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Tool #1: Two Conceptions of Cognitive Development

There are a number of ways to look at cognitive development, i.e. the development of thinking. Perhaps the most familiar is the conception of Jean Piaget, a Swiss philosopher, who looked at the development of his own children to try to understand the development of the intellect in general. From his sample of three, he saw a pattern of development that had, in its simplest terms, three stages:

  • Preoperational: Piaget used the word "operations" to refer to the logical structures of thinking. At the preoperational stage, logical structures really aren't much of a factor except in the most fundamental ways. The light comes on when you flip the switch simply because it does. There's very little, if any, understanding of cause and effect, or of the consequences of any but the simplest actions.

A defining moment in my own life came when I was three. I was coasting down an incline on my tricycle, and realized that I was about to hit some bushes. I turned right...down a flight of stairs I knew full well was there. It just hadn't occurred to me that my action would have a consequence in the future, even the future that was only two or three seconds ahead.

  • Concrete operations: At this stage, people can understand what they can take in through the evidence of their senses (things that are "concrete" enough to touch or see). Thus, addition and subtraction are easy -- you can manipulate objects to see how they work -- but algebra, which involves "unknowns" is harder. You can't see the unknowns, so they're a great deal more difficult to understand.

A professor of cognitive psychology used to tell his classes this story: "When the channel changer knob fell off my TV set, the channel had to be changed with a pair of pliers. Without the numbers on the channel changer, I could never find the stations. One day when I was struggling with the thing, my eight-year-old daughter asked what was wrong. I said,'I can't find Channel Four.' My daughter went over and picked up the knob, pointed to the number, and said'There's Channel Four.' That's concrete operations."

  • Formal operations: At this highest stage (which has a number of more narrowly defined substages within it), people are capable of abstract thought. This is often defined as the ability to think about thinking. It includes bringing ideas or events that aren't present or obvious to bear on a particular issue; being able to project consequences into the future; predicting what others might do, even if it's very different from what you might do; envisioning several possible outcomes from the same action; etc.

A couple of older-children examples of formal operations:

A sixth-grade class in the '50's was told that English newspapers were seldom longer than eight pages, and were printed on thin paper. The teacher asked why this was the case. Two of the children understood immediately that the answer had to do with a fact they had learned the week before: that England had cut down most of its forests. They realized that its relatively few trees were much too valuable to be used for making paper.

A nine-year-old was asked to explain why Earth was a sphere. After a few seconds of thought, he was able to explain that, since gravity pulls equally in all directions, the shape that would be formed by gravity pulling space debris and dust together from a central point would be a sphere. Every point on a ball, if it's perfectly spherical, is exactly the same distance from the center.

Since he observed, for many years, only his own children, Piaget assumed that their development was typical. He therefore assigned preoperational thinking to very early childhood; concrete operations to the elementary school years, about ages 6 to 11 or 12; and the start of formal operations to puberty or early adolescence.

As it happens, there are great variations in development, depending to a large extent upon an individual's experiences and stimulation, and probably upon brain development as well. A large number -- perhaps a majority -- of adults still function at concrete operations in at least some areas.

And that's another issue: even people who spend much of their cognitive lives at the highest levels of thought -- theoretical physicists, for instance -- probably don't use formal operations all the time. Certain issues, such as dealing with their parents, may present emotional barriers to thinking in critical or logical ways. In reality, few of us are able to turn the full force of our intellect on everything we encounter.

Piaget saw cognitive development as a process of increasing differentiation (understanding how things, people, events, ideas, etc. differ from one another) and increasing integration (understanding the connections among all those different things, people, etc.) The mechanism of that process is set off by a person coming into contact with something that doesn't match his view of reality.

Someone in this situation has two options: he can ignore the new phenomenon, and simply continue seeing the world as he always has; or he can try to make sense of the world in a different way in light of the new reality he has seen. It may take many encounters with reality to start a change in perception, especially if cognitive development means leaving behind some basic belief. Some people simply are unable ever to see anything that doesn't agree with their preconceptions.

Although textbooks tend to present this material as if changes happened abruptly, in fact change is going on all the time. People's thinking may get more sophisticated in some areas, but not others, which brings us to another theory of cognitive development.

Howard Gardner sees Piaget as looking at only one part of cognitive functioning. Gardner finds eight aspects of intelligence, rather than just one:

  • Logical-mathematical (what he believes Piaget was examining)
  • Verbal (speaking and writing ability, learning languages, etc.)
  • Interpersonal (relations with others)
  • Intrapersonal (understanding of self)
  • Spatial (ability to see, understand, and use spatial relationships, including talent for painting and the other visual arts)
  • Kinesthetic (physical and athletic ability)
  • Music
  • Environmental (Being able to recognize patterns in one's environment)

According to Gardner, each of these aspects is separate from the others. Different aspects develop at different rates in different people, so that some who are far advanced in, for instance, music at an early age, may still have very little interpersonal capacity. This is one way of explaining those theoretical physicists we mentioned earlier: some of their intelligence's are highly developed, while others are not.

For the most part, at least in the past century, schools and the society at large have valued the logical/mathematical and verbal abilities, while paying little attention to the others. If Gardner is right, his theory has major implications for education, as he himself has written. We should be stimulating children in all areas, so that they can become adults who are competent in every aspect of intelligence.