Background and aim

1. The theory: Piaget's stage theory says pre-operational children, aged about two to seven, centre on one feature of a display and cannot mentally reverse a change.
2. Concrete-operational children, aged about seven to eleven, can attend to more than one feature and reverse the change, so they can conserve.
3. Conservation of number: understanding that the number of items stays the same even when their appearance is changed.
4. Aim: Piaget (1952) tested conservation of number by spreading out one of two matched rows of counters.
5. Prediction: children in the concrete-operational stage would conserve number and pre-operational children would not.

Method

1. Design: the experimental method, with the independent variable being the age of the children.
2. The dependent variable was whether the child could conserve number.
3. Independent measures were used, because two separate age groups were compared.
4. Age cannot be manipulated by a researcher, so this counts as a natural experiment.
5. Sample: a small group of Swiss schoolchildren, including Piaget's own children.
   1. No reliable figure exists for how many children took part.

Procedure

1. Materials: two identical parallel rows of counters, laid out in one-to-one correspondence.
2. Each child was tested individually, so nobody could be swayed by another child's answer.
3. The child was shown the two rows and asked whether there was the same number of counters in each row.
4. One row was then spread out in front of the child, so it stretched further across the table.
5. The same question was asked again.

Results

1. Three and four year olds, who are pre-operational, said the spread-out row had more counters when asked the second time.
2. Five and six year olds, at the end of the pre-operational stage, often recognised that the number was unchanged.
   1. Those children could not justify the logic behind their answer.
3. Seven year olds and above, who are concrete-operational, recognised the rows were still equal and could explain why.

Conclusions

1. Conservation of number arrives with the concrete-operational stage, at around seven years of age.
2. The pre-operational failure is caused by centration on the length of the row and the absence of reversibility.
3. Link to the theory: the age pattern is evidence for Piaget's invariant stages, in which cognitive development follows biological maturation in a fixed order.

Criticisms

1. Strength: the procedure is simple, standardised and easy to repeat, so the findings can be checked.
2. The work also changed how primary maths is taught.
3. The same question twice: younger children may have changed their answer because they assumed the first one must have been wrong.
4. Sample: it was small and culturally biased, since only Swiss children took part.
   1. It also included Piaget's own children, so the sample cannot represent children in general.
5. Validity: the counters task was artificial, and children may conserve on a task that makes more sense to them.
   1. It also lacks construct validity, because conservation was measured in only one narrow way.
6. Reductionism and holism: this is the debate Piaget's theory sits in.
   1. The theory reduces development to fixed biological maturation and leaves out the holistic picture, in which teachers, parents, friends and culture all shape how a child thinks.

Turning this into marks

1. When the results are asked for, give a separate answer for each age band rather than one finding reworded.
2. Name the method as a natural experiment, because writing experiment on its own does not secure the knowledge mark.
3. The mark most often lost is describing the procedure without the second asking of the same question.
4. Use the words centration and reversibility in the conclusion, and give no figure for the sample.