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The 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.
- 1 The Nature of Intelligence: Operative and Figurative Intelligence
- 2 Piaget's four stages
- 3 Challenges to Piagetian stage theory
- 4 Post Piagetian and Neo-Piagetian stages
- 5 Postulated physical mechanisms underlying "schemes" and stages
- 6 Piagetian and post-Piagetian stage theories/heuristics
- 7 See also
- 8 References
- 9 External links
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 that change. 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).
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 refers to the active transformation of information so as to be integrated into the mental schemes already available. Its analog at the biological level might be the transformation of food by chewing and digestion to fit in with the structural and bio-chemical characteristics of the human body. Accommodation refers to the active transformation of these schemes so as to take into account the particularities of the objects, persons, or events the thinker is interacting with. Its analog at the biological level might be the adaptation of eating and digestion to the particulars of the different kinds of food we eat. For Piaget, none of these functions can exist without the other. To assimilate an object into an existing mental scheme, 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. We will see below that development increases the balance or equilibration between these two functions. When in balance with each other, they generate mental schemes of the operative intelligence. When the one dominates over the other, they generate representations which belong to figurative intelligence.
Following from this conception Piaget theorized that intelligence is active and constructive. In fact, it is active even 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. And it is constructive because actions, particularly mental actions, are coordinated into more inclusive and cohesive systems and thus they are raised to ever more stable and effective levels of functioning. Piaget believed that this process of construction leads to systems of mental operations better able to resist the illusions of perceptual appearances and thus less prone to error. In other words, the gradual construction of the system of mental operations involved in the operative aspect of intelligence enables the developing person to grasp ever more hidden and complex aspects of the world. Below we will summarize the development of operative intelligence.
Piaget's four stages
According to Jean Piaget's theory of cognitive development, intelligence is the basic mechanism of ensuring equilibrium in the relations between the person and the environment. This is achieved through the actions of the developing person on the world. At any moment in development, the environment is assimilated in the schemes of action that are already available and these schemes are transformed or accommodated to the peculiarities of the objects of the environment, if they are not completely appropriate. Thus, the development of intelligence is a continuous process of assimilations and accommodations that lead to increasing expansion of the field of application of schemes, increasing coordination between them, increasing interiorization, and increasing abstraction. The mechanism underlying this process of increasing abstraction, interiorization, and coordination is reflecting abstraction. That is, reflecting abstraction gradually leads to the rejection of the external action components of sensorimotor operations on objects and to the preservation of the mental, planning or anticipatory, components of operation. These are the mental operations that are gradually coordinated with each other, generating structures of mental operations. These structures of mental operations are applied on representations of objects rather than on the objects themselves. Language, mental images, and numerical notation are examples of representations standing for objects and thus they become the object of mental operations. Moreover, mental operations, with development, become reversible. For instance, the counting of a series of objects can go both forward and backward with the understanding that the number of objects counted is not affected by the direction of counting because the same number can be retrieved both ways. Piaget described four main periods in the development towards completely reversible equlibrated thought structures. These are the periods described below. As shown below, for Piaget intelligence is not the same at different ages. It changes qualitatively, attaining increasingly broader, more abstract, and more equlibrated structures thereby allowing access to different levels of organization of the world.
The Sensorimotor Stage is the first of the four stages of cognitive development. "In this stage, infants construct an understanding of the world by coordinating sensory 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":
|1 Simple Reflexes||Birth-6 weeks||"Coordination of sensation and action through reflexive behaviors". 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.).|
|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."  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.|
|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." 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.|
|4 Coordination of secondary circular reactions stage||8–12 months||"Coordination of vision and touch--hand-eye coordination; coordination of schemes and intentionality."  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 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."  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 .|
|6 Internalization of Schemes||18–24 months||"Infants develop the ability to use primitive symbols and form enduring mental representations."  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."
The Preoperative stage is the second of four stages of cognitive development. By observing sequences of play, Piaget was able to demonstrate that towards the end of the second year, a qualitatively new kind of psychological functioning occurs.
(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.
- The Symbolic Function Substage
- Occurs between about the ages of 2 and 4. 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.
- 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. In Piaget's most famous task, a child is represented 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 typically younger than 7 or 8 years old 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. Piaget believes that if a child fails the conservation-of-liquid task, it is a sign that they are at the preoperational stage of cognitive development. The child also fails to show conservation of number, matter, length, volume, and area as well. Another example is when a child is shown 7 dogs and 3 cats and asked if there are more dogs than cats. The child would respond positively. However when asked if there are more dogs than animals, the child would once again respond positively. Such fundamental errors in logic show the transition between intuitiveness in solving problems and true logical reasoning acquired in later years when the child grows up.
Studies have been conducted among other countries to find out if Piaget's theory is universal. Psychologist Patricia Greenfield conducted a task similar to Piaget's beaker experiment in the West African nation of Senegal. Her results stated that only 50 percent of the 10-13 year old understood the concept of conservation. Other cultures such as central Australia and New Guinea had similar results. If adults had not gained this concept, they would be unable to understand the point of view of another person. There may have been discrepancies in the communication between the experimenter and the children which may have altered the results. It has also been found that if conservation is not widely practiced in a particular country, the concept can be taught to the child and training can improve the child's understanding. Therefore, it is noted that there are different age differences in reaching the understanding of conservation based on the degree to which the culture teaches these tasks.
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 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. This stage, which follows the Concrete Operational stage, commences at around 11 years of age (puberty) and continues into adulthood. 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. The abstract quality of the adolescent's thought at the formal operational level is evident in the adolescent's verbal problem solving ability. The logical quality of the adolescent's thought is when children are more likely to solve problems in a trial-and-error fashion. Adolescents begin to think more as a scientist thinks, devising plans to solve problems and systematically testing solutions. 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. During this stage the young adult is able to understand such things as love, "shades of gray", logical proofs and values. During this stage the young adult begins to entertain possibilities for the future and is fascinated with what they can be. Adolescents are changing cognitively also by the way that they think about social matters. 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. 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.
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 goal). These basic assumptions may 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 Bruner, thought differently from Piaget, suggesting that language was more important than Piaget indicated in his cognitive development theory.
Another recent challenge to Piaget's theory is a new theory called Ecological Systems Theory. This is based on the contextual influences in the child's life like his/her immediate family, school, society and the world, and how these impact the child's development.
The experience of Sudbury model schools shows that a great variety can be found in the minds of children, against Piaget's theory of universal steps in comprehension and general patterns in the acquisition of knowledge: "No two kids ever take the same path. Few are remotely similar. Each child is so unique, so exceptional" (Greenberg, 1987).
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, Commons, Demetriou, Halford, 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; 1999, Section 8.4) 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
- 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
- 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. 
- Mattick, J.S. (2003). “Challenging the dogma: The hidden layer of non-protein-coding RNAs on complex organisms” Bioessays. 25, 930-939. 
- Mattick, J.S. (2004). “The hidden genetic program of complex organisms” Scientific American. 291(4), 30-37. 
- 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. 
- 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
- Traill, R.R. (2005 / 2008) Thinking by Molecule, Synapse, or both? — From Piaget's Schema, to the Selecting/Editing of ncRNA. Melbourne: Ondwelle.  — [also in French:  ]
- Jerome Bruner's views on Cognitive development
- Piaget, J., & Inhelder, B. (1973). Memory and intelligence. London: Routledge and Kegan Paul.
- Piaget, J. (2001). Studies in reflecting abstraction. London: Psychology Press
- Santrock, J.W. (2008). A Topical Approach To Life-Span Development (pp.211-216). New York, NY: McGraw-Hill
- Piaget, J. (1977). The essential Piaget, New York: Basic Books.
- Santrock, J.W. (2007). Cognitive Development Approaches. In Emily Barrosse (Ed.), A Topical Approach to Life-Span Development (pp. 225-230). New York, NY: Beth Mejia.
- Herbert Ginsburg and Sylvia Opper, Piaget's Theory of Intellectual Development, ISBN 0-13-675140-7, Chapter 3
- Jean Piaget, Play, Dreams and Imitation, 1955
- Herbert Ginsburg and Sylvia Opper (1979), Piaget's Theory of Intellectual Development, Prentice Hall, ISBN 0-13-675140-7, p. 152.
- Santrock, J.W. (2008). A Topical Approach to Life Span Development (pp.221-223). New York, NY: McGraw-Hill.
- Greenberg, D. (1987). Chapter 19, Learning, Free at Last, The Sudbury Valley School. Retrieved February 22, 2010.
- Piaget's Theory of Cognitive Development
- Cognitive development of a child
- Only one-third of adults can reason formally
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