The ability to consider two or more dimensions of a problem at once is called

By Dr. Saul McLeod, updated 2021

The concrete operational stage is the third stage in Piaget's theory of cognitive development. This period lasts around seven to eleven years of age, and is characterized by the development of organized and rational thinking.

Piaget (1954a) considered the concrete stage a major turning point in the child's cognitive development, because it marks the beginning of logical or operational thought. The child is now mature enough to use logical thought or operations (i.e. rules) but can only apply logic to physical objects (hence concrete operational).

Children gain the abilities of conservation (number, area, volume, orientation), reversibility, seriation, transitivity and class inclusion. However, although children can solve problems in a logical fashion, they are typically not able to think abstractly or hypothetically.

Conservation

Conservation is the understanding that something stays the same in quantity even though its appearance changes.This can apply to aspects such as volume, number, area etc.

To be more technical conservation is the ability to understand that redistributing material does not affect its mass, number, volume or length.

For example, Piaget and Szeminska (1952) showed that children below 7 or 8 years of age often believed that lengthening rows of counters (by spreading them out) increased the number and squashing balls of plasticine flat reduced their volume.

In Piaget’s standard procedure he asked the child a pre and a post transformation question.

He asked whether two instances (e.g. rows of counters or beakers of liquid) were the same or different both before and after a change was made to their physical appearance (e.g. by spreading out the counters or pouring the liquid into a taller vessel).

By around seven years the majority of children can conserve liquid, because they understand that when water is poured into a different shaped glass, the quantity of liquid remains the same, even though its appearance has changed. Five-year-old children would think that there was a different amount because the appearance has changed.

Conservation of number (see video below) develops soon after this. Piaget (1954b) set out a row of counters in front of the child and asked her/him to make another row the same as the first one. Piaget spread out his row of counters and asked the child if there were still the same number of counters.

Most children aged seven could answer this correctly, and Piaget concluded that this showed that by seven years of age children were able to conserve number.

Some forms of conservation (such as mass) as understood earlier than others (volume). Piaget used the term horizonal decalage to describe this (and other) developmental inconsistencies.

Evaluation of Conservation Tasks

Several aspects of the conservation tasks have been criticized, for example, that they fail to take account of the social context of the child's understanding.

Rose and Blank (1974) argued that when a child gives the wrong answer to a question, we repeat the question in order to hint that their first answer was wrong. This is what Piaget did by asking children the same question twice in the conservation experiments, before and after the transformation.

When Rose and Blank replicated this but asked the question only once, after the liquid had been poured, they found many more six-year-olds gave the correct answer. This shows children can conserve at a younger age than Piaget claimed.

Samuel and Bryant (1984)

Samueland Bryant (1984) investigated whether Piaget’s tests of conservation were flawed because the children were responding to being asked the same question twice.

Research questions:

• How does asking only one question about conservation affect the ability of children over a wide age range?
• Are conservation of mass, number and volume all affected?

Procedure:

• 252 boys and girls aged 5½ -8 years old were divided into four groups (by age).
• This study used an independent measures experimental design.
• Each group was subdivided into three conditions: standard (pre and post transformation questions); one judgement (post transformation question); fixed array (child didn’t see transformation).
• Squashed cylinders were used to test mass, spread out rows of counters for number and tall/narrow glasses for volume.

Findings:

• Children performed better with only the posttransformation question (for most ages and most materials, oddities being due to chance)
• Older children were better at all tasks than younger ones.
• The standard Piagetian was harder than both the post-transformation question only and the fixed array situation.
• The number task was the easiest.

Conclusion:

• Samuel & Bryant conclude that the problem lies with the effect of the experimenter asking a second question and unwittingly implying to the participant that a different answer is required.
• Asking both the pre and post-transformation questions causes children who can conserve to make conservation errors.

Evaluation:

• Samuel and Bryant tested 252 children which is a large sample. They tested children from the age of five to the age of eight which allowed them to draw conclusions about the age at which children started to be able to conserve. They all came from one area of the country (Devon) which might mean that they are not representative of children from other areas of the country. For example, if Devon used different teaching strategies to other parts of the country this might have an effect on the children’s cognitive abilities. This is not really a criticism of the study and overall the sample is large enough to allow generalisations to be made.
• The task itself is quite an artificial one. It is not an everyday occurence to ask children this type of question, although the skills that are being tested are everyday skills. Perhaps a more ecologically valid method would have been to ask children to choose which of two beakers of juice or rows of smarties they would prefer to have. This would be more ‘real’ to the children as well as demonstrating clearly that they could conserve.
• There are some difficulties in evaluating the actual question used as the researchers do not tell us the exact wording of the question. Asking a child ‘are they the same?’ may be a slightly ambiguous question. There are many ways in which this question might have been asked and it is possible that children may have interpreted the question differently.

Porpodas (1987) found that asking more than one question wasn’t really the problem. This research suggested that the questions provided ‘verbal interference’ which prevented children from transferring information across from the pretransformation stage. This implied that the problem was a cognitive one, but not exactly of the nature originally suggested.

In an attempt to answer the ‘conservation or conversation?’ question, ie whether the conservation failures are due to cognitive immaturity or the language use or power relations between the child participant and adult experimenter, Baucal & Stepanovic (2006) analysed the results of many tests of the repeated question hypothesis. They also conducted an additional test which aimed to distinguish between cognitive and social effects by using a repeated question about a ‘transformation’ which had not changed (pouring liquid back into the same glass so only the question and not the actual change could influence their response).

Interestingly, the results were not as predicted. They expected that any child’s response would be the same on the standard and modified tasks, but this was not the case. However, they were unable to conclude whether the cause was or was not repeating the question.

Research has gone on to explore the ‘conversation about conservation’ idea which underpins the interview method. Arcidiacono and Perret-Clermont (2009) suggested that children’s statements about conservation are not, as Piaget claimed, simply a product of their cognitive level but of their social interaction with the interviewer.

This suggests that the child’s reasoning is ‘co-constructed’ during the testing process. If adults ‘accept’ wrong (or right) answers without asking for a justification (argument about why it is so), which is what Piaget was really interested in.

Another feature of the conservation task which may interfere with children's under-standing is that the adult purposely alters the appearance of something, so the child thinks this alteration is important. McGarrigle and Donaldson (1974) devised a study of conservation of number in which the alteration was accidental.

When two identical rows of sweets were laid out and the child was satisfied there were the same number in each, a 'naughty teddy' appeared. Whilst playing around, teddy actually messed up one row of sweets. Once he was safely back in a box the children were asked if there were the same number of sweets.

The children were between four- and six-years-old, and more than half gave the correct answer. This suggests that, once again, Piaget's design prevented the children from showing that they can conserve at a younger age than he claimed.

Classification

Piaget also studied children's ability to classify objects – put them together on the basis of their color, shape etc.

Classification is the ability to identify the properties of categories, to relate categories or classes to one another, and to use categorical information to solve problems.

One component of classification skills is the ability to group objects according to some dimension that they share. The other ability to is order subgroups hierarchically, so that each new grouping will include all previous subgroups.

For example, he found that children in the pre-operational stage had difficulty in understanding that a class can include a number of sub-classes. For example, a child is shown four red flowers and two white ones and is asked 'are there more red flowers or more flowers?'. A typical five year old would say 'more red ones'.

Piaget and stated that the child focuses on one aspect, either class or sub-class (i.e. called this class inclusion). It is not until he can decentre that he can simultaneously compare both the whole and the parts, which make up the whole. The child can then understand the relationship between class and sub-class.

Evaluation of Classification Tasks

James McGarrigle designed an experiment that tested Piaget’s explanation that a child is unable to compare class with sub-class because of centration. Centration refers to a child’s tendency to only deal with one aspect of a situation at a time.

Piaget’s class inclusion test used wooden beads, some white some brown. He found that children in the preoperational stage were unable to give the right answer to the question, “Are there more brown beads or more wooden beads?”

McGarrigle used a slightly different version of this test. He sued four model cows, three of them black, and one white. He laid all the cows on their sides, as if they were sleeping. Six year-old children were then asked:

1. Are there more black cows or more cows? (This is the question Piaget asked)

2. Are there more black cows or sleeping cows?

Results: 25% percent of the children answered question 1 correctly, but 48% of the children answered question 2 correctly.

This suggests that children are capable of understanding class inclusion rather earlier than Piaget believed. This is probably because the task was made easier to understand.

McGarrigle concluded that is was the way Piaget worded his question that prevented the younger children from showing that they understood the relationship between class and sub-class.

Seriation

The cognitive operation of seriation (logical order) involves the ability to mentally arrange items along a quantifiable dimension, such as height or weight.

Critical Evaluation

Dasen (1994) showed that different cultures achieved different operations at different ages depending on their cultural context.

Dasen (1994) cites studies he conducted in remote parts of the central Australian desert with 8-14 year old Aborigines. He gave them conservation of liquid tasks and spatial awareness tasks. He found that the ability to conserve came later in the aboriginal children, between aged 10 and 13 ( as opposed to between 5 and 7, with Piaget’s Swiss sample).

However, he found that spatial awareness abilities developed earlier amongst the Aboriginal children than the Swiss children. Such a study demonstrates cognitive development is not purely dependent on maturation but on cultural factors too – spatial awareness is crucial for nomadic groups of people.

Greenfield (1966) that schooling influenced the acquisition of such concepts as conservation.

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How to reference this article:

McLeod, S. A. (2018, January 14). Concrete operational stage. Simply Psychology. www.simplypsychology.org/concrete-operational.html

APA Style References

Arcidiacono F & Perret-Clermont AN (2009) Revisiting the piagetian test of conservation of quantities of liquid: argumentation within the adult-child interaction. Культурноисторическая психология, 3: 25-33.

Dasen, P. (1994). Culture and cognitive development from a Piagetian perspective. In W .J. Lonner & R.S. Malpass (Eds.), Psychology and culture. Boston: Allyn and Bacon.

Greenfield, P. M. (1966). On culture and conservation. Studies in cognitive growth, 225-256.

McGarrigle, J., & Donaldson, M. (1974). Conservation accidents. Cognition, 3, 341-350.

Piaget, J. (1954). The development of object concept (M. Cook, Trans.). In J. Piaget & M. Cook (Trans.), The construction of reality in the child (pp. 3-96). New York, NY, US: Basic Books.

Piaget, J. (1954b). The child's conception of number. Journal of Consulting Psychology, 18(1), 76.

Piaget, J. (1968). Quantification, conservation, and nativism. Science, 162, 976-979.

Piaget, J. & Szeminska, A. (1952). The Child’s Conception of Number. Routledge & Kegan Paul: London.

Porpodas, C. D. (1987). The one-question conservation experiment reconsidered. Journal of Child Psychology & Psychiatry, 28, 343-349.

Rose S. A. & Blank, M. (1974). The potency of context in children’s cognition: an illustrationthrough conservation. Child Development, 45, 499-502.

Samuel, J. & Bryant, P. (1984). Asking only one question in the conservation experiment. Journal of Child Psychology & Psychiatry, 25(2), 315-8.

 Download this article as a PDF

How to reference this article:

McLeod, S. A. (2018, January 14). Concrete operational stage. Simply Psychology. www.simplypsychology.org/concrete-operational.html

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