task without showing them how to complete it? Why ask a question before telling one's students what they need to know in order to answer it? How could so experienced a teacher allow her lesson to falter in this way? Here's Hendry again.

I was having second thoughts about the enormity of the problem for a first-grader when, shyly, Cindy raised her hand. "I think it's three feet long," she said. "Why?" I asked. "Because the letter from the King said so," she responded. "I don't understand," I said. "Can you tell me why you think the ship is three feet?" "Because the King's letter said so. See!" Cindy said. "I'll show you."

[When the letter was held up], the light, filtering through the paper, made the capital "E" I had written for the word "Edict" look like a three to some of the children. I clarified this point with her and the others who agreed that they also had seen a three on the King's paper. The King, they thought, already knew the answer.

I felt we were back to square one again with more silence.(2)

Casting about for a response to their teacher's question, a few of the children look for a number, any number, to connect with the context. But once Cindy's confusion has been cleared up, silence descends again, and Hendry's doubts deepen.

Anne Hendry's behavior will no doubt puzzle readers whose images of teaching derive from the mathematics classrooms in which they themselves once sat as children: the teacher shows her students procedures for getting right answers and then monitors them as they reproduce those procedures. To ask students a question without having previously shown them how to answer it is actually considered "unfair."

However, viewed against the backdrop of a "constructivist" perspective on how learning takes place, on what "doing" mathematics can mean, and on what these processes imply for mathematics instruction, Hendry's behavior becomes comprehensible. …

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