Previous: piaget's experimentsNext: prioritiesContents

Society of Mind

10.2 reasoning about amounts

What do those egg and water jar experiments say about our growth from infancy? Let's consider several explanations.

QUANTITY: Perhaps the younger children simply don't yet understand the basic concept of quantity: that the amount of liquid remains the same.

In the next few sections I'll argue that we don not learn one single, underlying concept of quantity. Instead, each person must construct a multileveled agency, which we'll call the Society-of-More, that finds different ways to deal with quantities.

EXTENT: The younger children seem unduly influenced by the larger extent of space taken up by the spread-out eggs and taller water column.

That cannot be the whole story because most adults, too, judge that there's more water in the taller jar — if they merely see the final scene, without knowing from where the water was poured! Here are a few other theories about the younger child's judgment:

REVERSIBILITY: The older children pay more attention to what they think remains the same — while younger ones are more concerned with what has changed. CONFINEMENT: An older child knows that the amount of water stays the same, if none was ever added or removed or lost or spilled.

LOGIC: Perhaps younger children have not yet learned to apply the kinds of reasoning that one would need to understand the concept of quantity.

Every one of these explanations has some truth in it, but none reach the heart of the issue. It is clear that the older children know more about such matters and can do more complex kinds of reasoning. But there is ample evidence that most younger children also possess enough of the required abilities. For example, we can describe the experiment without actually doing it at all or we can perform it out of the child's sight, behind a cardboard screen. Then, when we explain what is happening, quite a few of the younger children will say, Of course they'll be the same.

Then what is the difficulty? Evidently, the younger children possess the ideas they need but don't know when to apply them! One might say that they lack adequate knowledge about their knowledge, or that they have not acquired the checks and balances required to select or override their hordes of agents with different perceptions and priorities. It is not enough to be able to use many kinds of reasoning;

one also must know which to use in different circumstances! Learning is more than the mere accumulation of skills. Whatever we learn, there is always more to learn — about how to use what was already learned.