Piaget proposed that the basic unit of understanding was a scheme, which is a mental representation of actions and knowledge. Infants start out with three basic schemes, sucking, looking and grasping. Operations are internal mental representations. Mental representations not based on physical activity.

Children modify their schemes using two processes: organisation and adaptation. Organisation is organising several schemes into a bigger scheme. Adaptation consists of assimilation and accommodation. Assimilation is incorporating new information into a pre-existing scheme. Accommodation is modifying the pre-existing schemes (or generating a new one) in order to fit new information.

Equilibration is the state in which children’s schemes are in balance and are undisturbed by conflict. When there are too many conflicts that cannot be solved by either assimilation or accommodation, a change of thinking is required and this is a stage shift. A stage shift is a qualitative shift in a child’s way of thinking.

The sensorimotor stage is characterised by thinking is doing and it lasts from birth to approximately two years. It consists of several substages:

1. Reflexive schemes (birth to 1 month)
   In this phase, infants use their reflexes to explore their world.
2. Primary circular reactions (1 month to 4 months)
   The infant starts to show a degree of coordination between the senses and their motor behaviour through the primary circular reactions. The infant keeps repeating actions and it is almost always focused around the infant’s body and not on the external world.
3. Secondary circular reactions (4 months to 10 months)
   The infant starts to direct behaviour towards the external world. The actions are still circular. The infant has begun to intentionally act on his environment.
4. Coordination of secondary schemes (10 months to 12 months)
   The infant begins to deliberately combine schemes to achieve specific goals. Goal-directed behaviour arises. Object permanence is solved in this stage.
5. Tertiary circular reactions (12 months to 18 months)
   The infant begins to search for novelty and uses trial and error to explore the characteristics and properties of objects and develops new ways of solving problems.
6. Beginning of thought (18 months to 24 months)
   The infant becomes able to form enduring mental representations. This is shown by deferred imitation, imitation some while after seeing the action.

The main criticism for these stages is that object permanence and deferred imitation occur much earlier in the development than Piaget suggested. The preoperational stage is a stage that is characterised by an increase in mental representations and it subdivides into two different substages:

1. Symbolic function substage (2 years to 4 years)
   In this substage, children acquire the ability to mentally represent an object that is not physically present. Symbols can be used. Children start participating in pretend play. Young children can’t use objects that do not look alike the original object to pretend it is something, while older children can (e.g: using a banana as a telephone). Children learn to use language in this stage and their vocabulary grows quickly.
2. Intuitive thought substage (4 years to 7 years)
   This stage is characterised by a shift in children’s reasoning. They begin to classify, order and quantify in a more systematic manner. A child’s reasoning is still largely based on intuition, rather than rational thinking.

There are also things the preoperational child cannot do. There are two main limitations of the preoperational stage:

1. Egocentrism
   Egocentrism is the tendency to perceive the world solely from one’s own point of view. Children often assume that others will perceive and think about the world in the same way they do. Criticism for this comes from rational imitation, which refers to when infants produce an action that they think the adult intended to do, rather than what the adult actually did. This demonstrates that 14-month-olds can infer others’ intentions and perspectives. Other research has shown that by 4 or 5 years o age, children understand that other people’s mental stage may differ from their own.
2. Animism
   This is the belief that inanimate objects have lifelike qualities and are capable of independent actions.

Transitive interference is the ability to seriate mentally between entities that can be organised into an ordinal series (e.g: A>B, B>C, so A>C). Children can do this, as long as they can remember the premises, although Piaget believed that children found these tasks very difficult. Failure of this during the preoperational stage occurs because of the inability to remember all the relevant information. Class inclusion is the ability to coordinate and reason about parts and wholes simultaneously in recognising relations between classes and subclasses. This explains children’s failure in the conservation task. Criticism for this comes from research that showed children’s ability to draw inferences about category membership based on non-observable characteristics.

Piaget proposed that the preoperational child’s inability to conserve is characterised by three main limitations:

1. Centration
   This limitation refers to the child’s inability to focus on two or more aspects at the same time (e.g: length and width).
2. Reversibility
   This limitation refers to the child’s inability to imagine a series of steps in both forward and backward directions
3. Focusing on the end state
   The child focusses on the end state instead of the means to the end.

The age at which children attain conservation varies across culture and depends on the substances and concept they are asked to conserve. Horizontal decalage refers to age differences in solving problems which appear to require the same cognitive processes. Different type of conservation tasks requires different degrees of abstraction. There is evidence that children have knowledge of conservation before Piaget stated that they did. Vertical decalage is where what the child understands at one level or stage must be reconstructed at a later age on a different level of understanding.

Piaget believed that young children tend to focus exclusively on the perceptual features of objects. This tendency makes it difficult for children to pass the appearance-reality task. Young children make phenomenism errors or realism errors. A possible explanation is that young children are not good at dual encoding and they are unable to represent an object in more than one way at the same time. Failure on the appearance-reality distinction might arise because of the difficulties of putting the relationship between the objects in words.

The concrete operations stage is characterised by a change in thought processes. Children develop a new set of strategies called concrete operations. It is called concrete because the thought is more logical and flexible, it is still tied to concrete situations. The objects necessary for the problem-solution need to be physically present. Children in this stage are highly dependent on the context of the situation to solve a problem. Culture and context play an important role in children acquiring the forms of logic required to pass classical Piagetian tasks.

Case interpreted cognitive changes occurring as a series of four stages: sensorimotor stage (0-2), interrelational stage (2-8), dimensional stage (5-11) and the vectorial stage (11-19), but adopted an information processing approach. He attributes the changes within each stage and across stages to increases in central processing speed and working memory capacity. The increased working memory capacity arose because of brain development, automatization and the formation of central conceptual structures. Case argues that when children form a new conceptual structure they move to the next stage of development. Conservation tasks vary in their processing demands, with those tasks which require more working memory capacity being acquired later.

Siegler suggests that when attempting to solve tasks, children may generate a variety of strategies. Children are most likely to use multiple strategies which compete with each other. Over time, less efficient strategies are replaced by more effective ones.

Vygotsky viewed the child as an active seeker of knowledge. Children’s thinking is influenced by social and cultural contexts. Psychological tools are acquired through social and cultural interactions. The most important psychological tool is language. As children master language, they can use internal, self-directed speech to guide their thinking and planning, instead of talking aloud. Scaffolding is the simplifying of the environment by adults for the children, in order to assist them with learning. Each domain has its own zone of proximal development. Pretend play assists children in developing symbolic skills and social rules and cultural norms.

The theory of core knowledge proposes that humans are endowed with a small number of domain-specific systems of core knowledge at birth and that this core knowledge becomes elaborated with experience. There are five systems of core knowledge:

1. Knowledge of objects and their motions.
2. Knowledge of agents and their goal-directed actions.
3. Knowledge of number and the operations of arithmetic.
4. Knowledge of places in the navigable layout.
5. Knowledge of geometric forms and their lengths and angular reactions.

These systems support knowledge acquisition in children.