John P. Crotty
Well then, how do we improve math and science courses so that students race down the hallways to be on time? Can the United States respond to Toyota like it did to Sputnik? I feel that the students need more hands-on activities. These will prepare the student for more abstract learning in a challenging and motivating manner. However, the increase in supplies will cost money. The classroom may also become noisy and appear unstructured.
Intellectual development for all of us is based on stages of growth in our ability to think and reason. Jean Piaget, a Swiss psychologist, did extensive research on an individual’s mental abilities and intellectual growth. He devised a theory that intellectual development is a four stage process; sensory-motor, preoperational, concrete operational and formal operational periods.
According to Piaget, there is an age range associated with each period. However, the starting or ending of a stage varies according to the child’s environment, abilities and socioeconomic position.
The concrete operational period involves the child during the approximate ages of seven to eleven. During this time period, children are exposed to the fundamentals of mathematics. Although the child’s thinking in this stage is becoming more logical and systematic, it is still limited to what he has experienced. When a child encounters a new situation, he compares it to physical situation that he has already experienced. He is comparing and learning from experience but not yet internalizing.
As the child grows older, he learns the ideas of conservation of number, area, weight and volume. If he develops a process to group and to organize information, then the child is ready to learn abstract concepts. The child s progress from the stage of concrete experiences to the stage of formal operational thought depends upon the kinds of experiences the child has had.
In the formal operational period, a child learns to try various possibilities to solve a problem. He learns cause and effect relationships; dropping things that don’t work and keeping things that help him discover the cause of events. A child learns to plan moves and predict likely outcomes.
In the United States today, the teaching of math seems to be stuck on the concrete operational stage based purely on the memorization of facts. I am interested in approaching the teaching of math on the concrete operational stage, but by the child experiencing concepts of math and then applying them to daily experiences. As the child draws on his experiences, he then progresses into the formal operational stage of thinking. In this period, math should become fun or at least interesting.
