Young children think differently than do older children and adults. Such thinking is not wrong, simply different and age-appropriate. When a preschooler asks, "If I eat spaghetti, will I become Italian?" she reflects, in an original and amusing way, her belief that "you are what you eat." Rather than "correct" the child, we might ask, "What do you think?" Children usually have answers to the questions they ask and are very happy to share these with us. The child might reply, "I think so, because my friend Robert eats spaghetti, and he's Italian."

Transductive Reasoning

The foregoing example illustrates a form of reasoning that is characteristic of young children. This transductive reasoning is from concrete event to concrete event, as opposed to deductive reasoning, which is from a general principle to a specific conclusion. If the child were reasoning deductively, she might think

People who eat spaghetti become Italian [major premise].

I eat spaghetti [minor premise].

Therefore, I will become Italian [conclusion].

In fact, though, her reasoning is transductive, and she thinks

Robert eats spaghetti, and he's Italian.

If I eat spaghetti, I will become Italian too.

What is missing in transductive reasoning is the major premise, the overriding rule from which a particular conclusion can be deduced. Instead the child reasons from case to case.

Transductive reasoning helps us to understand a number of otherwise puzzling features of young children's behavior. For example, young children often believe that when two events occur in succession, the first causes the second. A child who crosses her fingers before going to the doctor and does not get a shot will henceforth cross her fingers whenever she goes to the doctor. Transductive reasoning thus underlies what often appears to be superstitious behavior in young children (as well as in older children and adults!).

We can observe this transductive approach to causality in many other ways as well. For example, it helps to explain why children label things the way they do. When a mother and her preschool children were walking on an icy sidewalk, the mother slipped and fell. From then on, her children called the outfit she was wearing that day her "sliding clothes" because they saw the clothes as having made their mother slip and slide. Likewise, a child who was always served just one slice of pizza had trouble understanding that the whole round pie was a pizza. For this child, a pizza was triangular and not round.

Transductive reasoning also plays a part in the child's adoption of transitional objects. In the cartoon "Peanuts," Linus's blanket is a transitional object. Such objects help us to bridge the time interval between the loss of one source of gratification and the attainment of another. Once weaned, some children need a transitional object to carry them over until they find another form of gratification that is equally satisfying. At that point, the transitional object can be discarded. Transductive reasoning operates in the choice of the transitional object. A young child believes that if a blanket gave her comfort once, it will do so always.

Transitional objects are very important to young children, particularly those who are going through a difficult time in their lives, such as the divorce of their parents. If we recognize that the child needs this object to help deal with the separation and loss of gratification from parents, we can better accommodate to the object (blanket, doll, and so on) and encourage other children not to tease or joke about it. It is important to point out that adults use transitional objects as well. We sometimes rush into a new relationship after an old one is broken, simply to bridge the time period until we have regained our emotional balance. Young children use transitional objects in the same way.

Physiognomic Perception

Other facets of young children's thinking also relate to its transductive quality. Because young children tend to think on the concrete, observational level, they are apt to be more attentive to perceptual clues than are adults. This tendency appears in what has been called physiognomic perception. Such perception is not unknown among adults. When we visit an art gallery, some paintings make us feel happy and uplifted; others make us feel sad and depressed. These emotional reactions to what we see are examples of physiognomic perception.

Physiognomic perception helps account for the young child's fearfulness in strange situations. The waving of a branch or the flitting of a shadow can take on a frightening quality if it is perceived as reflecting angry forces. The frequent but transient phobias of young children are, in part, attributable to such physiognomic perception. A three-year-old of my acquaintance became frightened whenever he saw a broken object. This was a display of physiognomic perception. The broken object seemed to the child to betoken a disembodied anger that could be unleashed against him. In some cases, physiognomic perception in the young child reflects a tendency to project onto inanimate objects the angry impulses she senses within herself or in her parents.

Magical Thinking

Closely related to the young child's transductive reasoning is her tendency to engage in magical thinking the belief in the efficacy of her own thoughts and wishes. Such thinking is a direct product of transductive reasoning. If a child wishes for something to happen that does indeed occur, she will believe that her wish made it happen. Parents unwittingly reinforce this magical thinking when they tell their child not to say certain words. This gives the child the impression that if she says the forbidden word, something terrible will happen. Nonetheless, many young children tempt fate by saying forbidden words in the privacy of their own rooms while they wait, in fear and trembling, for the inevitable clap of thunder and flash of lightning.

Magical thinking also accounts for some of the emotional disturbances we see in young children. If a child secretly wishes that a younger brother or sister would be injured or go away and something does indeed happen to that sibling, the child may believe that the wish caused the event. Such a child will be very distressed and will try to undo the wish by giving away treasured possessions or promising to be good forever and ever. A similar dynamic is at work when a young child feels responsible for parental separation and divorce. A young child may want to possess one parent and may wish that the other would disappear. When this happens in reality, the child believes that she is the cause, and she suffers great guilt and remorse. Children to whom this has happened often become highly accident-prone.

To be sure, magical thinking, like the other forms of thinking we observe in young children, is not unknown among adults. I recall a game we played in high school. We would not allow ourselves to think that we might get a good grade in a difficult subject. Our fear was that if we thought we might get a good grade, this very thought would magically prevent us from getting the desired grade! Instead, we tried to convince ourselves we would get a bad grade to counter the power of the wish for a good grade. At a certain level, however, we knew that we were playing mind games and did not really believe that our thoughts would affect our grades. Young children, however, are much more likely to truly believe in the magical efficacy of their thoughts.

Concept Formation

Concepts are all important tools of thought. Once we have a concept of, say, dogs, we can talk about these animals in general without specifying their color, shape, the sounds they make, and so on. Young children form concepts, but their concepts are less general and differentiated than those of older children and adults. This again relates to the transductive, single-level nature of young children's thought. For example, young children often have trouble distinguishing between the "one" and the "many." When a three-year-old calls a strange man "Daddy," she is not really being disloyal. She does not yet clearly distinguish between the one Daddy and the many men.

Young children may also experience difficulty in nesting classes. If you ask a preschool child of four or five how many boys and how many girls are in the class, the child can often answer correctly. She might say, for example, seven boys and ten girls. Teachers usually take roll and the children are accustomed to hearing how many boys and girls are in the class. However, if you ask the child whether there are more girls or more children in the class, she is likely to reply that there are more girls than boys. To nest the classes of boys and girls within the larger class of children requires the mental abilities that usually appear at ages six or seven and that Piaget calls concrete operations.

Likewise, young children also experience difficulty in nesting size-graded materials. A child of four or five can copy a "stairway" made of sticks of different sizes aligned side by side. If, however, you give the child some additional sticks that are intermediate in size to those making up the stairway, the child usually cannot correctly insert or nest them within the series. To do so, the child would have to understand that the stick to be inserted is both larger than the stick on one side of it and smaller than the stick on the other side. The ability to appreciate that one stick can be both smaller and larger than other sticks must wait for the attainment of concrete operations that allows the child to grasp that one object can be in two relationships at the same time.

A number of investigators have shown that children can nest classes and series earlier than Piaget observed. These investigators, however, use different tasks that often make it possible for the child to nest classes or series by means of visual cues. Although the child's ability to accomplish these feats is interesting, it does not invalidate the limitations described above. It is the child's ability to nest classes and relations at the intellectual, rather than the perceptual, level that Piaget was interested in. The evidence is still consistent that perceptually unassisted classification and seriation must wait for the attainment of concrete operations.

The same argument can be made for children's concepts of number. Piaget demonstrated that children do not usually have a unit concept of number until they attain concrete operations. Young children can use nominal number, the use of number like a name. Numbers on football or baseball jerseys are nominal numbers that do not stand for quantities but for individuals. Likewise, young children can grasp ordinal number wherein the number stands for a rank order. When judges use numbers to rate the performance of ice skaters, for example, those numbers simply stand for ranks, not units. A skater who gets a ranking of 7.0 is not 0.5 units better than a skater who is given a score of 6.5. There are no units of skating performance, and the numbers are simply used by the judges to objectify their subjective rankings.

It is only when children attain concrete operations that they can form a true unit concept of number. When a child achieves a unit concept of number, she grasps that a number is like every other number in that it is a number, but different from other numbers in its order of enumeration. The number 4, for example, is like every other number in the sense that it is a number. It is also different from every other number in the sense that it is the only number that comes after 3 and before 5. It is only when the child can coordinate sameness and difference that she can arrive at the notion of unit quantities.

Piaget assessed the child's understanding of number by means of the conservation task. These tasks always offer the child a choice between reason and perception. In the case of number, a commonly used conservation task presents the child with a row of six or seven pennies. The child must first construct a similar row from a pile of pennies on the side. Four-year-old children often have trouble copying the row and may match the length and ignore the interval size or may match the interval size and ignore the length. Five-year-old children are often able to copy the row of pennies correctly. Many children at this age are often able to count the pennies correctly as well. If one row of pennies is now spaced out much farther than the other, however, young children are likely to judge the longer row as having more. They are basing their judgment on the appearance of one row being longer than the other rather than upon the rational understanding that if both have the same number they will be the same despite appearances. Concrete operational children do judge the two rows to be the same.

Other investigators have shown, however, that when you use only three or four pennies, young children do recognize that they are the same, even when one row is spread out. With small numbers, however, the child can solve the problem perceptually, by overall size of the array, and does not need to employ reasoning. So, although it is interesting that children can understand numerical sameness with small numbers, it is still no indication that they have a true number concept. Indeed, once children show a true number concept, they can engage in the simple operations of arithmetic. This is something that children who can see the sameness between three or four elements spread out and three or four elements together cannot do.

It is important to point out that in emphasizing that young children do not yet have a true concept of number, my intent is not to minimize or belittle their intellectual powers. Quite the contrary. What must be emphasized, and what is underplayed by those attempting to show how much young children can do, is the extraordinary complexity of concept formation and of mental processing generally. We are beginning to appreciate how difficult it is to program a computer to mimic the human brain. The difficulty arises because brain processes are very complex. A child's thinking mirrors that complexity. We do young children a disservice when we underestimate the enormity of the intellectual tasks they confront in constructing the concept of units in general and of number in particular.