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Piaget's Equilibration Theory and the Young Gifted Child: A Balancing Act.



This article describes the value of Piaget's equilibration equilibration /equi·li·bra·tion/ (e-kwil?i-bra´shun) the achievement of a balance between opposing elements or forces.

occlusal equilibration
 theory for understanding characteristics of the young gifted child gifted child

Child naturally endowed with a high degree of general mental ability or extraordinary ability in a specific domain. Although the designation of giftedness is largely a matter of administrative convenience, the best indications of giftedness are often those
. Key elements of equilibration theory are discussed. Differences in the equilibration patterns in gifted children are described and application of equilibration to other than cognitive systems is considered. The article concludes with some ideas for teachers and parents to help gifted young children search for equilibrium.

Although Piagetian theory focuses on universal child development, it can still illuminate important characteristics of intellectually gifted children whose abilities mark them as different. Feldman (1982) suggested that Piagetian notions of stage, interaction, and transitions could become building blocks for a developmental framework for understanding giftedness. He admitted, however, that "looking for Looking for

In the context of general equities, this describing a buy interest in which a dealer is asked to offer stock, often involving a capital commitment. Antithesis of in touch with.
 ideas about giftedness [in Piaget's work] is a little like looking for ideas about God from an atheist ATHEIST. One who denies the existence of God.
     2. As atheists have not any religion that can bind their consciences to speak the truth, they are excluded from being witnesses. Bull. N. P. 292; 1 Atk. 40; Gilb. Ev. 129; 1 Phil. Ev. 19. See also, Co. Litt. 6 b.
" (Feldman, 1982, p. 33), because Piaget did not seek unique achievement. Rather, Piaget identified the four familiar universal stages of development in which children understand the world differently.

Sensorimotor sensorimotor /sen·so·ri·mo·tor/ (sen?sor-e-mo´ter) both sensory and motor.

sen·so·ri·mo·tor
adj.
Of, relating to, or combining the functions of the sensory and motor activities.
 Stage (Birth to about 2 years): Infants think and understand the world around them through their senses using their eyes, ears, mouth, and hands. At this level, infants develop their abilities from coordination of sensation and their physical movements and actions in the environment.

Pre-Operational Stage (about 2 to 7 years): Preschool children begin to represent the world with symbols. Children at this stage have increased capacity for symbolic thinking and can go beyond their earlier sensorimotor discoveries through the use of language and images. However, their thinking is not yet logical.

Concrete-Operational Stage (about 7 to 11 years): Children can think logically and are able to conserve, seriate se·ri·ate  
adj.
Arranged or occurring in a series or in rows.



seri·ate
, classify and organize events or objects into different classes or sets. They can decenter decenter /de·cen·ter/ (-sen´ter) in optics, to design or make a lens such that the visual axis does not pass through the optical center of the lens.  and thus recognize others' points of views. However, they are not yet able to think abstractly.

Formal Operational Stage (about 11 to adult): Adolescents think in more logical and abstract ways. They can reason with symbols that are beyond the world of concrete experiences. They can imagine many possible combinations, separate real from the possible, deal with hypothetical propositions, and combine elements in a systematic way.

Although there are numerous studies conducted on Piaget's theory and stage development of gifted children, most were done between the late 1960's and mid 1980's, with a handful of studies following. General findings seem to agree that there is faster or different movement within a stage among intellectually gifted children than typically developing children, but mixed findings on earlier transition between stages.

Bear (1983), Billow (1975), Brekke, Johnson, Williams Johnson, William (1771–1834) Supreme Court justice; born in Charleston, S.C. He served in the South Carolina legislature (1794–98) and the state's high court (1798–1804) before President Jefferson named him to the U.S. , and Morrison (1976), Brown (1978), DeVries (1974), Feldman (1991), Kelly and Witters (1981), Roberts (1981), Roeper and Sigel (1966), Tan-Willams and Guttridge (1981), and Webb (1974) all found that gifted children do not generally enter a higher stage of development (either on traditional Piagetian tasks or in specific areas such as moral development, humor humor, according to ancient theory, any of four bodily fluids that determined man's health and temperament. Hippocrates postulated that an imbalance among the humors (blood, phlegm, black bile, and yellow bile) resulted in pain and disease, and that good health was , social development or analogical an·a·log·i·cal  
adj.
Of, expressing, composed of, or based on an analogy: the analogical use of a metaphor.



an
 reasoning) much earlier than their typically-developing peers, though the quality or breadth of ability within stage is evident. Webb suggested that it is the speed with which the structures are applied to subtle or difficult problems within a stage that is a function of intelligence. He found no evidence of consistent formal operational reasoning in the gifted before age 11. DeVries stated that the gifted child may be somewhat more advanced in a particular area of reasoning. Feldman's study of prodigies found that although there was extraordinary advancement in a particular domain, such as music, chess playing, or mathematics, these children did not demonstrate advanced development in the universal stages.

On the other hand, Carter and Ormrod (1982), Devall (1982), Goldschmid (1967), Goodnow and Bethon (1966), Hix (1990), Horworth (1981), Keating (1976), Lempers, Block, Scott, and Draper (1987), Rader (1976), Rosenfeld and Houtz (1978), and Verizzo (1970), found evidence of stage advancement in intellectually gifted children. However, training effects, the confounding confounding

when the effects of two, or more, processes on results cannot be separated, the results are said to be confounded, a cause of bias in disease studies.


confounding factor
 of rapid movement within stage with transition to the next stage, and different stages studied are factors which may have influenced the findings. Carter's (1985) research on a large sample of gifted young people found that stage advancement is at best two years ahead of typically-developing peers. Comparisons of moderate and highly gifted students (Bekey & Michael, 1987) found no significant difference between groups, although both groups were able to successfully perform at least one formal operations task by age 9 or 10. In the case of formal operations, domain specificity Domain-specificity is a theoretical position in cognitive science (especially modern cognitive development) that argues that many aspects of cognition are supported by specialized, presumably evolutionarily specified, learning devices.  appears to be a factor in studies reported by Berninger and Yates (1993), Keating (1991), and Marini and Case (1994), wherein transitions occurred within but not across preferred domains.

Stepping out of the stage advancement argument, Roberts (1981) presented the clearest evidence thus far. In a longitudinal conservation study on bright and average four to six year olds, she found that although gifted children did not conserve significantly earlier than their typically-developing peers, once they made the initial leap, they conserved across domains on conservation tasks very rapidly, a difference in equilibration. Roberts said it is unlikely that even a highly gifted child will be using extensive concrete operational thinking before age five, the earliest age described for typical onset of this stage, probably because certain neurological neurological, neurologic

pertaining to or emanating from the nervous system or from neurology.


neurological assessment
evaluation of the health status of a patient with a nervous system disorder or dysfunction.
 development must occur to support this new level of thinking.

Piaget's Theory of Equilibration

Less research has applied Piaget's equilibration theory to understanding giftedness with the exception of studies by Roberts (1981) and Heller (1979). However, this aspect of his theory can explain many qualities of intellectual giftedness “Gifted” redirects here. For other uses, see Gift (disambiguation).
Intellectual giftedness is an intellectual ability significantly higher than average.
. Piaget's equilibration theory states that when individuals encounter something new or foreign to their structures for understanding, an imbalance is created that requires restoring the balance, or re-equilibration. This process involves assimilating the new element by bringing it into the structure and simultaneously accommodating or modifying the learning structure to deal with the new aspects. For example, if one is familiar with gifted education Gifted education is a broad term for special practices, procedures and theories used in the education of children who have been identified as gifted or talented. Programs providing such education are sometimes called Gifted and Talented Education (GATE) or  but has not studied Piaget's theory, to fully comprehend the relationship between the two requires bringing Piaget's theory into one's gifted education structure (assimilation), then changing the gifted education structure to relate Piaget's theory to it, thereby creating a new and enriched understanding (accommodation). To better understand the differences in equilibration between the intellectually gifted and typically developing peers, Piaget's theory of equilibration is explained.

For Piaget, there are four factors that determine cognitive growth: maturation maturation /mat·u·ra·tion/ (mach-u-ra´shun)
1. the process of becoming mature.

2. attainment of emotional and intellectual maturity.

3.
 of the nervous system; social interactions; experiences based on interactions with the physical environment; and equilibration (Piaget, 1977a). Equilibration is the major force in tying together these and other factors. It is a balancing or self-regulating process in which the individual must respond even to the simplest environmental stimulus. It must be acted upon physically or mentally to understand it. The individual returns to a state of balance through assimilation and accommodation, but at a higher level (Gallagher & Reid, 1981), as the "spiral of knowing" ever widens (Piaget, 1980) (See Figure 1).

[Figure 1 ILLUSTRATION OMITTED]

In the spiral of Figure 1, E and [E.sup.1] represent interactions in the physical and the social environment (factors b and c above), the envelope of the child's world. Vector a represents the stages of development typical of maturation over time. Vector b represents assimilation (out to in) and Vector c (language) Vector C - A variant of C from CMU(?), similar to ACTUS.  represents accommodation (from in to out). Spiral A is the internal constructive process of equilibration.

In this theory, growth in learning requires structural change and is brought about when children find aspects in the environment incompatible with their present schemes (the simplest level of structural organization). Contradictions, gaps, inconsistencies or conflicts to the schemes or subsystems (more complex level of knowledge organizations in which schemes have been combined) trigger structural changes by putting the child into a state of imbalance or disequilibrium disequilibrium /dis·equi·lib·ri·um/ (dis-e?kwi-lib´re-um) dysequilibrium.

linkage disequilibrium
. The search for balance is ongoing, likened by Piaget (1980) to the "ever-widening spiral of knowing" in which the seeds of the new disequilibrium are ever present. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently
, the more one learns, the more one knows how little one knows! Piaget (1977b) stated, "there is a continual search for a better equilibrium, an increase in the number of possible compositions and in the sense of a growth in coherence" (p. 12). There is always a tendency to go beyond to a better equilibrium "to successive processes of increasing equilibration broken up with non-balance" (Piaget, 1977a, p. 82). Thus, the individual continues to learn and grow over the lifespan.

Two psychological mechanisms, dual aspects of equilibration, are at work in learning and cognitive growth. They are adaptation and organization.

Adaptation

Adaptation is the fit or adjustment to the environment. When something doesn't fit the individual's existing learning structures, the person has to assimilate as·sim·i·late
v.
1. To consume and incorporate nutrients into the body after digestion.

2. To transform food into living tissue by the process of anabolism.
 the new objects, actions, ideas or events to those structures (a taking in aspect) and modify the structures to accommodate the new information (Furth, 1981). A simple example might be a two-year-old's concept of apples as red fruit. When given a granny smith or golden delicious, the child has to assimilate (take in) the idea of different colored apples and accommodate (change) her knowing structure about apples to include their varied colors. A bright child might also begin to apply the concept of different colored fruits and vegetables to other foods or even other categories. Unlike the typically-developing peer, this gifted two-year-old uses what Heller (1979) called wide active inference in which the stimulus is applied to a wide range of schemes, enriching and enlarging them, making them more permeable permeable /per·me·a·ble/ (per´me-ah-b'l) not impassable; pervious; permitting passage of a substance.

per·me·a·ble
adj.
That can be permeated or penetrated, especially by liquids or gases.
 to each other.

Organization

Organization, the structural aspect, is the rules or laws for connecting thoughts that allow thinking in ever more complex ways. These organizations of rules and principles are also called logical structures in which schemes are continually rearranged and combined to form a strongly interconnected cognitive system. For example, the first time one drives a car, there is a very simple scheme consisting of a rudimentary rudimentary /ru·di·men·ta·ry/ (roo?di-men´tah-re)
1. imperfectly developed.

2. vestigial.


ru·di·men·ta·ry
adj.
1.
 set of rules - the steering wheel turns the car and the brakes stop it. After some practice, one's driving structure accommodates (is modified by) other drivers, switching lanes, and traffic signals. Development of driving principles becomes more complete. These logical structures allow anticipation and planning for all possibilities, leading to ever higher levels of adaptation. Thus an experienced driver can handle slippery roads, heavy traffic and erratic drivers.

In bright children, Heller (1979) suggests that because schemes are enlarged and enriched, they search for stimuli that helps to complete the structure. For example, a gifted two and a-half-year-old who is passionately interested in dinosaurs, voraciously vo·ra·cious  
adj.
1. Consuming or eager to consume great amounts of food; ravenous.

2. Having or marked by an insatiable appetite for an activity or pursuit; greedy: a voracious reader.
 consumes every picture book, artifact A distortion in an image or sound caused by a limitation or malfunction in the hardware or software. Artifacts may or may not be easily detectable. Under intense inspection, one might find artifacts all the time, but a few pixels out of balance or a few milliseconds of abnormal sound , and museum experience on the topic and relates it to monsters and present day reptiles reptiles

terrestrial or aquatic vertebrates which breathe air through lungs and have a skin covering of horny scales. They are poikilothermic, oviparous or ovoviviparous, and, if they have legs they are short and constructed solely for crawling.
. Heller calls this generalized assimilation, in which the child applies his scheme to every stimulus. In addition, the schemes are more networked, linked through extended and permeable schemes and sub structures.

Relationship between Equilibration and Stage Growth

Adaptation through assimilation, accommodation and organization through the evolution of more advanced structures or stages are the way equilibration and stage growth are related (Furth, 1981). This relationship can be expressed by the formula in Figure 2.

[Figure 2 ILLUSTRATION OMITTED]

The relationship between adaptation and organization is complementary (note the dotted lines), as in the particle-wave relationship in quantum physics quantum physics
n. (used with a sing. verb)
The branch of physics that uses quantum theory to describe and predict the properties of a physical system.



quantum physics

See quantum mechanics.
. The focus can be on one or the other, but not both at the same time, although they occur simultaneously. The relationship between adaptation and organization is also reciprocal (two-way arrows), connected by the inseparable processes of assimilation (taking in) and accommodation (modifying the structures to deal with the new material). As the individual's mental structures become increasingly organized and principled prin·ci·pled  
adj.
Based on, marked by, or manifesting principle: a principled decision; a highly principled person.
, the ability to adapt successfully increases as well, but may also lead to certain imbalances. This is the hallmark of thought in young gifted children.

Types of Equilibration

According to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 Piaget (1977a), there are three types of equilibration. In order of complexity, they are simple equilibration, reciprocal equilibration, and equilibration of totalities.

Type 1: Simple Equilibration. Equilibration of object to scheme: for example, legos to a scheme of building things; or comb to teaching gifted children. Schemes are defined as organized patterns of thought and action; that is, the cognitive structures and behavior that allow the assimilation of new elements and thus help in adapting to the environment. Although Piaget considered schemes to be focused on action (such as grasping grasping

a similar equine neurosis to windsucking; the horse grasps a fixed object with its teeth, but does not swallow air.
, eating, and drawing), concepts can also be thought of as schemes.

Type 2: Reciprocal Equilibration. Equilibration between schemes which build sub-systems: for example, when the bright 4-year-old child cuts out a snowflake from folded paper and invents the idea of using it like a stencil stencil, cutout device of oiled or shellacked tough and resistant paper, thin metal, or other material used in applying paint, dye, or ink to reproduce its design or lettering upon a surface.  to color a design through the holes, she coordinates two schemes--cutting and coloring.

Type 3: Equilibrations of Totalities. Hierarchical equilibrations in which the totality TOTALITY. The whole sum or quantity.
     2. In making a tender, it is requisite that the totality of the sum due should be offered, together with the interest and costs. Vide Tender.
 is differentiated into parts and then the parts integrated back into the whole. This type, Piaget (1977b) considered "the secret of development and of the transition from one stage to the next" (p. 12); for example, the child moves from pre-operational to concrete operational reasoning by constructing the operations or rules of identity (the object is the same if nothing is added or taken away, i.e., when the ball of clay is transformed into a pancake pancake, thin, flat cake, made of batter and baked on a griddle or fried in a pan. Pancakes, probably the oldest form of bread, are known in different forms throughout the world. , if nothing is removed, it is the same amount of clay), reciprocity reciprocity

In international trade, the granting of mutual concessions on tariffs, quotas, or other commercial restrictions. Reciprocity implies that these concessions are neither intended nor expected to be generalized to other countries with which the contracting parties
 (a change in one aspect is compensated by change in another aspect, i.e., the pancake is wider and flatter), and reversibility re·vers·i·ble  
adj.
1. That can be reversed, as:
a. Finished so that either side can be used: a reversible fabric.

b.
 (can be returned to the original form, i.e., a clay pancake rolled pancake roll nrollito de primavera

pancake roll nrouleau m de printemps

pancake roll n
 back into a ball).

A file cabinet analogy might clarify these three levels. In Type 1, simple equilibration, a paper is put into a file folder and the folder is rearranged to accommodate the new paper. In Type 2, reciprocal equilibration, two file folders are recombined into a new folder or additional folders are created to deal with increasingly complex information. In Type 3, hierarchical equilibration of totalities, the entire file cabinet is reorganized re·or·gan·ize  
v. re·or·gan·ized, re·or·gan·iz·ing, re·or·gan·iz·es

v.tr.
To organize again or anew.

v.intr.
To undergo or effect changes in organization.
 with a new system to classify and integrate all the material. In typically-developing children, the cabinet gets organized and reorganized bit by bit. In gifted children, the organization of this "file cabinet" is quite different. Once the first few files are established, the rules or system for organizing the whole cabinet are developed at the same time files are being filled.

Roberts' Longitudinal Study longitudinal study

a chronological study in epidemiology which attempts to establish a relationship between an antecedent cause and a subsequent effect. See also cohort study.
 of Equlibration in the Conservations

Equilibration is normally a slow building up of principles that progress through the three types of equilibrations, from schemes connected into subsystems, coordinated into hierarchical, structured totalities marked by differentiation and integration (Piaget, 1977a). In average IQ children, rules or principles are derived from and applied to the specific and are not rapidly generalized. This is essentially a vertical, within scheme, movement. In Roberts' (1981) longitudinal study of equilibration, children of average IQ were found to "work forward a domain at a time, consolidating as they go" (p. 223) in conservation. Their schemes appear to be more resistant to coordination and integration into total systems. However, in intellectually gifted individuals, according to Roberts, after the initial interactions which are harbingers of stage advancement, the individual either:

* Moves extremely rapidly within that stage through sequential domains normally attained over span of years, or

* Moves somewhat differently through these sequential levels.

Roberts (1981) noted that "conservation growth proceeds in waves. It includes both forward growth in leaps and generalization gen·er·al·i·za·tion
n.
1. The act or an instance of generalizing.

2. A principle, a statement, or an idea having general application.
 at a more constant rate. Everyone reaches the end of the road as a conserver. But children of higher mental ability levels appear to get to the end point in a manner different from those who are less bright" (p. 205). She found that brighter children strike off into new conservation domains, showing growth across domains, but not generalizing as much within a domain on the most difficult problems. They have the general principle but cannot consistently apply it. This is more a horizontal movement. For example, unlike his typically developing peers, the bright five-year-old quickly agrees that when one of the two equivalent balls of clay is flattened flat·ten  
v. flat·tened, flat·ten·ing, flat·tens

v.tr.
1. To make flat or flatter.

2. To knock down; lay low: The boxer was flattened with one punch.
 into a pancake, there is the same amount of clay in both the ball and the pancake "because they are the same." One ball is rolled into a snake. Again, the child applies his rule reasoning and recognizes that the quantity of clay is the same. However, if one ball is made into seven little bears, the child says, "There is more clay in the bears because there are so many!" The child has lost the conservation because perception has overcome the reason. He is at the beta level of compensation (a concept that will be explained shortly) and is likely sensing some puzzlement puz·zle·ment  
n.
The state of being confused or baffled; perplexity.

Noun 1. puzzlement - confusion resulting from failure to understand
bafflement, befuddlement, bemusement, bewilderment, mystification, obfuscation
. This is often visible, with a wrinkled brow or an admission of not feeling sure. Related to puzzlement, it is important to understand moderate novelty.

Moderate Novelty

The individual will assimilate that which is moderately novel - where previous experiences provide a basis from which to construct and where inconsistencies with what is known are still found. In other words, the individual has already constructed mental structures that can deal with the new aspect. If an element is too foreign, it will be ignored. If it is already familiar, no learning will take place. For gifted children, something too unfamiliar may lead not only to ignoring but to feelings Of great frustration. For example, one gifted second grader burst into tears over a math problem about racquet ball because he never experienced the game due to his impoverished rural background. He became so frustrated frus·trate  
tr.v. frus·trat·ed, frus·trat·ing, frus·trates
1.
a. To prevent from accomplishing a purpose or fulfilling a desire; thwart:
 that he could not focus on the numeracy numeracy Mathematical literacy Neurology The ability to understand mathematical concepts, perform calculations and interpret and use statistical information. Cf Acalculia.  aspect. On the opposite hand, many gifted children are bored because there is nothing new to learn. Ignoring is one way of compensating.

Compensations

The internal structures are accommodated to moderate novelties by means of compensations, actions aimed at canceling or neutralizing the disturbances (Gallagher & Reid, 1981). Furth, (1981) defined a compensation as "an act that, in response to a knowledge disturbance, restores the disturbed balance" (p. 273). He stated that every equilibration involves both construction and compensation. The compensations needed to accommodate schemes require the balancing of negations (constructing what is not visible or present - what the object, idea, etc. is not) with the affirmations (what is visible, present, evident) in the object. To do this requires reversibility of thought, the ability to mentally undo an action. Young children do not construct negations very successfully. Thus, their equilibrations tend to be unstable as they focus instead on the affirmation or positive characteristics (Piaget, 1977a). However, if there is no disturbance or contradiction because the assimilation is habitual Regular or customary; usual.

A habitual drunkard, for example, is an individual who regularly becomes intoxicated as opposed to a person who drinks infrequently.
 and requires no compensation, no growth occurs (Furth, 1981). The levels of compensations are:

Alpha - The child does not deal with the inconsistency and distorts, denies or ignores it. No instruction can occur at this level until the child has integrated needed underlying structures and concepts in order to be aware of the inconsistency or contradiction. Example: The year old baby has not had enough experiences with zoo creatures and ignores most of the zoo animals. As previously described, a gifted child might feel stressed when faced with too great a contradiction.

Beta - The child attempts to deal with the inconsistency but can only deal with partial modifications (partial accommodation). The novel element is distorted to fit his or her present schemes. The child is in a state of unstable equilibrium See Stable equilibrium, under Stable.

See also: Unstable
. This is probably the optimal level for learning. Example: The same baby notices the black panther Black Panther
n.
A member of an organization of militant Black Americans.

Noun 1. Black Panther - a member of the Black Panthers political party
 and calls it "keecat," distorting the object to fit her scheme of cat, the kitty she crawls after.

Gamma - If the item is not inconsistent to the child's internal schemes, she or he has already made a mental reorganization and can integrate the disturbance easily (Piaget, 1977a; Gallagher & Reid, 1981). Example: Two years later, the child easily recognizes most of the zoo animals and can quickly grasp the idea of another group of animals when told that the orangutan orangutan (ōrăng`tăn), an ape, Pongo pygmaeus, found in swampy coastal forests of Borneo and Sumatra.  is not a monkey.

These types of compensations are central to understanding qualitative differences in the thinking of intellectually gifted children.

Equilibration and the Gifted Child

It appears that the intellectually gifted child is a pattern seeker and tries to construct the general principles that apply to all domains, following feedback from the first few encounters. At the same time these children deal with the specific contents of number and quantity, they begin to develop the three operations or principles for conservation. For example, Roberts (1981) cited the case of the six year old girl who told her, "I don't care
This page is about the music single. For the meaning relating to digital logic, see Don't-care (logic)


"Don't Care" is a 1994 (see 1994 in music) single by American death metal band Obituary.
 what stuff you show me. As long as you don't take anything away or add anything, it's going to be the same!"

Roberts (1981) found that the explanations given by both average and gifted children up to about age 7 were surprisingly low as to the abstraction of these rules of conservation, even for older children. She attributed this lack of complete verbal justification to either Flavell's (1971) notion that emergence of a concept takes place in several phases so that explanations given represent the status of conservation at a provided point, not the final operational form of the concept; or to Piaget's (1978) notion that the child can perform a task successfully before being able to give a verbal justification (success before understanding).

Even the bright six-year-old mentioned earlier was giving only an identity explanation, not all the justifications to Roberts. Although the child grasped one of the underlying operations for conservation, her rule construction was incomplete. At the same time, she had constructed a principle to apply across domains, quite different from merely a more rapid coordination from one domain to the next. In summary, intellectually gifted children construct their knowing structures somewhat differently from their more typically-developing peers. Prior to specific experiences with those areas normally conserved over a four to six year period, the gifted child anticipates the unknown and generalizes the broad application of the principle. Anticipatory schemes, via constructive generalizations, are formed before formal operational structures are begun, but even here, the initial interactions and neurological maturation have to occur before structures can fully develop. As Roberts (1981) noted, chronological age chron·o·log·i·cal age
n. Abbr. CA
The number of years a person has lived, used especially in psychometrics as a standard against which certain variables, such as behavior and intelligence, are measured.
 gives the advantage to the older child. IQ and mental age are "important only after transitions have been made; but even then [they are] always tempered ... by chronological age" (p.227).

Bent-Wick Menorah menorah

Multibranched candelabra used by Jews during the festival of Hanukkah. It holds nine candles (or has nine receptacles for oil). Eight of the candles stand for the eight days of Hanukkah—one is lit the first day, two the second, and so on.
 Metaphor

A "bent-wick menorah" metaphor illustrates the difference in the equilibration of intellectually gifted individuals on the conservations, a major achievement of the concrete operational stage (see Figure 3).

[Figure 3 ILLUSTRATION OMITTED]

Each candle in Figure 3 represents a specific scheme. The Shammes sham·mes  
n. pl. sham·mo·sim Judaism
1. A sexton in a synagogue.

2. The candle used to light the other eight candles of a Hanukkah menorah.
 ("keeper" candle that is used to light the others) represents neurological maturation. When two or more candles are lit, reciprocal equilibration is represented. When all candles are lit, equilibration of totalities occurs. On the first day of Hanukkah, one candle is lit (number is conserved and simple equilibration occurs through assimilation and accommodation). On the second day, the first and second candles are lit (the child continues to conserve number and conserves discontinuous discontinuous /dis·con·tin·u·ous/ (dis?kon-tin´u-us)
1. interrupted; intermittent; marked by breaks.

2. discrete; separate.

3. lacking logical order or coherence.
 quantity, perhaps with a reciprocal equilibration between them). On the third day, candles one, two and three are lit, and so forth, each successive candle representing greater interiorization, or rule reasoning towards the general.

For the gifted child, it is as though once candle number one was lit and burning brightly, all the other wicks were bent towards and caught flame from the first candle. It would be a better image if the candle flames could represent a base (interiorized construction) and the flame could travel along the base of the menorah and up each candle almost simultaneously. The idea is that the rule or principle is applied directly to each new situation without having to extract the rule for that particular scheme and coordinate it with prior conservations. It is working from the general to the specific instead of the specific to the general, typified in big picture thinking and pattern seeking.

Although this may appear to be a violation of Piaget's sequence, Roberts (1981) found that the order of conservations appeared pretty consistent, with clusters or clumpings for all groups. Sequence has not been denied. Rather, it is the principle behind the conservations that is involved. Thus, gifted children differ in universal development because they are pattern seekers, equilibrating somewhat differently, adapting more efficiently and earlier, and, by necessity, organizing the structures somewhat differently.

The Balancing Act: Gifted as More and Less Equilibrated

Karmiloff-Smith and Inhelder (1975) noted that when children have a theory in mind (right or wrong), they are more successful in solving problems. Children who seek the underlying principles after a few examples from content, differ from more typically-developing peers, not only in rapidity of construction, but in a differential organization. They begin hierarchical equilibrations, an ordering (differentiating) and putting into relationship (integrating) under the totality, almost at the same time they are developing schemes through simple equilibrations. The organization is both horizontal -- across schemes and subsystems -- and vertical, within specific domains. In mentally gifted children, there is simultaneous vertical scheme building through Type 1 simple equilibrations and horizontal construction of structures, Type 3 hierarchical equilibration of totalities (See Figure 4).

Figure 4

Differences in Conservation: The Gibed Are : Simultaneously More Equilibrated and Less Equilibrated
G
GA       G
GA       G              G              G
GA       G              G              G
GA       GA             G              G           G
GA       GA             G              G           G

Number   Discontinues   Discontinues   Substance   Length
         Quantity       Quantity

G
G             G
Perspective   Weight   Volume


Gifted=G, CA=5 years, MA=8 years Average=A, CA=5 years, MA=8 years

In figure 4, the equilibrations of gifted and average children of the same chronological age on the conservations are illustrated. While the average children, "A," equilibrate e·quil·i·brate  
v. e·quil·i·brat·ed, e·quil·i·brat·ing, e·quil·i·brates

v.intr.
To be in or bring about equilibrium.

v.tr.
To maintain in or bring into equilibrium.
 through most of the examples in the domain of number and begin to grasp discontinuous quantity, coordinating one scheme at a time, gifted children, "G," equilibrate across almost all the domains of conservation. The simultaneous process in equilibration of gifted children leads to greater possibilities for disequilibrium. Certainly, the totality is in no way completely constructed (all the shaded areas are not filled in). The children make mental leaps across domains but must fill in the equilibrations to support their principles or rules, or must change their rules to fit the stimuli assimilated. The partial movement to a deeper level leads to an ability to anticipate - to see a glimpse of possibilities before having fully developed structures to deal with them. Such children are, therefore, more equilibrated.

Returning to the concept of compensations, the typically-developing child (A) in Figure 4 is at the beta level only in conserving discontinuous quantity (say corn granules Granules
Small packets of reactive chemicals stored within cells.

Mentioned in: Allergic Rhinitis, Allergies
 in cups). This child is likely to use alpha compensations and ignore the contradictions in the other areas, as she has not begun to conserve in these domains and does not have the schemes to build upon. The intellectually gifted child (G), on the other hand, is conserving across the board, but unstably. She is functioning at the beta level and is ready for wrestling with a broad array of domains. This child is working with a theory in mind, the principle(s) of which she has extracted that help in anticipating possibilities and seeing patterns. Conservations are just one example, but the idea applies to other learning structures.

However, this partial accommodation at the level of the total system (in this case conservations across most domains at the simplest levels) makes for greater depths of disequilibrium, as the principles may not explain all the data. Gifted children grasp the general pattern but their understanding is unstable. This increases the possibility for more equilibrations and further enrichment of the schemes, subsystems and totalities. Because the child generalizes, she can anticipate possibilities (as did the 6 year old described earlier) and there is greater equilibrium and stability to the world. But because the rule does not always fit or can be overcome with perceptual miscues (so many little bears!), there is also greater disequilibrium-the child is paradoxically less equilibrated. This means the child anticipates possibilities, but is more disequilibrated when the rule does not fit--all the shaded spaces that trigger questions and quests in Figure 4.

To work out the discrepancies--to deal with things and events that do not fit one's theories - requires questioning, critical thinking, and interest pursuit. Interest helps to restore the equilibrium (Cohen cohen
 or kohen

(Hebrew: “priest”) Jewish priest descended from Zadok (a descendant of Aaron), priest at the First Temple of Jerusalem. The biblical priesthood was hereditary and male.
, 1989, 1998; Cohen & Gelbrich, in press). When young children are passionately interested in dinosaurs, bugs, volcanoes, or fairy tales This is a list of fairy tales, the dates of their earliest known printed version, the author and, if known, the collection of tales in which it was published. It should be noted, however, that not all stories listed below would be categorized as fairy tales by a strict definition , the question arises, "Why is this interest so important to them?" "What questions/problems/conflicts is the child trying to work out?" These likely relate to the child having an awareness of possibilities but many gaps that trigger a quest for Verb 1. quest for - go in search of or hunt for; "pursue a hobby"
quest after, go after, pursue

look for, search, seek - try to locate or discover, or try to establish the existence of; "The police are searching for clues"; "They are searching for the
 answers. For example, a kindergartner kin·der·gart·ner also kin·der·gar·ten·er  
n.
1. A child who attends kindergarten.

2. A teacher in a kindergarten.
 who learns about a thief at school becomes preoccupied with "bad guys" and becomes aware of the possibility of her vulnerability. She pursues this as an interest in learning about police, laws, locks, and block safe homes.

These differences in equilibration are at the base of some of the most cited characteristics of the young gifted child:

curiosity, the ability to abstract and to generalize generalize /gen·er·al·ize/ (-iz)
1. to spread throughout the body, as when local disease becomes systemic.

2. to form a general principle; to reason inductively.
, passionate interests, asynchrony asynchrony /asyn·chro·ny/
1. lack of synchronism; disturbance of coordination.

2. occurrence at distinct times of events normally synchronous; disturbance of coordination.asyn´chronous
, unending questions, absorption in tasks, concerns about the world and spiritual questions, and preference for complexity or novelty (Cohen, 1998; Gallagher, 1995; Piirto, 1999; Silverman, 1993; Smutny, Walker, & Meckstroth, 1997). It is this underlying questing, this curiosity to seek principles and patterns that apply to a vast array of particulars that both structurally and functionally explain these observable characteristics. It is a movement to more interiorized hierarchical equilibrations of totalities, while simultaneously, the child is constructing schemes.

Strategies for Teaching

Recognizing the paradoxical nature in the uneasy equilibrium of the gifted child, the teacher or parent can accept both the intense curiosity and need to find out when the child's rules fail, as well as the frustration of not being able to apply the rules consistently. Being able to anticipate possibilities means that the child may appear wise beyond her years. At the same time, there is the great possibility that this is an unstable wisdom, one that can be overthrown when the events are too complex to maintain the rule reasoning. Patience and kindness in understanding both mature leaps and more juvenile behaviors is paramount, as is accepting the feelings. Rather than saying, "Well I think the horse you drew is nice," acknowledge the child's frustration: "It must be hard to see in your mind what you want to draw and not have it come out the way you wanted." Suggest that she will be able to control the drawing more when her hands catch up to her mind; or offer her a book on drawing horses to help her find ways to become more successful.

With intellectually gifted children, the regular school program often finds the child at the gamma level, or worse, at a habitual level of compensation. Opportunity for mental growth is limited, because material is not sufficiently inconsistent to the child's structures. Giving the child more of the same, such as extra long division problems, does not require any compensations (probably past gamma--habitual level). On the other hand, it is also possible to forget the child's developmental level (perhaps due to high verbal skills) and to present material the child cannot yet deal with (alpha level). Self-selection of areas for study and research avoids these problems. The teacher or parent then can become aware of the contradictions or puzzlements in the problem selected by the child.

Teaching can focus on utilizing those inconsistencies or contradictions that trigger the equilibration process by helping the children find questions or problems of interest to them to explore, by providing inquiry training, and by utilizing questioning strategies that help them deal with the inconsistencies. Negative as well as positive aspects of objects or actions can be brought to the attention of the child (e.g., explain which are not members of the rodent rodent, member of the mammalian order Rodentia, characterized by front teeth adapted for gnawing and cheek teeth adapted for chewing. The Rodentia is by far the largest mammalian order; nearly half of all mammal species are rodents.  family; what do you think would not be an action taken by Lassie Lassie

canine star of popular film and TV series. [TV: Terrace, II, 13–15; Radio: Buxton, 135]

See : Dogs
?; draw the shapes seen between the branches instead of drawing the tree).

Finally, in Piaget's (1980) model of The Ever-Widening Spiral of Knowing, a temporary equilibrium or balance may be reached, but it is never on the same level as before. Rather, each equilibration moves the system to a higher level of knowing, always implying a new disequilibrium and the requirement for further re-equilibration. Therefore, each equilibrium is only short-lived, and there will always be a new question or conflict that throws it into disequilibrium. As the systems are repeatedly equilibrated, they expand, ever upward and outward, an open and dynamic system leading to a still more perfect equilibrium. This is the paradox -- achieving both a more perfect balance and yet having a greater possibility for imbalance and transformation (Cohen, 1995). When thinking of a spiral, it helps to recognize that every time one comes to a temporary equilibrium, there is not a perfect circle, but a little space where the spiral does not touch the next layer. This is where the questions and puzzlements arise. Asking the child, "When you were in kindergarten, could you write like you do now? Will you write like you do now when you are in sixth grade?" is a starting point Noun 1. starting point - earliest limiting point
terminus a quo

commencement, get-go, offset, outset, showtime, starting time, beginning, start, kickoff, first - the time at which something is supposed to begin; "they got an early start"; "she knew from the
 to get children to consider their changing skills. Finally, try using the statement, "I am where I am today. I was different yesterday, I will be different tomorrow. But I am where I am today, and it's OK" (Cohen, 1996, p. 16)!

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JEF Junge Europäische Föderalisten (German: Young European Federalists)
JEF Joint Educational Facilities, Inc.
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per·fection·ist adj. & n.
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New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
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Harvard College, originally for men, was founded in 1636 with a grant from the General Court of the Massachusetts Bay Colony.
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sense of humour, humor, humour
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out-of-the-box thinking
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LeoNora M. Cohen is an Associate Professor in the School of Education at Oregon State University Oregon State University, at Corvallis; land-grant and state supported; coeducational; chartered 1858 as Corvallis College, opened 1865. In 1868 it was designated Oregon's land-grant agricultural college and was taken over completely by the state in 1885. . During her 30 years work in the field she has authored over 50 books, chapters and articles on gifted education. Her interests are in conceptual and theoretical issues, children's interests, young children, thinking and metacognition Metacognition refers to thinking about cognition (memory, perception, calculation, association, etc.) itself or to think/reason about one's own thinking. Types of knowledge , coping strategies The German Freudian psychoanalyst Karen Horney defined four so-called coping strategies to define interpersonal relations, one describing psychologically healthy individuals, the others describing neurotic states. , and practical applications relative to gifted children. Younghee M. Kim is an Assistant Professor in the School of Education at Oregon State University. Her specialties are early childhood education, early intervention ear·ly intervention
n. Abbr. EI
A process of assessment and therapy provided to children, especially those younger than age 6, to facilitate normal cognitive and emotional development and to prevent developmental disability or delay.
, assessment of young children, and children with special needs including the gifted.

Manuscript submitted November, 1997.

Revision accepted December, 1998.
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Title Annotation:Jean Piaget
Author:Kim, Younghee M.
Publication:Roeper Review
Date:Feb 1, 1999
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