The concrete operations stage is the third stage, and occurs between the ages of 7-11. Thinking becomes more logical, however can only be applied to objects that are real or can be seen. The most important cognitive operation is reversibility, which involves the cancelling out of effects of a perceptual change by imagining the opposite change. One task that can be performed in this stage and onwards is the notion of transitivity. This allows three elements to be placed in the correct order, however they an not solve abstract problems, such as “if A> B> C, then is A greater than or smaller than C?” According to Piaget, children find it easier to achieve conservation on some tasks than on others. Children who were asked if there are the same number of beads in the two rows before and after they are rearranged, could correctly say that the number of beads stayed the same. However the conservation of volume is harder to achieve, as it involves taking into account the operations involves in the conservation of liquids and of mass. According to Paiget, most children acquire the various forms of conservation in the same order. First comes conservation of number and liquid (age 6-7), then comes conservation of substance or quantity and length (age 7-8) and the conservation of weight (age 8-10). Finally there is conservation of volume at about the age of 12. Formal operations stage is the fourth and final stage, occurring in children aged 11 and upward. At this stage a child can think logically about potential events or abstract ideas, such as mathematics and hypothetical ethical issues. Thinking goes beyond limitations of immediate reality, so one is not tied to perceptions/concrete reality. Piaget tested formal operational thought by asking children to work out what would affect the frequency of the swings of the pendulum. When pre-operational children are presented with this problem they mistakenly thought that the strength of the push is the main factor. Concrete operational children argued that that the length of the string affects the frequency of swinging the pendulum, but they could not isolate that factor from all the others. Many formal operational children manage to solve the problem.
Many criticisms for Piaget’s experimental evidence can be identified. Some argue, for example, that the three-mountain task that Piaget asked three-year-old children to solve was too complex to test children's ability to see someone else's perspective. It is now believed that young children can see someone else's point of view in a simple way. Similarly, the conservation tests may also have been too complex, and further research has indicated that if a conservation task was presented in a simplified, fun manner, children were able to understand the concept of it much more easily. Pre-operational criticisms have suggested that Piaget's tasks at this stage may have underestimated the child's abilities due to a number of factors including complicated use of language, unfamiliar materials, lack of context and the child misinterpreting the experimenter's intention. However, Piaget was correct in that while children are capable for showing some understanding of these concepts, it does take maturity and experience before children can fully master logical structures and apply them to daily life. A major problem with Piaget's Sensori-motor tasks is that they required an active response from the infant (e.g. removing a cloth and grasping an object). Child may be limited by other factors (e.g. immature motor skills) rather than lack of understanding of situation. More recent studies have attempted to ask questions more clearly and to present situations to which children can relate more easily. Light et al. showed children two identical beakers with same amount of food in each. The experimenter then pointed out that one of the beakers are chipped, and suggested putting the contents in a third, different shaped container for the sake of safety. More children correctly say that there is still the same amount of food. This suggests that context of task may be important for children's understanding of the situation. As far as the formal operation stage is concerned, many adults answer the pendulum problem incorrectly, and Wason and Shapiro (1971) proved this through an abstract reasoning experiment, in which only 5-10% of university students were able to answer correctly.
Piaget’s actual experiments have either been supported, or been contradicted through other experimentation. For example, Bower realised that Piaget had underestimated the abilities of infants in the sensori-motor stage. Bower hid a toy behind a screen. When the screen was lifted, the toy was no longer there as it had been removed. Infants of 4 months showed surprise when the toy disappeared, suggesting some aspects of object permeance are present much earlier than Piaget claimed. Also, deferred imitation was found by Meltzoff (1988) to occur several months earlier than Piaget believed. In the pre operational stage, Piaget identified several limitations in the thinking of pre-operational children. However, Paiget underestimated again the cognitive abilities of children at this stage. Wheldall and Poborca (1980) claimed, as mentioned previously, that children often fail on conservation tasks as they do not understand the question. They devised a non-verbal version of the liquid task, which was based on operant conditioning. Only 28% of their 6-7 year old participants showed conservation with the standard verbal version, but 50% did so when tested on the non-verbal version. This shows that misunderstanding of language is one factor involved in non-conservation. The fact that only 50%, and not 100%, of participants showed conservation suggests other factors are involved. Hughes (1971) argued that the three-mountain task was poorly performed, as the task did not relate to a child’s normal experience. He tested this by using a piece of apparatus in which two walls were intersected at right angles. A boy doll and a policeman doll were put into the apparatus, and the child was asked whether the policeman doll could see the boy doll. After that, the child was told to hide the boy doll where neither the policeman could see him. According to paiget, the child should have hidden the doll where they themselves could not see it, however Hughes found that 90% of children aged 3 ½ and 5 were successful in the task. This proves that his task was more successfully conducted as his task was more meaningful and interesting for young children.
Piaget's theory can be compared to vygotsky’s four stage theory. Piaget took a very different approach to Vygotsky. He explained that children tended to interact more with the environment (self discovery) and develop through accommodation and assimilation. The role of social factors are not seemed as important. Both Piaget and Vygotsky agreed that children's cognitive development took place in stages. Piaget’s stages are more rigid in age, whereas Vygotsky was more abstract in his thinking. Vygotsky believes that speech moved from social speech (communicative) to inner egocentric speech. He believed that children began by voicing a personal dialogue and then moved to social speech. He argued that it became internalised as an adult. In contrast, Piaget claimed that egocentric speech was simply an accompaniment to a child’s actions and that egocentric speech went away with maturity. However, even though they both had different opinions on the purpose of egocentric speech both agreed on the importance that it played in cognitive development. Piaget ignored individual and cultural differences, but much of Vygotsky’s theories were based around this. Vygotsky’s stages are difficult to test therefore not much evidence is available to support his theory, whereas Piaget used much experimentation to support his research.