by Charles Troob
In the early 1970s, when preparing to teach in elementary school, I was introduced to the work of Jean Piaget. His essays deal with how children develop a cognitive understanding of the world. For example, Piaget observed that a small child couldn’t see—even after repeated demonstrations– that a tall thin beaker and a short fat one may hold the same amount of water. A few years later the child gets this concept quite easily. Piaget theorized that children go through cognitive stages, and he speculated that this is partly due to biological constraints—a six-year-old brain has wiring that is more complex than the wiring of a four-year-old, and can support more elaborate thinking.
I was skeptical about that brain wiring stuff. Based on my own experience, it was no surprise that children take years to see the world as adults do. Much of what grownups think of as common sense is miraculous to a child.
I taught myself to read when I was three. By the time I was five I chatted with adults in grown-up language. But daily life continually astounded and perplexed me. Light bulbs went on when you hit a switch. The refrigerator made cold air. Birds and airplanes stayed aloft. A needle in a phonograph record sent music to a speaker, and a radio played sounds that traveled through the air. None of this made sense, though it seemed to be true. I read a story in which a bean became a mile-high beanstalk. Was this a fantasy or was it possible? It did seem improbable—but really, no more unlikely than that a seed in my grandmother’s garden turned into a radish or a zinnia.
So if Piaget’s children—he first observed his own kids– failed to understand that water can assume many shapes, I wouldn’t rush to conclude that they had immature brains or logic. Maybe this property of liquids is just an example of everyday magic that a child must see many, many times to accept as true.
Here are two memories of how I struggled to distinguish the possible from the impossible, the true from the false.
In many stories someone is brought to a new place by entering a door—or going down a rabbit hole. In the game of Clue, two secret passages let you cross the board in a single move. Did such things exist in the real world? I wasn’t sure. Near our apartment a highway tunneled under Queens Boulevard. In the tunnel a sign on a door said “passage to Union Turnpike.” I used to wonder what would happen when you went through that door. You were transported to Union Turnpike, but how? Only years later did I realize there was a staircase to the roadway above.
I was amazed to find out that four times three equals three times four–and that this is not just a coincidence but a rule: seven times five equals five times seven, and so on. I’d put out four rows of three pennies. Then I’d shift them into three columns of four pennies. Then I’d shift them again. As four threes become three fours before my eyes, I sort of got it, but I didn’t really believe it. I did this over and over, just to confirm that the world hadn’t changed and this mysterious fact was still true.
I suspect that most children don’t much worry about stuff like this, but to me it was very important to learn about the “real” world in which adults lived. I was weak and awkward. Other kids might push their way through life with force and bluster—I would depend on knowledge, not my useless body and timid spirit.
From this point of view mathematics was particularly satisfying and promising. Even a small child can see that grownups depend on numbers. Money is exchanged, food is weighed, cars have speedometers and odometers. Best of all, arithmetic gives you definitive answers you can count on. I was thrilled to learn the rules for “carrying” in addition, “borrowing” in subtraction, and that marvelous complicated engine called long division. When I got to plane geometry in tenth grade I was dazzled by the strange theorems and even more by Euclid’s system for proving them.
Though I soaked up book learning and schoolwork like a sponge, one thing troubled me greatly. How would I put all this knowledge to use? What other kinds of skills were required to be effective in the real world, and how did you acquire them? I often asked older people this question. The only answer I ever got was, “Experience.” This was obviously true, but no answer at all.
*****
Throughout my adult life I have remained fascinated by the relationship between thinking and doing, knowledge and action, theory and practice. And my need to learn about things in advance—to have a map of the terrain before venturing out—evolved into a talent for making sense of data, for diagnosing problems, for streamlining work processes and creating new systems. For any job that could be described as “analyst” or “planner” or “evaluator” I was a natural.
As for the other parts of making things happen—I was not a natural at all. Only with many years of “experience”–and training—did I begin to learn to supervise, negotiate, make tough decisions, and deal with crises.
But I did learn all these to some extent. By the time I retired I was somewhat less perplexed and amazed by life in the real world than I had been as a little boy.
Charles Troob wrote this for an IRP study group in Guided Autobiography. Many thanks to David Grogan, the coordinator, and to the other participants, who gave so much of themselves in this remarkable journey.