In last week’s column, I introduced Jean Piaget and his theory
of cognitive development. Today we will look more closely at what
cognitive development theory implies for school aged children.
In last week’s column, I introduced Jean Piaget and his theory of cognitive development. Today we will look more closely at what cognitive development theory implies for school aged children.
At 5, 6 and 7 years old, kindergartners through second graders are still in the Pre-operational Stage. This is the stage during which the logical errors appeared that so fascinated Piaget.
Show a 5-year-old child some play-dough. Make two balls of equal size. Get him to agree that they have the same amount. Then flatten one of the balls. He will now say that the flattened one has more or is bigger. Reform it into a ball. He will now agree that they are the same.
Or take three glasses, two short, fat glasses, and one tall, thin one. Fill the two short, fat glasses equally. Get the child to agree that they have the same amount of liquid in them. Pour all the liquid from one of the short, fat glasses into the tall, thin glass. He will now be quite sure that the tall thin glass has more. You can pour back and forth from the tall, thin glass to the short, fat one. To him, the tall glass is more.
You can do a similar trick with quantities of items. He will believe that five coins in an extended line
@ @ @ @ @
are more than the same five coins pushed together
@ @ @ @ @
even if he counts the coins.
What exactly is going on? The child has not yet grasped the concept of conservation: that matter is conserved (remains the same) regardless of its shape, that volume is conserved regardless of shape of container, that number is conserved regardless of the arrangement of items.
Obviously it is quite useless to try to teach such a child chemistry, or algebra or anything requiring logic!
Many of the cute and amusing things our kids say at this age result from their interesting and non-adult mental processes. A child of this age has a tenuous grasp of cause and effect; if two events are associated in her mind, she assumes that one has caused the other. “When I don’t ride my bike, it gets a flat tire,” our little neighbor Stephanie said solemnly at age 7. (Actually, I can think of several adults who make similar assumptions.)
So what do you do with children age 2 to 7?
Resist the urge to impose logical structures on them. They will develop them later, I swear they will. Right now they are building up a model of the world. The inductions and deductions will come.
Let them play with the play-dough. They will gradually convince themselves that whether they make it into a pancake or a snake, it always ends up as the same size ball. Let them play in the sandbox, pouring sand from one bucket to another. They are building up the twin concepts of conservation of mass and volume.
Read aloud to them. Recite nursery rhymes. Teach them phonics: first consonants and short vowel sounds, then sounding out, then long vowel sounds, and so forth. Keep the lessons short and fun, 10 to 20 minutes at a stretch
There is a difference between chanting, “1, 2, 3, 4, 5…” and actually counting four cookies. The former is a trick of linguistic memory; the latter requires that the cognitive skill of one-to-one correspondence has been mastered. Work on both. The chanting is easier for most children. Use manipulatives as you move into simple addition and subtraction. Measure.
Garden with them: beans and corn and tomatoes appear from dirt and seed. Freeze water and melt ice. Visit the pumpkin patch, the zoo and the fire station. Build a foundation of experience to talk and read and write about. Let them draw, paint and color. Teach them how to cut with scissors and make collages. Sing with them.
This stage is the foundation for later learning as the child builds a model of how the world works. Next week, we will look at the stage most neglected in current pedagogy: ages 7 through 12: the Concrete Operations Stage.
