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Learning Alternatives. The child reaches the threshold of grown-up logic as early as seven and usually by eleven. Before that point, he may think that water becomes "more to drink" when it is poured from a short, squat glass into a tall, thin one with the same capacity. The reason for this stubborn misconception is that the child is paying attention only to static features of his environment, not to transformations. Now, at the age Piaget calls that of "concrete" intellectual activity, the child can deduce that pouring does not change the quantity of the water. He has begun to reason and to grasp the essential principle of the equation.
Between the ages of eleven and 15, the child begins to deal with abstractions and, in a primitive but methodical way, set up hypotheses and then test them, as a scientist does. In one experiment, Piaget handed children a weight at the end of a string and asked them to find out what determines the speed of the pendulum's swing. As he watched and asked questions, he found that the children were spontaneously considering all the possible variations: changing the weight, letting it drop from increasing heights, giving it stronger shoves, or changing the length of the string. Even children who never had seen pendulums before tried each possibility until they found that only shortening or lengthening the string did the trick. Quite possibly, Piagetians sometimes speculate, adolescents' fascination with their ability to visualize alternatives is what makes them so eager to test new life-styles and Utopian ideals.
Classroom Hens. The timetable that seems to control the development of intellectual skills, Piaget is convinced, suggests that man's capacity for logical thought is not learned but is embedded, along with hair color and sex, in his genes. These innate rational tendencies do not mature, however, unless they are used. Although Piaget has refrained from applying his findings directly to teaching, educators see some implications. A child cannot be forced to develop understanding any faster than the rate at which his powers mature to their full potential, and there is a limit to what overeager parents and teachers can achieve. At the same time, a child who does not get the chance to apply his developing abilities and test their limitations may never reach his full intellectual capacity. Thus programs aimed at the disadvantaged, like Operation Head Start, may greatly increase a child's chance of attaining that potential.