The contribution of Jean Piaget to constructivist learning theory was well stated by von Glasersfeld’s (1995)when he said, “Although I do not continually cite Piaget, I sincerely hope one realizes that almost everything I write herein can be written only because Piaget spent some 60 years establishing the basis for a dynamic constructivist theory of knowing” (p. 6).
In learning theory and learning psychology textbooks, most accounts of Piaget’s theory summarize four stages of development—sensorimotor, preoperational, concrete operational, and formal operational—but fail to even mention the six sub stages of which the sensorimotor period is comprised. This is unfortunate since the core substance of Piaget’s ideas regarding the mechanism and progression of development are revealed and developed in his description of these six sub stages (Piaget, 1963). One notable exception, is Brainerd’s undergraduate textbook entitled, Piaget’s Theory of Intelligence (1978), the entire content of which is devoted to a synopsis of Piaget’s theory.
From Piaget’s own writings I found two texts to be particularly useful in my search for local principles of learning: The Origins of Intelligence in Children (Piaget, 1963) and The Psychology of the Child (Piaget & Inhelder, 1969). The first is among Piaget’s earlier writings, originally published in French as La Naissance de l’Intelligence Chez l’Enfant (Piaget, 1936), and is Piaget’s most complete and detailed exposition of the six sub stages of the sensorimotor period. It is filled with quotations from Piaget’s original observations of children, which are cited as evidence of his conclusions about the mechanism of progression and the state of development at various ages and stages in the child’s development. The second text, The Psychology of the Child (Piaget & Inhelder, 1969), is intended as a synthesis of previous publications by Piaget up to that point (p. v). It summarizes both the sensorimotor period with its six sub stages and also the preoperational, concrete operational, and formal operational periods of development. These two books were selected as the main sources for studying the ideas of Jean Piaget, and the following summary is based on the content of these two books.
According to Piaget (Piaget & Inhelder, 1969), development occurs as a succession of three great periods:
The mental development of the child appears as a succession of three great periods. Each of these extends the preceding period, reconstructs it on a new level, and later surpasses it to an ever greater degree. This is true even of the first period. (p. 152)
During the first great period (sensorimotor ) “the evolution of the sensorimotor schemes extends and surpasses the evolution of the organic structures which takes place during embryogenesis” (p. 152). During the second great period (comprising both preoperational and concrete operational), “semiotic relations, thought, and interpersonal connections internalize these schemes of action by reconstructing them on the new level of representation, and surpass them until all the concrete operations and cooperative structures have been established” (p. 152). Finally, in the third great period (formal, preadolescent operational) “nascent formal thought restructures the concrete operations by subordinating them to new structures whose development will continue throughout adolescence and all of later life (along with many other transformations as well)” (pp. 152-153).
Piaget did not see the progression from one period to the next as abrupt or discontinuous, but rather as a very smooth transition from spontaneous movements and reflexes to acquired habits, and from acquired habits to intelligence:
What one actually finds is a remarkably smooth succession of stages, each marking a new advance, until the moment when the acquired behavior presents characteristics that one or another psychologist recognizes as those of “intelligence”…There is a continuous progression from spontaneous movements and reflexes to acquired habits and from the latter to intelligence. (Piaget & Inhelder, 1969, p. 5)
Perhaps in response to Bruner’s criticism that he was “deeply concerned with the nature of knowledge” and “less interested in the processes that make growth possible” (J. S. Bruner, 1966a, p. 7) Piaget and Inhelder (1969) emphasized that “the real problem is not to locate the first appearance of intelligence but rather to understand the mechanism of this progression” (p. 5). This mechanism, he described as one of assimilation (the fitting of new information into existing schemes) and accommodation (the creation of new schemes to organize information that cannot be assimilated into existing schemes):
The organizing activity of the subject must be considered just as important as the connections inherent in the external stimuli, for the subject becomes aware of these connections only to the degree that he can assimilate them by means of his existing structures….that is to say, the input, the stimulus, is filtered through a structure that consists of the action-schemes (or at a higher level, the operations of thought), which in turn are modified and enriched when the subject’s behavioral repertoire is accommodated to the demands of reality. The filtering or modification of the input is called assimilation; the modification of internal schemes to fit reality is called accommodation. (Piaget & Inhelder, 1969, pp. 5-6)
Through assimilation “reality data are treated or modified in such a way as to become incorporated” and “every newly established connection is integrated into an existing schematism” (Piaget & Inhelder, 1969, p. 5). In other words, through assimilation the data of life’s experiences become part of our mental framework:
Intelligence is assimilation to the extent that it incorporates all the given data of experience within its framework. Whether it is a question of thought which, due to judgment, brings the new into the known and thus reduces the universe to its own terms or whether it is a question of sensorimotor intelligence which also structures things perceived by bringing them into its schemata, in every case intellectual adaptation involves an element of assimilation, that is to say, of structuring through incorporation of external reality into forms due to the subject’s activity. (Piaget, 1963, p. 6)
The process of assimilation is intertwined with a second process, that of accommodation:
There can be no doubt either, that mental life is also accommodation to the environment. Assimilation can never be pure because by incorporating new elements into its earlier schemata the intelligence constantly modifies the latter in order to adjust them to new elements. Conversely, things are never known by themselves, since this work of accommodation is only possible as a function of the inverse process of assimilation. We shall thus see how the very concept of the object is far from being innate and necessitates a construction which is simultaneously assimilatory and accommodating. (Piaget, 1963, pp. 6-7)
In other words, accommodation is the process of adapting oneself to the universe by constructing schemata to fit reality data. Assimilation, on the other hand, is the process of adapting the universe to oneself by interpreting reality data in terms of one’s pre-established schemata. The balance between the two is controlled by a self-regulating function of equilibration:
An internal mechanism (though it cannot be reduced to heredity alone and has no preestablished plan, since there is in fact construction) is observable at the time of each partial construction and each transition from one stage to the next. It is a process of equilibrium, not in the sense of a simple balance of forces, as in mechanics, or an increase of entropy, as in thermodynamics, but in the sense—which has now been brought out so clearly by cybernetics—of self-regulation; that is, a series of active compensations on the part of the subject in response to external disturbances and an adjustment that is both retroactive (loop systems or feedbacks) and anticipatory, constituting a permanent system of compensations. (Piaget & Inhelder, 1969, p .157)
In Play, Dreams and Imitation in Childhood Piaget (1962) described this equilibrium in the child as a balance between imitation and play:
If every act of intelligence is an equilibrium between assimilation and accommodation, while imitation is a continuation of accommodation for its own sake, it may be said conversely that play is essentially assimilation, or the primacy of assimilation over accommodation. (p. 87)
This balance is necessary not only for the intellectual development of the child, but also to satisfy his affective needs:
Obliged to adapt himself constantly to a social world of elders whose interests and rules remain external to him, and to a physical world which he understands only slightly, the child does not succeed as we adults do in satisfying the affective and even intellectual needs of his personality through these adaptations. It is indispensible to his affective and intellectual equilibrium, therefore, that he have available to him an area of activity whose motivation is not adaptation to reality but, on the contrary, assimilation of reality to self, without coercions or sanctions. Such an area is play, which transforms reality by assimilation to the needs of the self, whereas imitation (when it constitutes an end in itself) is accommodation to external models. Intelligence constitutes an equilibration between assimilation and accommodation. (Piaget & Inhelder, 1969, pp. 57-58)
Sensory-motor intelligence is defined by the activities of assimilation and accommodation of which it is made:
Sensory-motor intelligence is, in our view, the development of an assimilating activity which tends to incorporate external objects in its schemas while at the same time accommodating the schemas to the external world. A stable equilibrium between assimilation and accommodation results in properly intelligent adaptation. (Piaget & Inhelder, 1969, p. 5)
Through assimilation and accommodation during the sensorimotor period, the initial cognitive substructures on which all subsequent intellectual development is based are established.
It is because the baby begins by constructing, in coordinating his actions, schemata such as those of the unchanging object, the fitting in of two or three dimensions, rotations, transpositions, and superpositions that he finally succeeds in organizing his “mental space” and, between preverbal intelligence and the beginnings of Euclidean spatial intuition, a series of “topological” intuitions are intercalated as manifested in drawing, stereognosis, the construction and assembling of objects, etc.; that is to say, in the areas of transition between the sensorimotor and the perceptual….It is primarily preverbal sensorimotor activity that is responsible for the construction of a series of perceptual schemata the importance of which in the subsequent structuring of thought cannot, without oversimplification, be denied….The sensorimotor substructure is necessary to the conceptual for the formation of the operational schema which are destined to function finally in a formal manner and thus to make language consistent with thought. (Piaget, 1963, Forward)
The six sub stages of which the sensorimotor period is comprised are (Piaget, 1963)
- The Use of Reflexes
- The First Acquired Adaptations and the Primary Circular Reaction
- The “Secondary Circular Reactions” and the Procedures to Make Interesting Sights Last
- The Coordination of the Secondary Schemata and Their Application to new Situations
- The “Tertiary Circular Reaction” and the “Discovery of New Means Through Active Experimentation”
- The Invention of New Means Through Mental Combinations
Piaget described mental growth as being connected to, and building upon physical growth:
Mental growth is inseparable from physical growth: the maturation of the nervous and endocrine systems, in particular, continues until the age of sixteen. This implies that in order to understand mental growth it is not enough to start with birth; there is an embryology of reflexes (E. Minkowski) dealing with the movements and responses of the fetus, and the preperceptive behavior of the fetus, for instance, is relevant to the study of the perception of tactilo-kinesthetic causality (Piaget & Inhelder, 1969, p. vii)
He also described mental development during the first several months of life as providing the foundation for all subsequent intellectual development:
Mental development during the first eighteen months of life is particularly important, for it is during this time that the child constructs all the cognitive substructures that will serve as a point of departure for his later perceptive and intellectual development, as well as a certain number of elementary affective reactions that will partly determine his subsequent affectivity. (Piaget & Inhelder, 1969, p. 3)
These cognitive structures he called action-schemes, which he defined as “the structure or organization of actions as they are transferred or generalized by repetition in similar or analogous circumstances” (Piaget & Inhelder, 1969, p. 4, footnote).
Development of action-schemes begins in stage one with repeated exercise of the reflex, by which “the reflex is consolidated and strengthened by virtue of its own functioning” (Piaget, 1963, p. 32). Such repeated exercise, he said, is the beginning of assimilation:
This need for repetition is only one aspect of a more general process which we can qualify as assimilation. The tendency of the reflex being to reproduce itself, it incorporates into itself every object capable of fulfilling the function of excitant. (p. 33)
This tendency toward repetition or, as Piaget called it, “cumulative repetition” (Piaget, 1963, p. 33) results in both generalized assimilation—e.g. “at nearly five months his hands will carry all objects to his mouth and he will end by using these behavior patterns to recognize bodies and even to compose the first form of space” (p. 35)—and in recognitory assimilation—e.g. distinguishing the nipple from other objects and rejecting the latter when trying to satisfy needs of hunger (p. 36). Thus, it is through repetitive use of the reflex, applied to different objects and in different circumstances that it is generalized, and through which recognition is acquired:
The reflex must be conceived as an organized totality whose nature it is to preserve itself by functioning and consequently to function sooner or later for its own sake (repetition) while incorporating into itself objects propitious to this functioning (generalized assimilation) and discerning situations necessary to certain special modes of its activity (motor recognition). (Piaget, 1963, p. 38)
In stage two “circular reactions” (Piaget, 1963, p. 49) appear. The circular reaction is “an acquired functional exercise which prolongs the reflex exercise and has the effect of fortifying and maintaining” (p. 66). Two examples are the systematic protrusion of the tongue and the sucking of the thumb or fingers:
Putting out the tongue and finger sucking thus constitute the first two examples of a behavior pattern which prolongs the functional use of the reflex (sucking-like movements), but with the acquisition of some element external to the hereditary mechanisms. The new use of the tongue seems to go beyond the simple reflex play involved in sucking. (Piaget, 1963, p. 55)
Also formed during stage two are a variety of sensorimotor associations—e.g. the “setting in motion of sucking by various signals: position, noises, optical signals, etc” (Piaget, 1963, p. 49)—and the coordination between sucking and vision. Piaget (1963) cites the following observation:
Three stages in the child’s behavior may be distinguished. The first stage comprises the first week: the nursling attempts to suck only when his lips are in contact with the breast or the bottle….The second stages extends from the second to the eighth or ninth week: the nursling seeks the breast as soon as he finds himself in situations which regularly precede the meal (dressing, diaper changing, a stretched-out position, etc.). Finally the third stage begins between 0;3 and 0;4 and can be recognized by the appearance of visual signals. It is enough that the child sees the bottle or the objects which remind him of the meal for him to open his mouth and cry. (p. 56)
Stage one, the use of reflexes, and stage two, the first acquired adaptations and the primary circular reaction, are categorized by Piaget as elementary sensorimotor adaptations. During these two stages, “by constantly renewing his acts through reproductive and generalizing assimilation, the child surpasses simple reflex use, discovers circular reaction and thus forms his first habits” (Piaget, 1963, p. 153). In contrast, stages three, four, five, and six he categorizes as intentional sensorimotor adaptations. In the descriptions that follow, we shall see why.
In stage three, Piaget describes a secondary circular reaction and procedures to make interesting sights last; beginning also to differentiate means from ends:
We can call the circular reactions of the second stage “primary.” Their character consists in simple organic movements centered on themselves (with or without intercoordination) and not destined to maintain a result produced in the external environment. So it is that the child grasps for the sake of grasping, sucking, or looking, but not yet in order to swing to and fro, to rub, or to reproduce sounds. Moreover the external objects upon which the subject acts are one with his action which is simple, the means being confused with the end. On the other hand, in the circular reactions which we shall call “secondary” and which characterize the present stage, the movements are centered on a result produced in the external environment and the sole aim of the action is to maintain this result; furthermore it is more complex, the means beginning to be differentiated from the end, at least after the event. (Piaget, 1963, p. 157)
And so it is that in stage three, rather than simple repeating of an action for the sake of repetition, the child begins to notice the results of his actions and to repeat actions in order to reproduce the result:
The simple example is doubtless that of the objects the child simply shakes as soon as he has grasped them. From this elementary schema, which is almost “primary,” the following is immediately derived: if the objects brandished produce a sound this is enough to make the child attempt to reproduce it. (Piaget, 1963, p. 166)
The child also begins to apply previously acquired schema, such as that of shaking the arm to produce a sound from an object held in the hand, as a generalized procedure, or means to prolong interesting events observed by the child from afar. From example,
He looks at a tin box placed on a cushion in front of him, too remote to be grasped. I drum on it for a moment in a rhythm which makes him laugh and then present my hand (at a distance of 2 cm from his, in front of him). He looks at it, but only for a moment, then turns toward the box; then he shakes his arm while staring at the box (then he draws himself up, strikes his coverlets, shakes his head, etc.; that is to say, he uses all the “procedures” at his disposition). He obviously waits for the phenomenon to recur (….)
It therefore seems apparent that the movement of shaking the arm, at first inserted in a circular schema of the whole, has been removed from its context to be used, more and more frequently, as a “procedure” to make any interesting spectacle last. (Piaget, 1963, p. 201)
Stage four is marked by the intentional coordination of schemata with one another into a single act, and their application to new situations. Piaget considers this the stage in which we see the appearance of “the first actually intelligent behavior patterns” (Piaget, 1963):
From the point of view of the functioning of intelligence this fourth stage marks considerable progress over the preceding one. The behavior patterns of the third stage, as we have seen, only consist in “circular reactions.” No doubt these reactions are related to the external environment and no longer only to the body itself. Moreover, we have called them “secondary” to distinguish them from the “primary” reactions. No doubt either that the activity of the secondary schemata can start whenever the child wishes to prolong any interesting phenomenon and no longer only the result in connection with which the schemata in question were constituted. But, as we have stated, that is only a simple generalization of schemata without elaboration of the special relations between each of them and the new goal to be reached. In short, reactions of the third stage therefore constitute the simple prolongation of the primary circular reactions; they own only to their complexity the fact of drawing, after the event, a distinction between transitive and final states, between means and ends. On the other hand, the behavior patterns of the fourth stage involve such a distinction from the very outset. The criterion of their appearance is, in effect, the intercoordination of the secondary schemata. Now, in order that two schemata, until then detached, may be coordinated with one another in a single act, the subject must aim to attain an end which is not directly within reach and to put to work, with this intention, the schemata thitherto related to other situations. Thereafter the action no longer functions by simple repetition but by subsuming under the principle schema a more or less long series of transitional schemata. Hence there exists simultaneously the distinction between the end and the means, and the intentional coordination of the schemata. The intelligent act is thus constituted, which does not limit itself merely to reproducing the interesting results, but to arriving at them due to new combinations. (pp. 210-211)
Piaget (1963) gave the following examples of intentional coordination of schemata:
- Obtaining items placed on the bassinet hood by pulling strings attached to the hood or in contact with the items themselves (pp. 213-216).
- Withdrawing material objects that intervene between the intention and the result—e.g. displacing the hand of the experimenter or a cushion in order to obtain an object such as a matchbox or watch first presented to the child then concealed behind the intervening object (pp. 216-222).
- Making use of intermediaries between the subject and the objective—e.g. using the hand of the experimenter or the child’s own feet to bring an object within reach (pp. 222-225).
From these examples we see the difference between (a) the primary circular reaction of stage two which “has no other end, in effect, than that of reproducing a result obtained earlier, or which has just been discovered by chance” (Piaget, 1963, p. 227); (b) the secondary circular reaction of stage three in which the “effect which is to be repeated is then posited in advance, as an end, and the child tries to rediscover the means which have just led him to it” which, “although intentional… is nevertheless the simple prolongation of an earlier effect” (p. 227); and (c) the coordination of secondary schemata and their application to new situations found in stage four:
In the present behavior patterns, the end is posited without having been attained beforehand, at least, not in the same situation. When the child tries to grasp his toys by pushing an obstacle away (Obs. 122-124), tries to act upon objects through the intermediary of someone’s else [sic] hand (Obs. 127-128), tries to shake a parrot from a distance (Obs. 129), these are projects which arise in the course of his action, in conformity, it is true, with his earlier circular reactions (the very nature of the end consequently does not differ from one behavior pattern to another), but in an actually new situation. (p. 227)
Stage five is marked by the appearance of a tertiary circular reaction in which the child “will not only submit to but even provoke new results instead of being satisfied merely to reproduce them once they have been revealed fortuitously” (Piaget, 1963, p. 266). This sensori-motor sub stage is one of experimentation and discovery:
These tertiary actions will lead the child to new complete acts of intelligence which we shall call “discovery of new means through active experimentation.” The acts of intelligence hitherto under study have only consisted in an application of familiar means (already acquired schemata) to new situations. But what will happen when the familiar means reveal themselves to be inadequate, in other words, when the intermediates between subject and object are not assimilable to the habitual schemata?…The subject will search on the spot for new means and will discover them precisely through tertiary reaction….The invention of new means through active experimentation…is to tertiary reaction what the “application of familiar means to new situations” is to secondary reaction: a combination or coordination of schemata in comparison to simple schemata. (p. 267)
As the child plays out his experiments, he somewhat systematically varies his movements:
The tertiary reaction brings several innovations. At first, even in repeating his movements to seek and find an interesting result, the child varies and gradates them. So it is that, when throwing objects from a distance or rolling them (Obs. 144 and 145), tilting up a box or making it slide (Obs. 146), etc., he drops these objects from increasingly high altitudes, places his finger on a certain part of the box or on another part, etc…the child does not know what will happen and he tries to ferret out new phenomena. (Piaget, 1963, pp. 273-274)
Stepping back to a view of a higher level, sensorimotor intelligence behavior patterns can be divided into two groups: (a) those which are “in some way imposed by the external environment” (Piaget, 1963, p. 321), and (b) those which are “due to the subject’s spontaneous intention” (p. 321). Behavior patterns, or simple action-schemes, of the first group are manifest in stages one and two of the sensorimotor period. The second group can be further divided into three distinct types. In stage four we saw the first: “application of familiar means to new situations” (p. 322), with the procedures to make interesting sights last of stage three being a precursor. In stage five we saw the second: “discovery of new means through active experimentation” (p. 322). In stage six we see the third type: “invention of new means through mental combination” (p. 322).
Stage six marks the end of the sensorimotor period, and the early stages of the pre-operational period. In this stage, the behavior patterns of the previous stages do not disappear, but they begin to be “completed by behavior patterns of a new type: “invention through deduction or mental combination” (pp. 331-356). Piaget referred to this as systematic intelligence, in which the behavior patterns are not only discovery, but also invention; not only sensorimotor groping, but also mental representation through signification:
The two essential questions raised by such behavior patterns in relation to the preceding ones are those of invention and representation. Henceforth there exists invention and no longer only discovery; there is, moreover, representation and no longer only sensorimotor groping. These two aspects of systematic intelligence are interdependent. To invent is to combine mental, that is to say, representative, schemata and, in order to become mental the sensorimotor schemata must be capable of intercombining in every way, that is to say, of being able to give rise to true inventions. (p. 341)
Piaget’s examples of invention through representation include cases such as his son, Laurent, “all at once” discovering “the use of the stick” (p. 333); the experience of his daughter, Lucienne, learning to use a stick very quickly through invention and representation, compared with her sister, Jacqueline, who learned it much more slowly through prolonged efforts of sensorimotor groping (p. 336); and an example in which a watch chain which was to be put into a small hole only 16 x 34 mm. Again, Lucienne solved the problem quickly through what Paiget counted to be means of invention, as compared to her sister who learned it more slowly through a “long apprenticeship” of sensorimotor experimentation (pp. 336- 337).
Thus, in moving from stages one through five into stage six, there is a “transition from directed gropings to invention, and from motor schema to representative schema” (p. 341). To establish continuity between these two apparent extremes, Piaget explained that although both are controlled by the same motor—i.e., the intellectual activity of assimilation and accommodation (p. 341)—the primary difference between them is the speed at which this motor operates;
It must be understood…that the contrast between directed groping and actual invention is primarily due to a difference in speed. The structuring activity of assimilation only operates step by step in the course of experimental groping, so that it is not immediately visible, and one is tempted to attribute the discoveries which result from it solely to fortuitous contact with external facts. In invention, on the contrary, it is so rapid that the structurization seems sudden. The structuring assimilatory activity thus once again passes unnoticed at first glance and one is tempted to consider the “structures” as organizing themselves. Thereafter the contrast between the empiricism of simple groping and the intelligence of deductive invention seems to be complete. But if one thinks about the role of intellectual activity peculiar to combined assimilation and accommodation, one perceives that this activity is neither absent from empirical groping nor useless to the structure of representations. On the contrary, it constitutes the real motor of both, and the primary difference between the two situations stems from the speed at which the motor goes, a speed slowed down in the first case by the obstacles on the road and accelerated in the second case by the training acquired. (Piaget, 1963, pp. 341-342)
From this we are to understand that the apparent, but not actual, conflict in the transition from discovery by empiricist groping of the first five stages to deductive invention in stage six is simply the spontaneous recombination of mental schemata, without dependence on sensorimotor experience:
In the present case…in which the question raised is addressed to a mind sufficiently furnished with already constructed schemata so that the reorganization of these schemata operates spontaneously, the structuring activity no longer needs always to depend on the actual data of perception and, in the interpretation of these data, can make a complex system of simply evoked schemata converge. Invention is nothing other than this rapid reorganization and representation amounts to this evocation, both thus extending the mechanisms at work in the ensemble of the preceding behavior patterns. (Piaget, 1963, pp. 342-343)
Piaget summarized the characteristics of the sixth stage by saying,
Thus may be seen the unity of the behavior patterns of the sixth stage: Mental combinations of schemata with possibility of deduction surpassing actual experimentation, invention, representative evocation by image symbols, so many characteristics marking the completion of sensorimotor intelligence and making it henceforth capable of entering the framework of language to be transformed, with the aid of the social group, into reflective intelligence. (p. 356)
As previously noted, stage six marks the end of the sensorimotor period, and the early stages of the pre-operational and succeeding periods. The order of succession of the four periods of development and the sub stages of the sensorimotor is constant, and although “the average ages at which they occur may vary with the individual, according to his degree of intelligence or with the social milieu,” (Piaget & Inhelder, 1969, p. 153) the general ages are as follows (pp. 93, 96, 130):
- Sensorimotor period – birth to 2 or 3 years (with the average age of the six sub stages being: Stage 1 – birth to 1 months, Stage 2 – 1 to 4 months, Stage 3 – 4 to 8 months, Stage 4 – 8 to 12 months, Stage 5 – 12 to 18 months, and Stage 6 – 18 to 24 months)
- Pre-operational period – 2 or 3 to 6 or 7 years
- Concrete operational period – 6 or 7 to 11 or 12
- Formal operational preadolescent period – 11 or 12 to 14 or 15
The pattern of development established in the six sub stages of the sensori-motor period—a process of assimilation and accommodation in equilibrium—continues through the remaining periods (pre-operational, concrete operational, and formal operational) with each progressive attainment building on the previous period. A description of each of the remaining periods will not be given since what is of primary interest to the present study—the process by which learning occurs—has already been quite thoroughly addressed.
 In the translated works of Piaget “period” and “stage” are used interchangeably.
 In reviewing Piaget’s own writings, I have noticed that although the number of stages is commonly accepted among educators to be four, Piaget himself (Piaget & Inhelder, 1969) seemed to be in some conflict as to whether the number should be three or four. On the one hand he noted the existence of a delay between the development of the semiotic function (just after the initial establishment of sensorimotor schemes between age 0 to 24 months) and the internalization of actions into operations (age 6 or 7). He felt this was proof that there is “another level” between the two which “is not merely transitional” (p. 93). However, on the other hand, in the same text he later referred to the mental development of the child as appearing in “a succession of three great periods” (p. 152), lumping what are commonly referred to as the pre-operational and the concrete-operational stages into one. Brainerd (1978, p. 95) called attention to this same discrepancy and cited additional references in which “the pre-operational stage is treated somewhat equivocally in Piaget’s own writings” but chose to treat the pre-operational and concrete-operational as two distinct stages in his own coverage of Piaget’s theory.
 It seems that Sternberg and Williams’ (2010, p. 39) classification of Piaget’s theory as discrete and discontinuous with “sharp gains at some points of development and virtually no gains” does not agree with Piaget’s own view of either continuity or attainment through the progression of stages.
 Note that the three stages mentioned in this citation are different from, and should not be confused with, Piaget’s six sub stages of the sensori-motor period.
 cf. Vygotsky’s example of the development of pointing, in which a previously “object-oriented movement…becomes a movement aimed at another person, a means of establishing relations” (Vygotsky, 1978, p. 56)
 When confronted with the same problem a year later Jacqueline solves the problem through invention rather than experimentation and discovery.
 Here Piaget mentions image symbols and a preparation for a framework of language. In order to maintain some semblance of brevity, and to avoid confusion and complexity in my review of his ideas, I have omitted discussion of the development of signs, signals and language. Let me briefly address this here. From the beginning, during stages one through three, although signifiers are present they are, in those stages, undifferentiated:
Although representation does not yet exist, the baby forms and uses significations, since every sensori-motor assimilation (including perceptual assimilations) already implies the attribution of a signification, of a meaning. Significations and consequently also a duality between “signified” (the schemes themselves with their content; that is, the action) and “signifiers” are already present. However, these “signifiers” remain perceptual and are not yet differentiated from the “signified.” This makes it impossible to talk about semiotic function at this level. An undifferentiated signifier is, in fact, as yet neither a “symbol” nor a “sign” (in the sense of verbal signs). It is by definition an “indicator” (including the “signals” occurring in conditioning, like the sound of the bell that announces food). An indicator is actually undifferentiated from its signified in that it constitutes an aspect of it (whiteness for milk), a part (the visible section for a semi-hidden object), a temporal antecedent (the door that opens for the arrival of Mama), a causal result (a stain), etc.
(Piaget & Inhelder, 1969, p. 52-53)
The first clear use of true, differentiated signs occurs during stage four (Piaget, 1963, p. 248):
We recall that to each of the preceding stages a particular type of signs and meanings corresponds. To the reflex stage corresponds a type of recognitions and of meanings immanent in the use of the reflex. The child recognizes whether he is sucking without an object, whether he is sucking a tegument or is really nursing. The primary circular reactions then engender a second type of signs, the “signals” acquired by insertion of a new perceptive element in the familiar schemata. Whether they are simple or derived from the coordination of heterogeneous schemata, the signals thus form part of the act which they set in motion in the manner of direct perception of the objective. So it is that a heard sound provokes the search for the corresponding image, etc. As we have seen, with the secondary reactions a third type of signs begins which are intermediate between the “signal” and the “sign,” that is to say, form the transition between the sign which simply releases the action and that which permits independent prevision of the act. For instance, when a child hears a bed creak and by this sign recognizes the presence of his mother who will be able to feed him (Obs. 108) he limits himself to inserting a new perception in the complex schemata coordinated with sucking and in that respect the sign is still only a “signal” but he is on the way to attributing to his mother an activity independent of himself and, to this extent, the prevision under consideration presages the true “sign.”
This decisive progress, which consists in bringing prevision to bear upon events independent of the action itself, is achieved during the fourth stage in correlation with the objectifying of the relations which characterize this stage in general. In other words, a fourth type of sign is now constituted which we shall call the actual “sign,” which permits the child to foresee, not only an event connected with his action, but also any event conceived as being independent and connected with the activity of the object.
By the sixth stage, and continuing on, five behavioral patterns appear “which imply the representative evocation of an object or event not present and which consequently presuppose the formation or use of differentiated signifiers” (Piaget & Inhelder, 1969, p. 53):
Deferred imitation – “imitation which starts after the disappearance of the model” (p. 53)
- Symbolic play – “the game of pretending, which is unknown at the sensori-motor level” (p. 53)
- Drawing or graphic image (p. 54)
- Mental image – “no trace of which is observed on the sensori-motor level” but “it appears as an internalized imitation,” for example, “pointing to the sloping path [grandpa] took when he left” (p. 54)
- Verbal evocation of events that are not occurring in real time – “When the little girl says ‘meow’ after the cat has disappeared, verbal representation is added to imitation” (p. 54)
 Not also in this quote Piaget’s attribution to the role of the “social group” in transforming previously acquired intelligence, through language, into what he calls “reflective intelligence.”
 The reader interested in learning more is referred to Brainerd (1978), which contains a thorough accounting of which of Piaget’s publications concern which periods of development, an excellent summary of each period, and a review of relevant research.