Repetition

This is perhaps the most intuitive principle of learning, traceable to ancient Egyptian and Chinese education, with records dating back to approximately 4,400 and 3,000 B.C., respectively (Aspinwall, 1912, pp. 1, 3).  In ancient Greece, Aristotle commented on the role of repetition in learning by saying “it is frequent repetition that produces a natural tendency” (Ross & Aristotle, 1906, p. 113) and “the more frequently two things are experienced together, the more likely it will be that the experience or recall of one will stimulate the recall of the other” (p. 35).

Through repeated pairing of a conditioned stimulus (or stimulus which is to be conditioned) and an unconditioned stimulus (i.e., a stimulus which naturally produces a reflex response) Pavlov was able to condition the reflex to be triggered by the conditioned stimulus (Pavlov et al., 1928, p. 23). Thorndike plotted learning curves showing that cats repeatedly placed in puzzle boxes were able to escape in less time and with fewer unproductive movements on subsequent trials (Thorndike, 1898). Watson extended the work of Pavlov and Thorndike to the experimental study of man (Watson, 1930, p. v) and called out repetition as one of two factors[1] which establish a habit (Watson, 1914, p. 271). In the course of repeated trials, Skinner was able to employ contingencies of reinforcement (Skinner, 1938) to sustain or produce a desired behavior. Through shaping[2] he was able to teach new behaviors that do not naturally occur (Peterson, 2004; Skinner, 1961e; Skinner, 1961f), and through vanishing[3] (Skinner, 1986, p. 107) he enabled the performance of behavior without the need for detailed cues to prompt its occurrence. Skinner also discovered that “a significant change in behavior is often obvious as the result of a single reinforcement” (1961g, p. 146):

My rats learned to press the lever in one trial, and no learning could be faster than that. (I noted, with a touch of regret, that because the change was so quick I could not record a learning curve. But “it should not be difficult,” I said, “with some suitable change in conditions, to retard the process.)” (Skinner, 1979, p. 89)

One explanation for why his rats learned to press the lever in one trial is that what they were actually learning was not how to press a lever, but rather the conditional relationship between pressing the lever and receiving food. Having already learned to use their paws for similar movements and in the employ of obtaining the objective of food, the incremental attainment required to learn the relation of the bar to the dispensing of food would be quite small. Skinner interpreted the one-trial learning result in basically the same way when he highlighted the dependency on prior learning of later reflexes in the chain before the final act of ‘pressing the lever and obtaining food’ could be learned in a single trial:

I may point out that the result depends upon the preliminary development of the later reflexes in the chain. It could not be obtained consistently when the total act of ‘pressing the lever and obtaining food’ is regarded as a unit and treated experimentally as such. If reinforcing power is not first given to the sound of the magazine through the establishment of a discrimination, a certain interval of time will elapse between response [pressing the food lever] and the stimulation from the food, and the effectiveness of the reinforcement will be severely reduced. In rare cases instantaneous conditioning may be observed, but the consistent result obtained in the present case will necessarily be lacking. (Skinner, 1938, pp. 71-72)

This explanation—which explains the need for repetition, at least in part, as a function of the size of attainment[4] to be made—is similar to Guthrie’s reconciliation between his theory of one trial learning and the obvious need for practice and repetition in most real-world learning tasks. Although his central premise was that “a stimulus pattern gains its full associative strength on the occasion of its first pairing with a response” (Guthrie, 1942, p. 30) he clearly and directly stated the importance of repetition in learning any skill:

In the psychology of learning we often confuse the effects of repetition on a single association of stimulus and response with the effects of practice on the development of skill, which is something quite different. In learning any skill, what must be acquired is not an association or any series of associations, but many thousands of associations that will connect specific movements with specific situations. One lesson or trial is all that is necessary to learn to depress the brake pedal on a car. Learning to drive the car requires a varied experience which will cause the pedal to be depressed in many situations and left severely alone in many others.” (Guthrie, 1942, p. 36)

Repetition was also at the core of Hull’s theory, showing up as variable N in his equation for habit strength. Habit strength referred to the strength of the association between a stimulus and a response. According to this equation, as the number of pairings between the two increases, habit strength increases. The mathematical formula that describes this relationship is as follows, where N represents the number of pairings between stimulus and response:

_SH_R= 1 – 10^{-0.0305 N}

This equation for habit strength was embedded as a key component of reaction potential, which was expressed as a function of both Habit Strength (_SH_R) and Drive (D):[5]

Reaction Potential = _SE_R = _SH_R x D

Repetition was critically important to Este’s stimulus sampling theory. In fact, the entire theory was founded on the assumption that through multiple trials in which (a) the successive sampling of active stimulus elements, and (b) the relative proportion of those elements conditioned to a desired response class R are carefully controlled, one can guarantee a response of type R, thereby associating all remaining elements in the stimulus sample which were not previously conditioned to R to become so (W. K. Estes, 1950).

The repeated stimulus-response pairing and multiple reinforced trials of behavioral learning theory is paralleled in cognitive learning theory by notions of repeated presentation, rehearsal, and review.  Ebbinghaus (1913) reported that frequent repetitions were necessary to both (a) get to the point where content could be reproduced from memory, and (b) prevent forgetting of the content once it had been learned:

Under ordinary circumstances, indeed, frequent repetitions are indispensable in order to make possible the reproduction of a given content. Vocabularies, discourses, and poems of any length cannot be learned by a single repetition even with the greatest concentration of attention on the part of an individual of very great ability. By a sufficient number of repetitions their final mastery is ensured, and by additional later reproductions gain in assurance and ease is secured. (p. 4)

Left to itself every mental content gradually loses its capacity for being revived, or at least suffers loss in this regard under the influence of time. Facts crammed at examination time soon vanish, if they were not sufficiently grounded by other study and later subjected to a sufficient review. But even a thing so early and deeply founded as one’s mother tongue is noticeably impaired if not used for several years. (p. 4)

Although Ebbinghaus worked according to carefully planned schedules of review in order to ascertain certain characteristics of acquisition and forgetting, in general learning, repetition need not be intentional. For example, incidental repetition was evident in Tolman’s studies of latent learning in which rats were allowed to freely explore during a “long series of preliminary training” in order to build up a cognitive map of the maze without reward of food (Tolman, 1938, p. 22; 1948, p. 194). Kohler’s accounts of chimpanzees engaged in learning through insight were characterized by a series of failed attempts, followed by a period of reflection, followed by sudden success (Kohler, 1951). The chimpanzees were not acting with intention to repeat a process, but a desire to obtain the goal objective banana. Repeated attempts naturally arose as they were unable to acquire their target on the first attempt and without the employment of some intermediary means which was to be discovered through insight.

Repetition, in the form of short term retention of information through maintenance rehearsal and long term encoding through elaborative rehearsal (Sternberg & Williams, 2010, p. 274), provided the keys to knowledge acquisition in the general model of cognitive information processing, based on the memory stores and memory processes proposed by Atkinson and Shiffrin (1968).

Ausubel’s theory of meaningful learning relied heavily and explicitly on repetition in several ways:

1. Perpetuation of dissociability: Without repetition “specific items of meaningful experience…tend gradually to undergo obliterative subsumption” (Ausubel, 1962, p. 218).
2. Discriminability: “Discriminability of new materials could be enhanced by repetition” (Ausubel, 1962, p. 219).
3. Clarity and stability: “The most immediate effect of practice is to increase the stability and clarity, and hence the dissociability strength, of the emergent new meanings in cognitive structure” (Ausubel et al., 1978, p. 311).
4. Transferability: Transfer can be facilitated through varied repetition by “providing opportunity for learning principles in as wide a variety of situations as possible, by explicitly emphasizing the similarity between training and criterial tasks and by presenting the latter tasks continuously or in close succession” (Ausubel et al., 1978, p. 200).
5. Criterial attributes: Criterial attributes of a concept are acquired by  “ (1) [exposure to a] heterogeneity of instances after consolidation in a more homogeneous setting; (2) appropriate blending and sequencing of positive and negative instances; and (3) the relevance of the presented or available information to the concept in question” (Ausubel et al., 1978, p. 87).
6. Consolidation: Consolidation of previously learned material “is achieved through confirmation, correction, clarification, differential practice, and review in the course of repeated exposure, with feedback, to learning material” (Ausubel et al., 1978, p. 197).

Ausubel also suggested that explicit instruction might replace or diminish the need for repetition[6] by the instructor “pointing out similarities and differences between [examples] and their presumed subsumers in cognitive structure” (Ausubel, 1962, p. 219). Additionally, he talked about a special type of repetition, in which multiple instances are presented simultaneously.[7] In such a case, the pattern of repetition is revealed not in multiple occurrences in time, but in the simultaneous comparison of variants of form:[8]

When an entire array of instances is simultaneously available to the learner rather than being presented successively, concept acquisition is significantly facilitated….This effect presumably reflects the avoidance of memory loss and the possibility of closer grouping during the process of abstracting the criterial attributes of a concept. (Ausubel et al., 1978, p. 114)

Repetition in schema theory is found in the elements that are “common to a large number of things or situations” (Anderson et al., 1978, p. 434). Schemata represent multiple instances of things that may be grouped based on a recurrent pattern of common features, functions, or characteristics. They are created, developed, tuned, and restructured through repeated experience (Rumelhart & Norman, 1976):

Learning through tuning…involves actual changes to the very categories we use for interpreting new information. Thus tuning involves more than merely an addition to our data base. Upon having developed a set of categories of interpretation (as you will see below, we call these schemata) these categories presumably undergo continual tuning or minor modification to bring them more in congruence with the functional demands placed on these categories… a young child learns that not all animals are ‘doggies.’ Slowly his ‘doggie’ schema becomes modified into congruence with the actual demands on his interpretation system. (Rumelhart & Norman, 1976, p. 4)

The role of repetition in constructive learning theory is in the similarities found when relating new experience to previous experience. “Deep understanding occurs when the presence of new information prompts the emergence or enhancement of cognitive structures that enable us to rethink our prior ideas” (Brooks & Brooks, 1993, p. 15). According to Piaget, development is the result of repeated patterns of exercise of the reflex (Piaget & Inhelder, 1969, p. 8), the circular reaction (Piaget, 1963, p. 66), the reuse of known schemes of assimilation employed in novel situations (Piaget & Inhelder, 1969, p. 10), the “gradual accommodation to external reality” through repeated use (Piaget, 1963, p. 29), and—in short—the “the tendency toward repetition of behavior patterns and toward the utilization of external objects in the framework of such repetition” (p. 42).

According to Bruner, it is only through “the exercise of problem solving and the effort of discovery that one learns the working heuristics of discovery”(J. S. Bruner, 1961, p. 31). “The more one has practice, the more likely is one to generalize what one has learned into a style of problem solving or inquiry that serves for any kind of task…or almost any kind of task” (p. 31). Bruner also believed that it was by “translating redundancy [in the environment] into a manipulable model” that the child is able “to go beyond the information before him” (J. S. Bruner, 1964, p. 13). The importance of repetition to Bruner’s concept of learning was particularly clear in his description of the spiral curriculum which, he said, “as it develops [revisits] basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them” (J. S. Bruner, 1960, p. 13).

Bruner’s concept of the spiral curriculum builds on Vygotsky’s ideas. According to Vygotsky, “through repeated experiences…children learn covertly (mentally) to plan their activities” (Vygotsky, 1978, p. 29). Such repeated experience he said, “proceeds here not in a circle but in a spiral, passing through the same point at each new revolution while advancing to a higher level” (p. 56). Through repetition the need for sign-mediated association “becomes no longer necessary” (Vygotsky, 1994b, p. 66) and the process of internalization takes place (this process of internalization is exemplified in the experiments with pictures described in Luria, 1994, pp. 53-55; and Vygotsky, 1994b, pp. 64-66).

Although Bandura (1965) referred to his “nonresponse acquisition procedure” (p. 3) as “no-trial learning” (p. 3) since “a subject simply observes a model’s behavior but otherwise performs no overt instrumental responses, nor is administered any stimuli during the period of acquisition” (p. 3) he also noted that “as will be shown later, [the observer] may require multiple observational trials in order to reproduce the modeled stimuli accurately” (p. 3). Bandura also stated that “the behavior repertoires which constitute an enduring part of a culture are to a large extent transmitted on the basis of repeated observation of behavior by social models” (Bandura, 1965, p. 48) and that “the people with whom one regularly associates, either through preference or imposition, delimit the types of behavior that will be repeatedly observed and hence learned most thoroughly” (Bandura, 1977b, p. 24). In addition to repeated exposure to observational models, repetition also plays a role in the self-corrective adjustment process of refining newly acquired behaviors:

In most everyday learning, people usually achieve a close approximation of the new behavior by modeling, and they refine it through self-corrective adjustments on the basis of informative feedback from performance and from focused demonstrations of segments that have been only partially learned. (Bandura, 1977b, p. 28)

Heider (1958) spoke of the perception of patterns defined “spatially or temporally” (p. 58). He noted that it seems to be “approximately true that the smaller the part of the pattern taken into account, the more ambiguous it is” (p. 58), thus implying that increased exposure to the pattern brings greater clarity, and in the case of attribution theory, promotes more accurate attribution to appropriate causal factors. Self-efficacy and self-worth are likewise built up through progressively independent and varied circumstances that give induction a chance to operate and “strengthen and generalize expectations of personal efficacy” (Bandura, 1977a, p. 202). Zimmerman (1998, pp. 2-3) described learning in terms of self-regulated learning cycle phases consisting of three repeating stages: forethought, performance, and self-reflection.

In situated learning research Lave (1988) found that participants in her studies often made multiple attempts before solving problems. In the process they checked their partial or interim solutions to see if they were consistent with reality and if they were likely to reach a satisfactory answer using their chosen method. Repetition in activity theory is in the form of cycles of expansive learning (Engestrom, 2001, p. 152; Engestrom, 2009, p. 70; Engestrom, 2010, pp. 7-8). And in cognitive apprenticeship repetition coupled with a sequence of increasingly complex tasks is an important characteristic of practice (A. Collins et al., 1991, pp. 15-16). Table 2 summarizes the local principles from the theories reviewed that are subsumed by the universal principle of repetition.

Table 2

Principles of Learning Subsumed by the Universal Principle of Repetition

Theory Group		Local principles
Behavioral		Aristotle: Frequent repetition produces a natural tendency Law of frequency Exercise strengthens the memory of an image Thorndike: Law of exercise Repetition alone does not produce learning Pavlov: Association through repeated pairing of CS and UCS Watson: Frequency (repetition) is one of two principles that produce learning Skinner: Multiple trials for initial conditioning to approach food tray Significant change in behavior after a single reinforcement One-trial learning requires preliminary development of later reflexes in the chain Periodic reconditioning Shaping: reinforcement of successive approximations to the goal behavior Vanishing: gradual fading out of prompts Hull: Habit strength as a function of number of S-R pairings   Guthrie: One trial learning (acquisition of movements) Obvious need for repeated practice (learning of acts or skills) Estes: Successive sampling of stimulus elements across repeated trials
Cognitive		Ebbinghaus:Frequent repetitions necessary to produce content from memory Surplus repetition is not wasted Insufficient repetition for reproduction is still useful Frequent repetitions necessary to prevent forgetting Clarity and longevity of new material increases in memory with repetition Number of repetitions needed to memorize a series increases with length Increased repetition in one study period produces a savings in later relearning Greater repetition to learn a longer series results in longer lists being more easily relearned Tolman: Repetition through repeated, non-goal-directed experience Repetition through mental review and comparison Kohler: Series of repeated failed attempts, followed by reflection, followed by success Cognitive Information Processing: Concept learning through multiple, systematically varied examples Maintenance rehearsal: short term retention of information Elaborative rehearsal: long term encoding Rehearsal increases the length of stay in STS and gives coding and other storage processes time to operate Almost any kind of operation on information is a form of rehearsal Only a limited number of items can be rehearsed at any given time Flashbulb memories: repeated mental rehearsal of shocking experiences Automaticity and possible entrenchment through repeated experience Mindless drilling does not lead to improvement Effective practice or drill must be mindful and deliberate Revisiting material with variation of time, context, purpose, and perspective Incidental learning as a result of repeated, periodic presentation Organization through repeated exposure Ausubel: Overlearning (excessive repetition) makes even rotely learned materials less vulnerable to forgetting Repetition is critical to the “perpetuation of dissociability” of subsumable or correlative concepts Explicit instruction can reduce or possibly eliminate the need for repetition Clarity and stability are influenced by repetition Criterial or defining attributes of a concept are acquired by successive encounters Multi-contextual learning facilitates abstraction of commonality and strengthens transferability Sequential stages in concept acquisition Simultaneous availability of multiple instances in array Progressive differentiation Integrative reconciliation in response to additional experience Controlled sequencing of stimuli that provide successive contrast Consolidation of previously learned material through differential practice, review, and repeated exposure Transferability through application to a large number of different, specific contexts Practice and drill and the significance of repetition in meaningful learning Spaced review over long periods of time is required for retention of more complex ideas Value of both early and delayed review Benefits of repetition through practice Incidental practice often is not effective, due to haphazard frequency and distribution of trials Relation between repetition and feedback Fidelity of practice to the actual task to be learned Appropriate balance of repetition for consolidation versus diversification Schema Theory: Schema represent multiple instances of things that may be grouped based on a recurrent pattern of common features, functions, or characteristics Schema are created, developed, tuned, and restructured through repeated experience Typical and default values for schema variables are learned through encountering multiple instances Increased precision of schema through experience
Constructive		General:Revisiting what has previously been learned to relate new information to it Piaget: Action schemes are the structure of actions generalized by repetition Consolidation: A reflex becomes stronger and more precise by exercising it First habits are formed through patterns of exercise Circular reactions Schemes of assimilation are repeated and elaborated as the child develops Adaptation comes through repeated use and accommodation Only practice leads to normal functioning Coordination of reflexes occurs through repeated contact with the environment Repetition of the reflex leads to a generalizing assimilation of objects to activity There is a natural or fundamental tendency toward repetition of behavior Bruner: Spiral curriculum Representing redundancy in the environment Cumulative constructionism: use of previously acquired information in guiding further discovery Learning the heuristics of discovery through practice
Human		Attribution Theory:Perception of patterns defined spatially and temporally Self-Efficacy: Repetition in progressively independent and varied circumstances to build self-efficacy Beliefs of self-worth and self-efficacy are built through repeated experiences of success Self-Regulation Theory: Self-regulated learning cycle phases (forethought, performance, self-reflection)
Social		Vygotsky:Children learn mental planning through repeated experiences Internalization occurs through repeated encounter Development proceeds in a spiral, passing through the same point at each new revolution The need for sign mediation subsides with repetition Bandura: Multiple observational trials may be required to reproduce modeled stimuli accurately Behavior repertoires of culture are transmitted on the basis of repeated observation Behavior that is repeatedly observed is learned most thoroughly New behavior is refined through self-corrective adjustments (in repeated practice) Situated learning: Multiple attempts made in solving problems Activity theory: Cycles of expansive learning Cognitive apprenticeship: Importance of repeated practice of a new skill in increasingly complex tasks

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[1] The other being recency.

[2] Shaping is the teaching of a goal behavior by reinforcement of successive approximations to that behavior.

[3] Vanishing is the gradual fading of cues which prompt a desired behavior so that the behavior will eventually continue or occur without necessity of the prompt.

[4] This relationship between repetition and step size is an example of the interrelations that appear to exist between the various principles of learning which have been identified in the present study. More will be said on this type of interrelation in chapter 5.

[5] Hull (1952) later added Incentive Motivation (K) and Stimulus-intensity Dynamism (V) to the equation:

Reaction Potential = _SE_R = _SH_R x D x V x K

[6] A relation between the principle of repetition and the role of a teacher

[7] A relation between the principles of repetition and time

[8] Repetition often occurs in two dimensions (time and variation of form), Ausubel draws attention to the insightful possibility that repetition of form, while holding time constant, might provide a more efficient way of learning concepts through varied examples presented all at once.