Theory of cognitive development

# Overview
The Theory of Cognitive Development, one of the most historically influential theories was developed by Jean Piaget, a Swiss Philosopher (18961980). His genetic epistemological theory provided many central concepts in the field of developmental psychology and concerned the growth of intelligence, which for Piaget, meant the ability to more accurately represent the world and perform logical operations on representations of concepts grounded in interactions with the world. The theory concerns the emergence and construction of schemata  schemes of how one perceives the world  in "developmental stages", times when children are acquiring new ways of mentally representing information. The theory is considered "constructivist", meaning that, unlike nativist theories (which describe cognitive development as the unfolding of innate knowledge and abilities) or empiricist theories (which describe cognitive development as the gradual acquisition of knowledge through experience), it asserts that we construct our cognitive abilities through self-motivated action in the world. For his development of the theory, Piaget was awarded the Erasmus Prize.
Piaget divided schemes that children use to understand the world through four main periods, roughly correlated with and becoming increasingly sophisticated with age:
- Sensorimotor period (years 02)
- Preoperational period (years 27)
- Concrete operational period (years 711)
- Formal operational period (years 11 and up)

# Piaget's four stages

## Sensorimotor period
Infants are born with a set of congenital reflexes that allow them to float in the heavily dense world, according to Piaget, in addition to a drive to explore their world.   Their initial schemas are formed through differentiation of the congenital reflexes. 
The sensorimotor period is the first of the four periods. According to Piaget, this stage marks the development of essential spatial abilities and understanding of the world in six sub-stages:
- The first sub-stage, known as the reflex schema stage, occurs from birth to one month and is associated primarily with the development of reflexes.
- The second sub-stage, primary circular reaction phase, occurs from one month to four months and is associated primarily with the development of habits.
- The third sub-stage, the secondary circular reactions phase, occurs from four to eight months and is associated primarily with the development of coordination between vision and prehension.
- The fourth sub-stage; called the co-ordination of secondary course round modest circular reactions stage, which occurs from eight to twelve months, is when Piaget (1954) thought that object permanence developed.
- The fifth sub-stage; the tertiary circular reactions phase, occurs from twelve to eighteen months. New means through active experimentation and creativity in the actions of the "little scientist".
- The sixth sub-stage, considered "beginnings of symbolic representation", from eighteen months to twenty four months. New means through mental combinations considering before doing provides the child with new ways of achieving a goal without resorting to trial-and-error experiments.

## Preoperational stage
The Preoperational 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 in Piagetian theory 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 and words, in other words they learn to use symbolic thinking. Thinking is still egocentric: The child has difficulty taking the viewpoint of others.
The child can classify objects by a single feature: e.g. groups together all the red blocks regardless     of shape or all the square blocks regardless of color. According to Piaget, the Pre-Operational stage of development follows the Sensorimotor stage and occurs between 26 years of age.  In this stage, children develop their language skills.  They begin representing things with words and images.  However, they still use intuitive rather than logical reasoning.  At the beginning of this stage, they tend to be egocentric, that is, they are not aware that other people do not think, know and perceive the same as them. Children have highly imaginative minds at this time and actually assign emotions to inanimate objects.  The theory of mind is also critical to this stage.
The Preoperational Stage can be further broken down into the Preconceptual Stage and the Intuitive Stage.
The Preconceptual stage (2-4 years) is marked by egocentric thinking and animistic thought. A child who displays animistic thought tends to assign living attributes to inanimate objects, for example that a glass would feel pain if it were broken.
The Intuitive(4-6 years) stage is when children start employing mental activities to solve problems and obtain goals but they are unaware of how they came to their conclusions. For example 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.
Piaget considered that children primarily learn through imitation and play throughout these first two stages, as they build up symbolic images through internalized activity.

## 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:
Seriationthe 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.
Classificationthe 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.
Decenteringwhere 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.
Reversibilitywhere 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 8, 84 will equal 4, the original quantity.
Conservationunderstanding that quantity, length or number of items is unrelated to the arrangement or appearance of the object or items. For instance, when a child is presented with two equally-sized, full cups they will be able to discern that if water is transferred to a pitcher it will conserve the quantity and be equal to the other filled cup.
Elimination of Egocentrismthe 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).

## 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 12 years of age (puberty) and continues into adulthood. It is characterized by acquisition of the ability to think abstractly, reason logically and draw conclusions from the information available. During this stage the young adult is able to understand such things as love, "shades of gray", logical proofs, and values. Lucidly, biological factors may be traced to this stage as it occurs during puberty (the time at which another period of neural pruning occurs), marking the entry to adulthood in Physiology, cognition, moral judgement (Kohlberg), Psychosexual development (Freud), and psychosocial development (Erikson).  Some two-thirds of people do not develop this form of reasoning fully enough that it becomes their normal mode for cognition, and so they remain, even as adults, concrete operational thinkers.

# General information regarding the stages
These four stages have been found to have the following characteristics:
- They apply to thought rather than children
- Although the timing may vary, the sequence of the stages does not.
- Universal (not culturally specific)
- Generalizable: the representational and logical operations available to the child should extend to all kinds of concepts and content knowledge
- Stages are logically organized wholes
- Hierarchical nature of stage sequences (each successive stage incorporates elements of previous stages, but is more differentiated and integrated)
- Stages represent qualitative differences in modes of thinking, not merely quantitative differences

# Stages reconsidered from a "Bottom-up" viewpoint:
In view of its complexity, Psychology-as-an-academic-study is still in a comparatively undeveloped form in which endless "hermeneutic" debates are often required when it comes to detail. That should not surprise us.  After all, Chemistry and Genetics have both been through that stage, and have since left it!
(1) Probably the key progress-step arises when we can get a clear understanding of what constitutes the building-blocks of the physical mechanisms. Piaget's "scheme"-concept is a good step in the right direction (just as Mendel's "gene"-concept was a useful half-solution)  but both these concepts are mere abstractions unless we can say something more concrete about them.
Piaget himself clearly toyed tentatively with the idea that his most basic schemes might be RNA, but confessed that biochemistry was beyond his competence (Piaget, 1967). This is documented in some detail by Traill (2005), who goes on to show that subsequent evidence does indeed support the RNA idea.  But even if RNA is not the answer, it seems that some such physical embodiment must eventually be found if Non-clinical Psychology is to follow the lead of Genetics and Chemistry.
(2) The next needed progress is probably to find some plausible way in which these building-blocks could be harnessed. In principle this could be done
experimentally, but that hardly seems possible for the current scheme-and-Psychology problem  at any rate not until the topic is taken seriously enough to attract a large budget.
The alternative is to build up a theoretical model (based on as much existing evidence and interdisciplinary knowledge as possible) and see what can be done to "re-design" mind-mechanisms, at least in principle  meanwhile giving due credit to Piaget's stages, equilibration, decalage, etc., along with info-tech, physics, and anything else deemed relevant.
One such attempt (though without reference to Piaget), was made by the eminent Medical-Cybernetician Ross Ashby (1903-1972) in
his book Design for a Brain (1952, espec. Chapter 7). The main point of interest here is that he postulated a system of hierarchical controls in which active units at level-n, would be controlled by those at level-(n+1)  which in turn might have their parameters re-set by level-(n+2)  and so on. Note (i) that he did actually build robot "tortoises" by this formula (alarming observers by their uncanny abilities), and that (ii) this has an apparently-significant resemblance to Piaget's stages. (iii) Ashby suggested that human-intelligence may be chiefly due to a "runaway" capability, with no hard limit on how many "n" levels there might be  whereas other animals would always have a greater-or-lesser limit, for some reason. The same might well be claimed for Piaget's stages, even if they are actually different.
(3) Ashby confessed to certain shortcomings of his model, notably the fact that he had to fine-tune its details himself, whereas a proper bio-model should have been self organizing. The theoretical aspects of this venture were later carried forward (whilst incorporating Piagetian aspects) by Traill (1978, 1999, 2005), who chose to label the Sensorimotor level (or its earliest substage) "M0L", with subsequent higher levels being called M1L, M2L, etc. (e.g. 1978, section C2.3)  which could sometimes be more convenient than Piaget's names: "Pre-operational" etc.

# 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).  However, more recent cognitive developmentalists have been much influenced by trends in cognitive science away from domain generality and towards domain specificity or modularity of mind, under which different cognitive faculties may be largely independent of one another and thus develop according to quite different time-tables.  In this vein, many current cognitive developmentalists argue 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 understand some basic principles of physics (e.g. that one object cannot pass through another) and human intention (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. Psychologist's such as Vygotsky thought differently to Piaget and suggested that language was more important that Piaget implied.

# Post Piagetian and Neo-Piagetian stages
There are four major changes to the number of stages and their definitions.  First and foremost, the half stages are now shown to be stages.  Pascual-Leone (1987? Please confirm)discovered this.  Almost all Post Piagetians accept this.(E.g. ... ?)
Second, postformal stages have been shown to exist.  Kurt Fischer suggested two, Michael Commons presents evidence for four postformal stages: the systematic, metasystematic, paradigmatic and cross paradigmatic. (Commons & Richards, 2003; Oliver, 2004).
Thirdly, Fischer has considered a stage suggested by Biggs and Biggs. It is a stage before the early preoperational.  Commons and Richards call this stage the sentential because organisms can sequence representations of concepts.
Fourthly Traill (1978, Section C5.4; 1999, Section 8.4) suggests that there may be pre-sensorimotor stages ("M1L", "M2L", ... ... )  evolved either prenatally in-the-womb and/or transmitted genetically, having been developed by the species and hence describable as "instincts". This is in the context of a search for a micro-physiological basis for human mental capacity.  Here then, we are trying to complete the picture of the extreme-lower levels of the hierarchy, whereas the other three cases above are more concerned with application to the higher levels dealing with education and related macro effects.
 For various reasons it had been concluded that those most-basic micro-elements for logic-related thinking must have essentially a 1D stringlike structure (probably ncRNA). If so, then even the known sensorimotor Piagetian-schemes seem to be too complex, too evolved. Hence the need to seek lower levels which could be seen as the building-blocks. (Traill 1976, 2005).

# Piagetian and post-Piagetian stage theories/heuristics
- Michael Barnes' stages of religious and scientific thinking
- Michael Lamport Commons' Model of Hierarchical Complexity
- 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 Raddings theory of the medieval intellectual development
- R.J. Robinson's stages of history and theory of the origins of intelligence
- Stafford Beer, a cybernetician and business-consultant, attempted to apply Ashby's principles to Companies and Government organizations. (e.g. Beer, 1972).