Many children who can DO mathematics don't UNDERSTAND what they are doing, a University of Utah professor of education says.
"American children come through math without acquiring useful meanings for mathematical symbols," says Dr. Donald M. Peck, associate professor of educational studies.Peck would like to see some fundamental changes in math education, a process in which children see, feel and count objects rather than merely follow the rules teachers give them.
He supports his push for reform with studies showing that children lack basic understanding of math concepts, even when they get high scores. Videotaped interviews with one group of children who scored in the upper third among their peers showed they couldn't explain such simple concepts as fractions.
Failure to understand arithmetic processes puts these youngsters onto rocky ground when they move into more abstract math, Peck said.
He uses non-standard methods to help students solve problems that stump many adults who memorized math facts.
Rather than telling children how to solve problems, he challenges them to find their own way to solve them. He uses objects and drawings to lure them to conclusions. The teacher poses the question then turns the students loose to build physical models, such as stacking small blocks to form a larger cube.
Eventually, the children are writing their own formulas for solving many versions of the same type of problems.
"They're getting a picture in their minds. They're bridging the gap between real world experience, arithmetic and the algebraic world of the unknown," Peck says. "What pleases me is that girls do as well as boys. Girls are supposed to be poor in spatial relationships, but the problem is really lack of experience."
The university professor has tested his ideas extensively and shared his concepts with school teachers across the country. He brings children to the university to participate in experiments in computer labs. He uses computers to draw models just as they would be built from blocks
This winter, students in Teresa Cryns' fifth grade class at Rowland-Hall-St. Mark's School visited his lab.
Peck threw out the question: If you built a solid cube of smaller blocks, how could you figure the number of blocks that don't touch the outer surface? In other words, how would you figure the volume of a box within a box? Then he sat back to watch.
Stephanie Paulos built an inner box from red blocks, surrounding them with a layer of green blocks. As she worked with the blocks, counting and observing, the formula evolved naturally: the volume of the small box was the length minus two, times the width minus two, times the height minus two. The inner box was one block smaller than the outer box on all six sides, so subtracting that number from the formula used to find the volume of the total box produced the inner volume.
Peck believes she will remember the process much longer for having arrived at the conclusion on her own, rather than applying a formula given her by the teacher. Along with the answer to a specific problem, the student has learned a thinking process that can lead to other solutions,
"I didn't know much about math and my teacher didn't think I was good at math," Stephanie said. "But since Dr. Peck has been teaching us, I'm more confident about math and now my teacher says I'm good at math."