Conservation of Number Piaget

Fig. 1 - At the beginning of the preoperational stage, children do not understand the concept of conservation, but by the end, they can understand it.

What is Piaget's Theory of Cognitive Development?

Piaget's observations started with his own children. He noticed that children of different ages make specific mistakes that reflect their level of cognitive development. Piaget outlined four stages of cognitive development, universal for every child. Based on the theory of conservation, we will focus on the first two stages:

• First is the sensorimotor stage, which lasts until two years of age; in this stage, children learn about the world through senses and interactions and develop the ability to represent objects that are not around them mentally.

• And the second is the pre-operational stage which lasts until the age of 7. In this stage, children overcome egocentrism and begin to have more centric thinking.

Piaget's study of the conservation of numbers gives us a particular insight into an error typical for children in the second stage, the pre-operational stage of cognitive development, known as the conservation error.

Conservation of Number Piaget: The Conservation Error

Children make the conservation error when they fail to recognise that an object can conserve its main qualities despite a change in its appearance.

Piaget observed that in the pre-operational stage, children tend to assume that if one aspect of the object changes, it must mean that the object is different now.

Why does the Conservation Error Occur?

Piaget suggested that the conservation error occurs because of centration.

When one aspect of how an object appears changes, children in the pre-operational stage conclude that the object's main qualities have changed (e.g. it got bigger or smaller).

Piaget's Conservation Task

Piaget investigated when children make conservation errors using conservation tasks. Conservation tasks help us understand how children understand the qualities of objects.

During the task, the experimenter changes the appearance of an object by, for example, moving it and asks children whether that affected the object's volume, length or number.

Examples of Conservation in Piaget's Theory

We discussed an example of understanding the conservation of solid objects based on a play dough ball. Even though it is flattened, it is still made of the same material.

According to Piaget, children in the pre-operational stage consistently state that changing the shape of the ball changes its mass.

To investigate children's understanding of the conservation of liquid, the experimenter first presents a child with the same volume of liquid in two identical glasses. After, the children are asked whether both glasses have the same amount of liquid. The experimenter then pours coloured water from one of the wider glasses into a taller, narrower glass in front of the child.

Fig. 2 - A demonstration of the conservation of liquid task can show that children in the pre-operational stage have difficulties understanding conservation.

Children focus on the fact that the level that the liquid reaches changes when the liquid is transferred and disregard the smaller width of the tall glass. Children in the pre-operational stage are likely to conclude that there must be more liquid in the narrow glass than in the wider glass.

To investigate the conservation of numbers, an experimenter puts two rows of coins of equal lengths in front of a child. The child is then asked whether row 1 has more coins, row 2 has more coins or whether they are the same.

After the child agrees that the two rows are the same, the experimenter spreads the distance between coins in one of the rows and asks the child again which row has more coins.

Fig. 3 - Children under seven cannot understand equal coins in both rows in the Piaget conservation of number experiment.

Children below the age of 7 tend to answer that the spread-out row has more coins inaccurately.

Piaget Conservation of Number Experiment

The aim of Piaget's experiment was to investigate children's understanding of the conservation of numbers and how it changes with age.

He conducted cross-sectional studies to compare children's performance at different ages on the conservation task.

The procedure used was:

1. Children were shown two rows consisting of an equal number of counters.
2. The experimenter asked children whether the first row had more counters, the second row had more counters or whether they were the same.
3. After the child confirmed that the rows were the same, the experimenter changed one of the rows - they spread the objects further apart. Children observed the action.
4. Children were asked again which row had more counters or whether they were the same.

Piaget Conservation of Number Experiment: Results

Piaget found that children below seven stated that the rearranged row had more counters because it was longer. When the appearance of the row changed, children assumed the number of counters also changed.

By seven, children understood number conservation and didn't make conservation errors.

Piaget concluded children in the pre-operational stage do not understand that when a row changes in length, it doesn't impact the number of counters.

Piaget's Study into the Conservation of Number Evaluation

Piaget's experiments have made a significant contribution to psychology. He pioneered the study of children's cognitive abilities development, and his findings have been widely replicated. However, his experiments, including the conservation of number experiment, remain heavily criticised.

Conservation of Number Piaget: Interpreting Adult Intention

It's been argued that the conservation of numbers Piaget used is confusing for young children because of how they interpret the adult's intentions. When children see the adult performing an intentional action, like changing an aspect of the stimulus, children can think that the action was related to the question and should affect their answer.

McGarrigle and Donaldson (1974) replicated the Piagetian conservation of number tasks with four to six-year-old children. In one experimental condition, the stimulus was changed due to the experimenter's action. In the second condition, the change was accidental and performed by a "naughty teddy bear".

Results of the McGarrigle and Donaldson (1974) study revealed:

• 63% of children showed the ability to conserve when the change was made accidentally by the teddy bear.
• In the standard Piagetian condition, only 16% of children could conserve.

It was concluded that children get confused about how they should report what they see after witnessing an adult intentionally move or change stimuli. From the results of the McGarrigle and Donaldson (1974) study, we can see that the conservation of numbers may not reflect children's true abilities.

Fig. 4. Artificial experiments like the Piagetian conservation of number task can confuse young children.

Conservation of Number Piaget: Asking Children the Question Twice

Rose and Blank (1974) recognised that when children are asked the question twice, it can make them think that their first answer was incorrect. In real life, adults often repeat questions that children answer wrong to encourage them to rethink their answers. Therefore asking the question twice in the experiment might affect children's answers.

Rose and Blank (1974) conducted Piaget's conservation studies but only asked the question once after the changes to the stimuli were made. In their study, six-year-olds often did not make the conservation error.

Conservation of Number Piaget: Sample Limitations

Piaget concluded that conservation error is universal for children under seven. However, he was criticised for concluding that based on his limited sample. He primarily studied his children and didn't report his experiments in a standard way. In the report, he describes his observations but doesn't inform us about the number of participants he tested or their specific characteristics. Therefore, it is difficult to generalise the findings to the general population.