Piaget's theory of cognitive development

For more information, see Neo-Piagetian theories of cognitive development.

Piaget's theory of cognitive development is a comprehensive theory about the nature and development of human intelligence first developed by Jean Piaget. It is primarily known as a developmental stage theory, but in fact, it deals with the nature of knowledge itself and how humans come gradually to acquire it, construct it, and use it. Moreover, Piaget claims the idea that cognitive development is at the centre of human organism and language is contingent on cognitive development. Below, there is first a short description of Piaget's views about the nature of intelligence and then a description of the stages through which it develops until maturity.

The Nature of Intelligence: Operative and Figurative Intelligence

Piaget believed that reality is a dynamic system of continuous change, and as such is defined in reference to the two conditions that define dynamic systems. Specifically, he argued that reality involves transformations and states. Transformations refer to all manners of changes that a thing or person can undergo. States refer to the conditions or the appearances in which things or persons can be found between transformations. For example, there might be changes in shape or form (for instance, liquids are reshaped as they are transferred from one vessel to another, humans change in their characteristics as they grow older), in size (e.g., a series of coins on a table might be placed close to each other or far apart) in placement or location in space and time (e.g., various objects or persons might be found at one place at one time and at a different place at another time). Thus, Piaget argued, that if human intelligence is to be adaptive, it must have functions to represent both the transformational and the static aspects of reality. He proposed that operative intelligence is responsible for the representation and manipulation of the dynamic or transformational aspects of reality and that figurative intelligence is responsible for the representation of the static aspects of reality.^[1]

Operative intelligence is the active aspect of intelligence. It involves all actions, overt or covert, undertaken in order to follow, recover, or anticipate the transformations of the objects or persons of interest. Figurative intelligence is the more or less static aspect of intelligence, involving all means of representation used to retain in mind the states (i.e., successive forms, shapes, or locations) that intervene between transformations. That is, it involves perception, imitation, mental imagery, drawing, and language. Therefore, the figurative aspects of intelligence derive their meaning from the operative aspects of intelligence, because states cannot exist independently of the transformations that interconnect them. Piaget believed that the figurative or the representational aspects of intelligence are subservient to its operative and dynamic aspects, and therefore, that understanding essentially derives from the operative aspect of intelligence.

At any time, operative intelligence frames how the world is understood and it changes if understanding is not successful. Piaget believed that this process of understanding and change involves two basic functions: Assimilation and accommodation.

Assimilation and Accommodation

Through studying the field of education Piaget focused on accommodation and assimilation. Assimilation, one of two processes coined by Jean Piaget, describes how humans perceive and adapt to new information. It is the process of taking one’s environment and new information and fitting it into pre-existing cognitive schemas. Assimilation occurs when humans are faced with new or unfamiliar information and refer to previously learned information in order to make sense of it. Accommodation, unlike assimilation is the process of taking one's environment and new information, and altering one's pre-existing schemas in order to fit in the new information.

Through a series of stages, Piaget explains the ways in which characteristics are constructed that lead to specific types of thinking; this chart is called Cognitive Development. To Piaget, assimilation is integrating external elements into structures of lives or environments or those we could have through experience. It is through assimilation that accommodation is derived. Accommodation is imperative because it is how people will continue to interpret new concepts, schemas, frameworks, etc.^[2] Assimilation is different from accommodation because of how it relates to the inner organism due to the environment. Piaget believes that the human brain has been programmed through evolution to bring equilibrium, and to move upwards in a process to equilibriate what is not. The equilibrium is what Piaget believes ultimately influences structures because of the internal and external processes through assimilation and accommodation.

Piaget's understanding is that these two functions cannot exist without the other. To assimilate an object into an existing mental schema, one first needs to take into account or accommodate to the particularities of this object to a certain extent; for instance, to recognize (assimilate) an apple as an apple one needs first to focus (accommodate) on the contour of this object. To do this one needs to roughly recognize the size of the object. Development increases the balance or equilibration between these two functions. When in balance with each other, assimilation and accommodation generate mental schemas of the operative intelligence. When one function dominates over the other, they generate representations which belong to figurative intelligence.

Following from this conception Piaget theorized that intelligence is active and constructive. It is active in the literal sense of the term as it depends on the actions (overt or covert, assimilatory or accommodatory), which the thinker executes in order to build and rebuild his models of the world. It is also constructive because actions, particularly mental actions, are coordinated into more inclusive and cohesive systems, thus they are raised to more stable and effective levels of functioning.

Sensorimotor stage

The sensorimotor stage is the first of the four stages in cognitive development which "extends from birth to the acquisition of language".^[3] "In this stage, infants construct an understanding of the world by coordinating experiences (such as seeing and hearing) with physical, motoric actions. Infants gain knowledge of the world from the physical actions they perform on it. An infant progresses from reflexive, instinctual action at birth to the beginning of symbolic thought toward the end of the stage. Piaget divided the sensorimotor stage into six sub-stages"^[4]:0–2 years, Infants just have senses-vision, hearing, and motor skills, such as grasping, sucking, and stepping.---from Psychology Study Guide by Bernstein, Penner, Clarke-Stewart, Roy

Sub-Stage	Age	Description
1 Simple Reflexes	Birth-6 weeks	"Coordination of sensation and action through reflexive behaviors".[4] Three primary reflexes are described by Piaget: sucking of objects in the mouth, following moving or interesting objects with the eyes, and closing of the hand when an object makes contact with the palm (palmar grasp). Over the first six weeks of life, these reflexes begin to become voluntary actions; for example, the palmar reflex becomes intentional grasping.[5]).
2 First habits and primary circular reactions phase	6 weeks-4 months	"Coordination of sensation and two types of schemes: habits (reflex) and primary circular reactions (reproduction of an event that initially occurred by chance). Main focus is still on the infant's body." [4] As an example of this type of reaction, an infant might repeat the motion of passing their hand before their face. Also at this phase, passive reactions, caused by classical or operant conditioning, can begin.[5]
3 Secondary circular reactions phase	4–8 months	Development of habits. "Infants become more object-oriented, moving beyond self-preoccupation; repeat actions that bring interesting or pleasurable results."[4] This stage is associated primarily with the development of coordination between vision and prehension. Three new abilities occur at this stage: intentional grasping for a desired object, secondary circular reactions, and differentiations between ends and means. At this stage, infants will intentionally grasp the air in the direction of a desired object, often to the amusement of friends and family. Secondary circular reactions, or the repetition of an action involving an external object begin; for example, moving a switch to turn on a light repeatedly. The differentiation between means and ends also occurs. This is perhaps one of the most important stages of a child's growth as it signifies the dawn of logic.[5]
4 Coordination of secondary circular reactions stages	8–12 months	"Coordination of vision and touch--hand-eye coordination; coordination of schemes and intentionality." [4] This stage is associated primarily with the development of logic and the coordination between means and ends. This is an extremely important stage of development, holding what Piaget calls the "first proper intelligence." Also, this stage marks the beginning of goal orientation, the deliberate planning of steps to meet an objective.[5]
5 Tertiary circular reactions, novelty, and curiosity	12–18 months	"Infants become intrigued by the many properties of objects and by the many things they can make happen to objects; they experiment with new behavior." [4] This stage is associated primarily with the discovery of new means to meet goals. Piaget describes the child at this juncture as the "young scientist," conducting pseudo-experiments to discover new methods of meeting challenges.[5]
6 Internalization of Schemes	18–24 months	"Infants develop the ability to use primitive symbols and form enduring mental representations." [4] This stage is associated primarily with the beginnings of insight, or true creativity. This marks the passage into the preoperational stage.

By the end of the sensorimotor period, objects are both separate from the self and permanent. Object permanence is the understanding that objects continue to exist even when they cannot be seen, heard, or touched. Acquiring the sense of object permanence is one of the infant's most important accomplishments, according to Piaget.^[4]

Preoperational stage

The preoperative stage is the second of four stages of cognitive development. Cognitive Development Approaches. By observing sequences of play, Jean Piaget was able to demonstrate that towards the end of the second year, a qualitatively new kind of psychological functioning occurs.^[6]

(Pre)Operatory Thought is any procedure for mentally acting on objects. The hallmark of the preoperational stage is sparse and logically inadequate mental operations. During this stage, the child learns to use and to represent objects by images, words, and drawings.The child is able to form stable concepts as well as mental reasoning and magical beliefs. The child however is still not able to perform operations; tasks that the child can do mentally rather than physically. Thinking is still egocentric. The child has difficulty taking the viewpoint of others. Two substages can be formed from preoperative thought.^[6]

• The Symbolic Function Substage

Occurs between about the ages of 2 and 7.During 2-4 years old , kids cannot yet manipulate and transform information in logical ways, but they now can think in images and symbols. The child is able to formulate designs of objects that are not present. Other examples of mental abilities are language and pretend play. Although there is an advancement in progress, there are still limitations such as egocentrism and animism. Egocentrism occurs when a child is unable to distinguish between their own perspective and that of another person's. Children tend to pick their own view of what they see rather than the actual view shown to others.An example is an experiment performed by Piaget and Barbel Inhelder. Three views of a mountain are shown and the child is asked what a traveling doll would see at the various angles; the child picks their own view compared to the actual view of the doll. Animism is the belief that inanimate objects are capable of actions and have lifelike qualities. An example is a child believing that the sidewalk was mad and made them fall down.^[6]

• The Intuitive Thought Substage

Occurs between about the ages of 4 and 7. Children tend to become very curious and ask many questions; begin the use of primitive reasoning. There is an emergence in the interest of reasoning and wanting to know why things are the way they are. Piaget called it the intuitive substage because children realize they have a vast amount of knowledge but they are unaware of how they know it.'Centration' and 'conservation' are both involved in preoperative thought. Centration is the act of focusing all attention on one characteristic compared to the others. Centration is noticed in conservation; the awareness that altering a substance's appearance does not change its basic properties. Children at this stage are unaware of conservation.Example, In Piaget's most famous task, a child is presented with two identical beakers containing the same amount of liquid. The child usually notes that the beakers have the same amount of liquid.When one of the beakers is poured into a taller and thinner container, children who are younger than 7 or 8 years old typically say that the two beakers now contain a different amount of liquid. The child simply focuses on the height and width of the container compared to the general concept.^[6]

Concrete operational stage

The concrete operational stage is the third of four stages of cognitive development in Piaget's theory. This stage, which follows the preoperational stage, occurs between the ages of 7 and 11 years^[7] and is characterized by the appropriate use of logic. Important processes during this stage are:

Seriation—the ability to sort objects in an order according to size, shape, or any other characteristic. For example, if given different-shaded objects they may make a color gradient.

Transitivity- The ability to recognize logical relationships among elements in a serial order, and perform 'transitive inferences' (for example, If A is taller than B, and B is taller than C, then A must be taller than C).

Classification—the ability to name and identify sets of objects according to appearance, size or other characteristic, including the idea that one set of objects can include another.

Decentering—where the child takes into account multiple aspects of a problem to solve it. For example, the child will no longer perceive an exceptionally wide but short cup to contain less than a normally-wide, taller cup.

Reversibility—the child understands that numbers or objects can be changed, then returned to their original state. For this reason, a child will be able to rapidly determine that if 4+4 equals t, t−4 will equal 4, the original quantity.

Conservation—understanding that quantity, length or number of items is unrelated to the arrangement or appearance of the object or items.

Elimination of Egocentrism—the ability to view things from another's perspective (even if they think incorrectly). For instance, show a child a comic in which Jane puts a doll under a box, leaves the room, and then Melissa moves the doll to a drawer, and Jane comes back. A child in the concrete operations stage will say that Jane will still think it's under the box even though the child knows it is in the drawer. (See also False-belief task).

Children in this stage can, however, only solve problems that apply to actual (concrete) objects or events, and not abstract concepts or hypothetical tasks.

Formal operational stage

The formal operational period is the fourth and final of the periods of cognitive development in Piaget's theory.^[8] This stage, which follows the Concrete Operational stage, commences at around 11 years of age (puberty) and continues into adulthood.^[8] In this stage, individuals move beyond concrete experiences and begin to think abstractly, reason logically and draw conclusions from the information available, as well as apply all these processes to hypothetical situations.^[8] The abstract quality of the adolescent's thought at the formal operational level is evident in the adolescent's verbal problem solving ability.^[8] The logical quality of the adolescent's thought is when children are more likely to solve problems in a trial-and-error fashion.^[8] Adolescents begin to think more as a scientist thinks, devising plans to solve problems and systematically testing solutions.^[8] They use hypothetical-deductive reasoning, which means that they develop hypotheses or best guesses, and systematically deduce, or conclude, which is the best path to follow in solving the problem.^[8] During this stage the adolescent is able to understand such things as love, "shades of gray", logical proofs and values. During this stage the young person begins to entertain possibilities for the future and is fascinated with what they can be.^[8] Adolescents are changing cognitively also by the way that they think about social matters.^[8] Adolescent Egocentrism governs the way that adolescents think about social matters and is the heightened self-consciousness in them as they are which is reflected in their sense of personal uniqueness and invincibility.^[8] Adolescent egocentrism can be dissected into two types of social thinking, imaginary audience that involves attention getting behavior, and personal fable which involves an adolescent's sense of personal uniqueness and invincibility.^[8]

The stages and causation

Piaget sees children’s conception of causation as a march from "primitive" conceptions of cause to those of a more scientific, rigorous, and mechanical nature. These primitive concepts are characterized as magical, with a decidedly nonnatural or nonmechanical tone. Piaget attributes this to his most basic assumption: that babies are phenomenists. That is, their knowledge "consists of assimilating things to schemas" from their own action such that they appear, from the child’s point of view, "to have qualities which in fact stem from the organism." Consequently, these "subjective conceptions," so prevalent during Piaget’s first stage of development, are dashed upon discovering deeper empirical truths. Piaget gives the example of a child believing the moon and stars follow him on a night walk; upon learning that such is the case for his friends, he must separate his self from the object, resulting in a theory that the moon is immobile, or moves independently of other agents. The second stage, from around three to eight years of age, is characterized by a mix of this type of magical, animistic, or “nonnatural” conceptions of causation and mechanical or "naturalisitic" causation. This conjunction of natural and nonnatural causal explanations supposedly stems from experience itself, though Piaget does not make much of an attempt to describe the nature of the differences in conception; in his interviews with children, he asked specifically about natural phenomena: what makes clouds move? What makes the stars move? Why do rivers flow? The nature of all the answers given, Piaget says, are such that these objects must perform their actions to "fulfill their obligations towards men." He calls this "moral explanation."^[9]

Challenges to Piagetian stage theory

Piagetians' accounts of development have been challenged on several grounds. First, as Piaget himself noted, development does not always progress in the smooth manner his theory seems to predict. 'Decalage', or unpredicted gaps in the developmental progression, suggest that the stage model is at best a useful approximation. More broadly, Piaget's theory is 'domain general', predicting that cognitive maturation occurs concurrently across different domains of knowledge (such as mathematics, logic, understanding of physics, of language, etc.). During the 1980s and 1990s, cognitive developmentalists were influenced by "neo-nativist" and evolutionary psychology ideas. These ideas de-emphasized domain general theories and emphasized domain specificity or modularity of mind. Modularity implies that different cognitive faculties may be largely independent of one another and thus develop according to quite different time-tables. In this vein, some cognitive developmentalists argued that rather than being domain general learners, children come equipped with domain specific theories, sometimes referred to as 'core knowledge', which allows them to break into learning within that domain. For example, even young infants appear to be sensitive to some predictable regularities in the movement and interactions of objects (e.g. that one object cannot pass through another), or in human behavior (e.g. that a hand repeatedly reaching for an object has that object, not just a particular path of motion), as its be the building block out of which more elaborate knowledge is constructed. More recent work has strongly challenged some of the basic presumptions of the 'core knowledge' school, and revised ideas of domain generality—but from a newer dynamic systems approach, not from a revised Piagetian perspective. Dynamic systems approaches harken to modern neuroscientific research that was not available to Piaget when he was constructing his theory. One important finding is that domain-specific knowledge is constructed as children develop and integrate knowledge. This suggests more of a "smooth integration" of learning and development than either Piaget, or his neo-nativist critics, had envisioned. Additionally, some psychologists, such as Vygotsky and Jerome Bruner, thought differently from Piaget, suggesting that language was more

Post Piagetian and Neo-Piagetian stages

Main article: Neo-Piagetian theories of cognitive development

In the recent years, several scholars attempted to ameliorate the problems of Piaget's theory by developing new theories and models that can accommodate evidence that violates Piagetian predictions and postulates. These models are summarized below.

• The neo-Piagetian theories of cognitive development, advanced by Case, Demetriou, Halford, Fischer, and Pascual-Leone, attempted to integrate Piaget's theory with cognitive and differential theories of cognitive organization and development. Their aim was to better account for the cognitive factors of development and for intra-individual and inter-individual differences in cognitive development. They suggested that development along Piaget's stages is due to increasing working memory capacity and processing efficiency. Moreover, Demetriou´s theory ascribes an important role to hypercognitive processes of self-recording, self-monitoring, and self-regulation and it recognizes the operation of several relatively autonomous domains of thought (Demetriou, 1998; Demetriou, Mouyi, Spanoudis, 2010).

• Postformal stages have been proposed. Kurt Fischer suggested two, Michael Commons presents evidence for four postformal stages: the systematic, metasystematic, paradigmatic and cross paradigmatic. (Commons & Richards, 2003; Oliver, 2004).

• A "sentential" stage has been proposed, said to occur before the early preoperational stage. Proposed by Fischer, Biggs and Biggs, Commons, and Richards.

• Searching for a micro-physiological basis for human mental capacity, Traill (1978, Section C5.4 [1]; - 1999, Section 8.4 [2]) proposed that there may be "pre-sensorimotor" stages ("M⁻¹L", "M⁻²L", … … ) — developed in the womb and/or transmitted genetically.

Postulated physical mechanisms underlying "schemes" and stages

Piaget himself (1967) considered the possibility of RNA molecules as likely embodiments of his still-abstract "schemes" (which he promoted as units of action) — though he did not come to any firm conclusion. At that time, due to work such as that of Holger Hydén, RNA concentrations had indeed been shown to correlate with learning, so the idea was quite plausible.

However, by the time of Piaget's death in 1980, this notion had lost favour. One main problem was over the protein which (it was assumed) such RNA would necessarily produce, and that did not fit in with observation. It then turned out, surprisingly, that only about 3% of RNA does code for protein (Mattick, 2001, 2003, 2004). Hence most of the remaining 97% (the "ncRNA") could now theoretically be available to serve as Piagetian schemes (or other regulatory roles now under investigation). The issue has not yet been resolved experimentally, but its theoretical aspects have been reviewed; (Traill 2005 / 2008).

Piagetian and post-Piagetian stage theories/heuristics

• Cheryl Armon's Stages of the Good Life
• Michael Barnes's stages of religious and scientific thinking
• Michael Lamport Commons' Model of Hierarchical Complexity
• Andreas Demetriou's Neo-Piagetian theories of cognitive development
• Kieran Egan's stages of understanding
• Suzy Gablik's stages of art history
• Christopher Hallpike's stages of moral understanding
• Lawrence Kohlberg's stages of moral development
• Loevinger's stages of ego development
• Don Lepan's theory of the origins of modern thought and drama
• Charles Radding's theory of the medieval intellectual development
• R.J. Robinson's stages of history and theory of the origins of intelligence
• Ashby, W.Ross (1952/1960) Design for a Brain. London: Chapman & Hall — gives a theoretical brain model which implies stages of development comparable to Piaget's; see Traill (1978).
• Stafford Beer, a cybernetician and business-consultant, attempted to apply Ashby's principles to Companies and Government organizations. (e.g. Beer, 1972).
• Biggs, J. & K.Collis (1982). A system of evaluating learning outcomes: The SOLO Taxonomy. New York: Academic Press.
• Chapman, M. (1988). "Constructive Evolution: Origins and Development of Piaget’s Thought". New York: Cambridge University Press.
• Cole, M, et al. (2005). The Development of Children. New York: Worth Publishers.
• Commons, M.L. & F.A. Richards (1984). "A general model of stage theory" — and — "Applying the general stage model".  In M.L.Commons, F.A.Richards, & C.Armon (Eds.). Beyond formal operations: Vol.1: Late adolescent and adult cognitivedevelopment (pp. 120–140, 141-157). New York: Praeger.
• Commons, M.L. & F.A. Richards (2002). "Organizing components into combinations: How stage transition works". Journal of Adult Development, 9(3), 159-177.
• Commons, M.L. & F.A. Richards (2003). "Four postformal stages". In J. Demick & C. Andreoletti (Eds.), Handbook of adult development (pp. 199–219). New York: Kluwer Academic/Plenum.
• Demetriou, A. (1998). Cognitive development. In A. Demetriou, W. Doise, K. F. M. van Lieshout (Eds.), Life-span developmental psychology (pp. 179–269). London: Wiley.
• Demetriou, A., Mouyi, A., & Spanoudis, G. (2010). The development of mental processing. Nesselroade, J. R. (2010). Methods in the study of life-span human development: Issues and answers. In W. F. Overton (Ed.), Biology, cognition and methods across the life-span. Volume 1 of the Handbook of life-span development (pp. 36–55), Editor-in-chief: R. M. Lerner. Hoboken, NJ: Wiley.
• Fischer, K.W. (1980). "A theory of cognitive development: The control and construction of hierarchical skills". Psychological Review, 87(2), 477-531.
• Oliver, C.R. (2004). Impact of catastrophe on pivotal national leaders' vision statements: Correspondences and discrepancies in moral reasoning, explanatory style, and rumination. Dissertation: Fielding Graduate Institute. http://dareassociation.org/Carl.Oliver_Dissertation_2004.pdf
• Marcus, G. F. (2001). The Algebraic Mind: Integrating Connectionism and Cognitive Science. Cambridge, MA: MIT Press.
• Mattick, J.S. (2001). “Noncoding RNAs: the architects of eukaryotic complexity”. EMBO Reports 2(11), 986-991. [3]
• Mattick, J.S. (2003). “Challenging the dogma: The hidden layer of non-protein-coding RNAs on complex organisms” Bioessays. 25, 930-939. [4]
• Mattick, J.S. (2004). “The hidden genetic program of complex organisms” Scientific American. 291(4), 30-37. [5]
• Pascual-Leone, J. (1970). "A mathematical model for the transition rule in Piaget's developmental stages", Acta Psychologica, 32(4), 301-345.
• Pascual-Leone, J. (1987). "Organismic processes for neo-Piagetian theories: A dialectical causal account of cognitive development". In: A.Demetriou (Ed.) The neo-Piagetian theories of cognitive development: Towards an integration. Amsterdam: North-Holland; pp. 531–569.
• Piaget, J. (1937/1954). La construction du réel chez l'enfant   /  The construction of reality in the child. New York: Basic Books.
• Piaget, J. (1967). Biology and Knowledge, Chicago University Press.
• Piaget, J. (1977). The Essential Piaget. ed by Howard E. Gruber and J. Jacques Vonèche, New York: Basic Books.  [An anthology of Piaget's works, with editorial comment].
• Piaget, J. (1983). "Piaget's theory". In P. Mussen (ed). Handbook of Child Psychology. 4th edition. Vol. 1. New York: Wiley.
• Piaget, J. (1995). Sociological Studies. London: Routledge.
• Piaget, J. (2000). "Commentary on Vygotsky". New Ideas in Psychology, 18, 241–259.
• Piaget, J. (2001). Studies in Reflecting Abstraction. Hove, UK: Psychology Press.
• Seifer, Calvin Educational Psychology
• Traill, R.R. (1976/2007) Short papers and letters on the 'linear micro-element' theory of mental mechanism, and related questions of scientific method. Monograph 18, Cybernetics Department, Brunel University. [6]
• Traill, R.R. (1978) Molecular Explanation for Intelligence, including its growth, maintenance, and failings. Thesis, Brunel University, Uxbridge, Middx. http://hdl.handle.net/2438/729 [or separate chapters via http://www.ondwelle.com]
• Traill, R.R. (1999) Mind and Micro-Mechanism: a Hunt for the Missing Theory. Melbourne: Ondwelle. ISBN 0-9577737-0-6 [7]
• Traill, R.R. (2005/2008) Thinking by Molecule, Synapse, or both? — From Piaget's Schema, to the Selecting/Editing of ncRNA. Melbourne: Ondwelle. [8] — [also in French: [9] ]
• Jerome Bruner's views on Cognitive development

References

1. ^ Piaget, J., & Inhelder, B. (1973). Memory and intelligence. London: Routledge and Kegan Paul.
2. ^ "Block, Jack" "Assimilation, Accommodation, and the Dynamics of Personality Development"
3. ^ Tuckman, Bruce W., and David M. Monetti. Educational Psychology. Belmont, CA: Wadsworth, 2010. Print
4. ^ ^{a b c d e f g h} Santrock, J.W. (2008). A Topical Approach To Life-Span Development (pp.211-216). New York, NY: McGraw-Hill
5. ^ ^{a b c d e} Piaget, J. (1977). Gruber, H.E.; Voneche, J.J.. eds. The essential Piaget. New York: Basic Books. 
6. ^ ^{a b c d} Santrock, John W. (2004). Life-Span Development (9th Ed.). Boston, MA: McGraw-Hill College - Chapter 8
7. ^ Herbert Ginsburg and Sylvia Opper (1979), Piaget's Theory of Intellectual Development, Prentice Hall, ISBN 0-13-675140-7, p. 152.
8. ^ ^{a b c d e f g h i j k} Santrock, J.W. (2008). A Topical Approach to Life Span Development (pp.221-223). New York, NY: McGraw-Hill.
9. ^ Piaget, J. (1928). La causalité chez l’enfant. British Journal of Psychology, 18, 276-301

External links

• Piaget's Theory of Cognitive Development
• Cognitive development of a child
• Only one-third of adults can reason formally