Pour juice from a low, wide cup into a tall, narrow glass in front of a four-year-old and ask: is there more juice now, less, or the same? Many four-year-olds answer confidently: “More — look how high it is!” For the Swiss scientist Jean Piaget (1896–1980), answers like this were not amusing slips but a window into how a child's mind works.
Piaget and his method
Piaget studied children's thinking for about half a century. His method was a flexible conversation: rather than just marking answers right or wrong, he asked, “Why do you think so?” and followed the child's reasoning. For Piaget, a wrong answer was information, because it revealed the logic behind it.
He saw intelligence as the mind's adaptation to the world, carried out with four key tools:
- scheme — a repeatable pattern of action or thought: grasping, sucking, later sorting or counting;
- assimilation — fitting a new experience into an existing scheme: a toddler who knows the word “cat” calls a small dog “cat” too;
- accommodation — changing the scheme when it does not fit: “This one barks — it's a dog”;
- equilibration — the drive to restore balance: a mild puzzlement pushes the child to rebuild their understanding at a steadier level.
For Piaget, equilibration was the main engine of development, which is why children learn best from tasks that are a little new but not overwhelming.
Four periods of development
The order of the periods is the same for everyone; the ages are approximate.
Sensorimotor period (0–2). The baby thinks through senses and actions. Inborn reflexes grow into repeated actions (shaking a rattle again and again), then into means to an end (pushing a cushion aside to reach a toy), then into experiments and, in the second year, into the first solutions found “in the head”. Gradually object permanence develops. At first a toy hidden under a cloth seems to vanish from the world. Later the baby searches, but makes a curious mistake: if a toy has been found several times under one cushion and is then hidden, in full view, under another, the baby looks under the first one again.
Preoperational period (2–7). Words, images and symbolic play arrive: a stick becomes a horse, a doll is put to bed. But thinking is egocentric — not selfish, simply centred on the child's own point of view: a three-year-old nods into the telephone instead of saying “yes”, as if Grandma could see him. The child also fixes on one striking feature (centration): juice in a tall glass seems “more” because the level is higher; of two equal rows of buttons, the spread-out row seems to have more.
Concrete operations (7–11). The child grasps conservation: “You only poured it — you can pour it back” or “It's higher, but the glass is narrow.” Reversibility appears, along with classification (sorting by two features at once) and seriation (arranging sticks from shortest to longest without trial and error). Logic works best with real objects, and conservation comes in steps: amount of matter at about 7–8, weight at 9–10, volume at 11–12.
Formal operations (from 11–12). Teenagers can reason about possibilities and hypotheses. Ask what makes a pendulum (a weight on a string) swing faster: the length of the string, the weight or the push. A teenager plans to change one thing at a time and keep the others the same; a younger child changes everything at once and cannot draw a conclusion. (The answer: its length.)
What later research changed
Piaget's central insight stands: children actively build their own understanding. Later studies, however, made important corrections. When tasks are simple and familiar, babies and young children are more capable than he thought. Ages vary between children and between cultures, and progress is uneven across areas. Formal reasoning does not switch on by itself in adolescence: many adults use it mainly in fields they know well, and schooling and familiarity with such tasks matter a great deal. Piaget himself stressed that discussion among equals helps children step outside their own point of view.
In practice: what to expect and how to help
Ages 2–6. One-sided, sometimes magical reasoning is normal at this age, and so are mistakes about quantity. Play pretend, draw and build together. Ask, “What do you think will happen?” and then check together: pour the water, roll the dough. Rather than correcting with words, let the child see. Play a “through other eyes” game: “What does the teddy see from the other side of the table?”
Ages 7–11. Expect solid logic with real objects and uneven progress. Sort stones or leaves, cook with measuring cups, put things in order of size, play backgammon or chess. Ask your child to reverse a process (“How do we get back to the start?”) and to explain: “How do you know?”
Ages 12–18. Expect hypotheses, arguments and big ideals, and also weaker abstract reasoning in unfamiliar subjects. Discuss “What if…?” questions, ask for evidence and try small home experiments that change one thing at a time, such as growing plants in different light. Take your teenager's arguments seriously, even when you disagree.
At every age, a wrong answer is a window, not a failure, and a single test score says little about how a child reasons.