Wrong in the Same Way

Jean Piaget started out marking intelligence tests, and became interested in the answers that were wrong.

Not because they were wrong, but because children of the same age were wrong in the same way. That pattern does not look like ignorance, which would be random. It looks like a system: a way of reasoning that is internally consistent and different from an adult's.

That reframing created developmental psychology. Children are not small adults with less information; they are reasoning with different structures, and the errors are the visible edge of the structure. Study the errors and you can map it.

The specific map Piaget drew has been substantially revised. The method has not been improved on.

His four stages (sensorimotor, preoperational, concrete operational, formal operational) came with characteristic tasks. In the conservation task, liquid is poured from a short wide glass into a tall thin one and the child is asked whether there is more, less or the same. Before about seven, children reliably say there is more, attending to height as the salient dimension.

In the object permanence task, an infant watches a toy hidden under a cloth. Before about eight months, Piaget reported, they do not retrieve it, for them, out of sight is out of existence.

The trouble with both is that they measure the ability to handle the task as much as the underlying concept.

Renée Baillargeon tested object permanence without asking infants to reach for anything. Infants habituate to a screen rotating through 180 degrees, then a box is placed in its path. In the possible event the screen stops at the box; in the impossible event it rotates straight through the space the box occupies. Infants of three and a half months look reliably longer at the impossible event.

Looking longer is not a rich measure and it is a measure, and it puts some representation of a hidden object roughly five months earlier than Piaget's reaching task.

The A-not-B error tells a similar story. An infant who has retrieved a toy several times from location A will often reach for A even after watching it hidden at B. Piaget read this as incomplete object permanence. But the infants look at B while reaching for A; the error depends on the length of the delay; and it depends on how many times they previously reached at A. It now reads as a failure to inhibit a practised motor habit, which is a deficit in executive control rather than in the concept of an object.

Even conservation turns out to be partly about the conversation. Margaret Donaldson and colleagues showed that if the glasses are knocked over by a "naughty teddy" rather than deliberately rearranged by the experimenter, children conserve at younger ages. The reason appears to be pragmatic: when an adult asks the same question twice, having just changed something in front of you, the cooperative inference is that they want a different answer. Part of the classic error was a child being a good conversational partner.

The theoretical alternative that has worn best came from a contemporary Piaget never met.

Lev Vygotsky, working in the Soviet Union and dead of tuberculosis at thirty-seven, argued that Piaget had the direction wrong. Development is not primarily a lone child constructing an understanding of the world through their own experiments. It is social: capacities appear first between people, in interaction with someone more capable, and only afterwards inside the individual. Language is the paradigm: first a tool for talking to others, then internalised as a tool for thinking.

His most useful idea is the zone of proximal development: the gap between what a child can do alone and what they can do with help. That gap, rather than the solo performance, is where instruction should aim, and it is a better predictor of what the child is about to be able to do than any test of independent ability.

The practical prescription that follows is scaffolding (supporting the parts the learner cannot yet manage, and withdrawing the support as they can) which is now so embedded in how teaching is discussed that its origin is invisible.

The modern position on what infants start with sits between Piaget's constructivism and anything nativist. Core knowledge theory, associated with Elizabeth Spelke, proposes a small set of early-emerging systems: objects that persist and move on continuous paths, approximate numerical magnitude, agents that act toward goals, and basic spatial geometry. The evidence is that infants look longer at violations of these principles at ages too young for the relevant experience.

That is not innate knowledge of the world in any rich sense. It is a small number of assumptions that make learning about the world possible at all, which is roughly what you would expect an evolved learning system to arrive with.