On this page
Teachers and parents often hear that a child "is not ready for abstract ideas yet". That phrase comes from Jean Piaget, the Swiss psychologist who spent decades studying how children think. For anyone teaching or learning physics and chemistry in Classes 8 to 12 the question is practical: how many teenagers can actually reason about variables and hypotheses, and can teaching change that? This post covers what Piaget proposed, what large studies found, and what to do in class.
Who was Piaget?
Piaget was born in Neuchâtel, Switzerland, on 9 August 1896 and died in Geneva on 16 September 1980. At 11 he published a short note on an albino sparrow, and as a teenager he became an expert on molluscs. He later studied the intellectual development of his own three children from infancy and wrote, according to the Jean Piaget Society, over sixty books and several hundred articles. His central question was how knowledge grows.
What are Piaget's four stages?
Piaget proposed that thinking develops through four stages, roughly tied to age. The OpenStax *Psychology* textbook summarises them as sensorimotor (birth to about 2), preoperational (about 2 to 6), concrete operational (about 7 to 11) and formal operational (from about 12).
In the concrete stage children understand conservation: pour water from a short wide glass into a tall thin one and the amount is unchanged. In the formal stage they can reason about abstract ideas and hypothetical situations. That last step is the one science teaching depends on.
What does formal reasoning look like in a science problem?
Piaget and Bärbel Inhelder's book *The Growth of Logical Thinking from Childhood to Adolescence* has a chapter on "The Oscillation of a Pendulum". The task asks what controls how fast a pendulum swings: the length of the string, the mass of the bob or how far it is pulled back. A formal thinker changes one factor at a time and keeps the others fixed.
Physics gives the answer you should find. For small swings the period is T = 2π√(L/g). With L = 1.00 m and g = 9.8 m/s², T = 2π × √0.102 = 2π × 0.319 = 2.01 s. Cut the length to 0.25 m and T = 2π × √0.0255 = 2π × 0.160 = 1.00 s. A quarter of the length gives half the period. Mass does not appear in the formula at all. A student who changes length and mass together cannot tell which one mattered, and that is the error the task exposes.
Do most teenagers reach formal operations?
Large surveys say many do not, at least not by 16. Michael Shayer and colleagues tested 10,000 British children aged 9 to 14 with group versions of Piaget's tasks. Most showed rapid growth in concrete thinking in early adolescence, but only one-fifth showed formal operational thought. A follow-up with 1,200 pupils aged 15 and 16, which included a pendulum problem, found no increase in formal thinking beyond 15.
That matters for a Class 11 physics syllabus written as if every student can already handle several variables at once.
What has not held up?
Strict stages have drawn criticism. The OpenStax textbook notes that several contemporary studies support more continuous development than Piaget's discrete stages, and that many suggest children reach milestones earlier than he described. Experiments such as Baillargeon, Spelke and Wasserman's Object permanence in five-month-old infants are part of that line of work.
Defenders argue that many objections misread him. Lourenço and Machado's reply to ten common criticisms contends that critics often ignore how Piaget's theory changed after 1970 and treat conceptual questions as if one experiment could settle them.
Can teaching speed up formal thinking?
Philip Adey and Michael Shayer tested this inside school science. Over two years, teachers gave up to 30 special lessons built around Piaget's reasoning patterns. Boys who started at 12 or older gained 0.89 standard deviations on Piagetian tests compared with control classes, moving from the 51st to the 74th percentile on British norms; other groups gained less or not at all, and science marks did not rise during the programme. A year later, the follow-up study found the gap on Piagetian tests had closed but the intervention groups now did better in science achievement.
So reasoning is not fixed by age, but changing it takes sustained, deliberate teaching, and the payoff can lag.
What does this mean for a science classroom?
Start concrete. Let students handle the pendulum, the circuit or the beaker before the formula.
Teach control of variables by name. Do not assume it; model it and ask students to plan a fair test.
Do not use stages as labels. Shayer's figures describe groups, and Adey's results show reasoning can grow.
Pair with support. Lev Vygotsky's zone of proximal development explains why a well-placed hint helps.
For ideas a student needs to see before they can reason about them, the Fermi Simulation Lab has interactive simulations for ideas easier to see than read; use one to practise the fair-test habit before meeting the formula.
Tonight, take one formula from your syllabus and write down which variables it says do and do not matter, then test one with a quick experiment.
