Show a young child two identical short glasses, each filled with the same amount of water, and ask which has more. They'll correctly say neither — they're equal. Now, in full view, pour one of the glasses into a taller, thinner glass, so the water sits higher up. Ask again which has more. A four-year-old will very reliably point to the tall glass, confident and unbothered by the fact that they just watched the entire pour happen and nothing was added or taken away. This isn't a fluke or a trick question landing wrong — it's one of the most replicated findings in developmental psychology, and Jean Piaget used it to map something real about how children's reasoning changes with age.
What the child is actually tracking
Piaget's explanation centres on a skill he called conservation — understanding that a quantity stays the same even when its shape or arrangement changes. A child who has developed conservation of liquid volume can hold two facts in mind at once: the water got taller, and the water also got thinner, and those two changes cancel out. A younger child, in what Piaget called the preoperational stage — roughly ages two to seven — tends to fix on the single most visually striking dimension in front of them, which here is height, and judges the whole amount by that one dimension alone. The width narrowing to compensate doesn't register as a fact that needs weighing against the height; the height is simply what "more" looks like to a mind that hasn't yet learned to hold two changing dimensions in balance at the same time.
What makes the result stick as a demonstration rather than a curiosity is watching the switch happen with age. Ask the same question of a child a few years older, safely into what Piaget called the concrete operational stage, and the answer changes from confident-and-wrong to confident-and-right, sometimes with visible mild offence at being asked something so obvious. Nothing about the water changed between the two ages. What changed is the mental operation available to reason about it — Piaget's term for it was reversibility, the ability to mentally run the pour backwards and confirm that undoing it would restore the original, equal glasses.
Why a "wrong" answer is the useful data
The value of the conservation task isn't in catching children being bad at maths — it's that the specific, consistent shape of the mistake reveals which cognitive tool is missing, rather than just confirming that a younger child scores lower on some test. A random or scattered wrong answer wouldn't tell you much. A wrong answer that nearly every child that age gives, for the same underlying reason, is evidence about how reasoning itself is organised at that developmental stage, not just evidence about liquid.
What we're still unsure about
Piaget's original ages have held up less rigidly than his broader stage sequence. Later researchers, notably Rochel Gelman, found that changing how the conservation task is presented — framing it as a game, reducing the number of confusing questions, or using more relatable objects — could get younger children to succeed earlier than Piaget's studies suggested, implying the task itself, and not only the child's underlying reasoning, was partly responsible for the original age boundaries. The broad idea that reasoning develops through describable stages has survived scrutiny well. The specific ages attached to each stage are now understood to be more method-dependent and less fixed than the classic textbook version presents them.
This sits inside Piaget's Stages of Cognitive Development, one of seven topics in Developmental Psychology, one of four domains in Psychology, one of seventeen subjects the app can quiz you on.