Sequence

Based on the amount of evidence collected during the present study, it seems that this might possibly be the most frequently addressed principle of learning among the theories reviewed. Aristotle declared that “in all arts and crafts we require a preliminary education and habituation to enable us to exercise them” (Aristotle & Burnet, 1913, p. 106). He also explained the association of connected ideas as starting with the central most idea, or “middle member” of the series[1] (Ross & Aristotle, 1906, p. 113). Thus, having established the central most idea, other subsequent ideas may be grouped around it.

Thorndike discussed the concept of sequence under the topics of (a) partial activity or prepotency of elements, i.e., based on prior learning some elements of a stimulus situation will have greater influence in determining a response than others (Thorndike, 1914a, p. 134); (b) assimilation , i.e., due to the assimilation of analogous elements between two stimuli, an animal will respond to a novel stimulus in the way it has previously responded to a similar stimulus (p. 135); (c) associative shifting, or the shifting of a previously learned response to a new stimulus cue (Thorndike, 1898, pp. 14, 28; Thorndike, 1914a, p. 136); and (d) in report of his tests of the influence of prior experience on the shape of learning curves (Thorndike, 1898, pp. 17, 28).

In Pavlov’s conditioning the mechanism of association relied on the prior existence of nerve innervations that could be conditioned. The dogs, presumably, would never have acquired the salivating reaction to the site of meat powder had they not first smelled or tasted it (Pavlov et al., 1928, p. 22). The prior experience of smelling and tasting created a situation in which the dogs anticipated consumption simply by seeing the meat powder, and then subsequently simply by other coincident stimulus elements, such as the assistant wearing a lab coat, or the sounding of a bell. Pavlov also demonstrated higher order conditioning, or the conditioning of a stimulus to produce a response with which it has never been paired (p. 105).  Higher order conditioning is carried out by presenting a stimulus to be conditioned in conjunction with a stimulus that has already been conditioned to the response.

Watson described individual acquisitions of elementary habits as building blocks of learning (Watson, 1914, pp. 48-49; Watson, 1919, p. 269). He also talked about the integration of previously acquired separate movements to form new unitary wholes (Watson, 1919, p. 272). Skinner took advantage of previously learned simple behaviors to create chains of more complex behavior (Skinner, 1953, p. 224) ). By reinforcing progressive approximations to an end goal behavior which does not naturally occur in the organisms repertoire of behavior he was able to shape behavior, with each subsequent attainment building on what had previously been learned shaping (Skinner, 1953, p. 91; Skinner, 1961e, p. 413; Skinner, 1961f, p. 132). And his rats which learned to press the food bar in one trial were certainly not lifting and pressing their paws or dashing to grab the resultant food pellet for the first time, but were simply integrating the two previously learned behaviors to play out the required sequence that provided the reward of food (Skinner, 1979, p. 89). Hull (as cited in Hergenhahn, 1982, p. 132) believed that learning was only necessary when the organisms existing hierarchy of innate or previously learned responses fails to satisfy a need. His notion of fractional antedating goal response (1934, p. 43) was his explanation for maze learning, and comparable to Skinner’s chaining. By demonstration of a convergent habit-family hierarchy chain, Hull demonstrated that habits can generalize, or function with little or no delay, in “new situations having nothing whatever as objective stimuli in common with the conditions under which the habit was originally formed” (p. 35).

Like Watson,[2] Guthrie believed that it is natural to make use of prior learning in present and future situations—so natural in fact that a subject’s response to a given situation could be predicted based on “that one of his practiced movements that was last in evidence when on some former occasion he solved his problem in circumstances like those now prevailing” (Guthrie, 1940, p. 145). He also agreed with Thorndike’s concept of pre-potent elements, i.e., that “in a new situation the animal will respond in terms of familiar parts of the situation” (p. 142). Guthrie described the process of learning any skill as requiring “not an association or any series of associations, but many thousands of associations that will connect specific movements with specific situations” (Guthrie, 1942, p. 36).

Another way in which the principle of sequence shows up in Guthrie’s theory is in his description of forgetting. He believed that forgetting “is not a passive fading of stimulus-response associations contingent upon the lapse of time, but requires active unlearning, which consists in learning to do something else under the circumstances” (Guthrie, 1942, p. 29). Under this view, new learning may be negatively influenced by previous learning in that it may require not only the acquisition of new associations, but the breaking of those which have been previously established.[3]

Ebbinghaus explicitly studied the effects of prior learning on later learning and observed both positive and negative effects (Ebbinghaus, 1913, p. 104). Having first learned a list of syllables he created a derivative list compose of the same syllables, in the same order, but left some of them out (e.g., every other, every third, every fifth, every seventh, etc.). He found that the time required for learning the derivative list, created by skipping items, took less time to learn. This is a case of the positive effects of sequence. What was previously learned made new learning easier and more efficient. In contrast, when his derivative list was created by permutation—changing the order of the syllables—it took longer to learn the new list than it would have taken, on average, to learn a new list of the same length where no previous familiarity existed. This is an example of the negative effects of sequence, in which his previous learning interfered with the new list he was trying to learn.

Other examples from cognitive theory come from Tolman’s latent learning and Kohler’s experiments with apes. Although Tolman’s rats could not have known at the time they were exploring the maze that their knowledge would later be useful in obtaining food more directly, they were able to transfer latent knowledge of the maze to that very task when it was needed (Tolman, 1948, p. 195). Kohler found that “the possibility of utilizing old methods generally inhibits the development of new ones” (Kohler, 1951, p. 39) and that it was necessary to remove all possibility of using the old method in order that the apes would learn a new approach. He also observed that once Koko had learned to use the box in a certain situation, he quickly generalized it as the means of obtaining food in all cases (Kohler, 1951, p. 45).

One of the most obvious examples of sequence in cognitive learning theory is evident in the process of pattern recognition, which Leahey and Harris (1997) define as the process by which we “recognize environmental stimuli as exemplars of concepts already in memory” (p. 113). Clearly, a pattern can only be recognized if it has already been learned. Once  present and available in the mind, it can be used to facilitation recognition and interpretation of new material or experience.

The positive and negative effects of prior learning on new learning are currently studied in cognitive learning theory under the topic of transfer. Sternberg and Williams (2010) defined transfer as “carrying over  knowledge from one problem or situation to a new problem” (p. 334). In their review they drew a contrast between positive and negative transfer, low-road and high-road transfer, and forward-reaching and backward-reaching transfer. Positive transfer occurs “when the solution of an earlier-encountered problem facilitates the solution of a later-encountered problem” (p. 334). Negative transfer occurs “when the solution of an earlier-encountered problem impedes the solution of a later-encountered problem” (p. 334). Low-road transfer is “spontaneous and automatic” and occurs “when a highly practiced skill is carried over from one situation to another, with little or no reflective thinking” (p. 335). High-road transfer occurs “when you consciously apply abstract knowledge you have learned in one situation to another situation” (p. 335). Note that in this type of transfer one must first abstract the general principles from one situation so they can be applied in another. Forward-reaching transfer occurs when “you intend the transfer to occur at the time you are learning” (p. 336). In backward-reaching transfer “you realize the applicability of what you learned in the past only after it becomes relevant” (p. 336).

Another aspect of sequence often discussed in cognitive information processing theory is the benefit on present learning that comes from having previously learned knowledge or skill to a point where it happens without any direct attention control. This is usually referred to as automaticity and has the primary benefit of enabling certain procedures to be executed with “hardly any effort or even conscious awareness” of what is being done (Wenke and Frensch, 2003, as cited in Sternberg & Williams, 2010, p. 333). Once component tasks have been learned to a point of automaticity more complex tasks may be learned or performed by adding additional component tasks that could not have been included previously because the limits of attention had been reached.

Ausubel et al. (1978) clarified the importance of sequence in learning by saying, “If we had to reduce all of educational psychology to just one principle, we would say this: The most important single factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly” (p. 163). Because this theme was so central to his ideas of learning, extensive references to this concept were directly made in Ausubel’s writing. At the core are his forms of meaningful learning: (a) subordinate learning, (b) superordinate learning, (c) combinatorial learning, and (d) assimilation learning (Ausubel et al., 1978, p. 68). Each of these describes a particular type of integration of new material with existing cognitive structure. Also relevant to the principle of sequence in learning are the ideas of: progressive differentiation (Ausubel et al., 1978, pp. 67-68, 124, 189-190); prior consolidation (Ausubel et al., 1978, p. 345); the stability of anchoring ideas (Ausubel et al., 1978, p. 165); the sequential organization of subject matter (Ausubel et al., 1978, p. 196); the use of advance organizers to provide to introduce appropriate subsumers “prior to the actual presentation of the learning task” (Ausubel, 1962, p. 219; Ausubel et al., 1978, pp. 164-165); the transition from learning through “direct empirical and nonverbal contact with data” as children to learning through higher order abstractions as adults(Ausubel, 1962, p. 213; Ausubel et al., 1978, p. 140); concept acquisition through exposure to “a heterogeneity of instances after consolidation in a more homogenous setting” (Ausubel et al., 1978, p. 87); representational learning (Ausubel et al., 1978, p. 127); rote learning (Ausubel, 1962, pp. 216, 217, 223); and the dependence of transfer on both overlearning (Ausubel et al., 1978, p. 197) and the “relevance, meaningfulness, clarity, stability, integrativeness, and explanatory power of the originally learned subsumers” (Ausubel et al., 1978, p. 198).

Sequence is also at the core of schema theory, both in the influence that previously acquired schema have on the learning of new materials—with “the schemata a person already possesses are a principal determiner of what will be learned” (Anderson et al., 1978, p. 439)—and in the ongoing process of developing schemata through accretion, tuning, and restructuring (1976).

In constructivist learning theory it is believed that “each of us makes sense of our world by synthesizing new experiences into what we have previously come to understand” (Brooks & Brooks, 1993, p. 4). One particular paradigm of constructivism, endogenous constructivism, is even more sharply focused on the importance of prior knowledge in constructing new knowledge and “emphasizes internal construction of holistic knowledge structures, or the construction of new knowledge from old” (Harris & Graham, 1994, p. 234).

Much has already been said regarding Piaget’s theory of development and the dependence of one stage on what has been acquired during previous stages. During the first eighteen months of life “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). Sensori-motor schemes are revealed through three broad successive forms—rhythm structures, regulations, and reversibility (Piaget & Inhelder, 1969, pp. 19-20)—and the universe becomes “increasingly structured by the sensori-motor intelligence according to a spatio-temporal organization and by the formation of permanent objects” (Piaget & Inhelder, 1969, pp. 18-19). Sensori-motor knowledge is then later reconstructed at the perceptual level (Piaget, 1963, forward) with the appearance of the semiotic function (Piaget & Inhelder, 1969, p. 51). Piaget’s mechanism of development is one of assimilation and accommodation—integrating new knowledge to conform with existing schemes on the one hand, and modifying those schemes to adjust to new elements on the other (Piaget & Inhelder, 1969, pp. 5-7).

In The Act of Discovery (1961) Bruner wrote, “Discovery, like surprise, favors the well prepared mind” (p. 22). The premise of his spiral curriculum is that “any subject can be taught effectively in some intellectually honest form to any child at any stage of development” (J. S. Bruner, 1960, p. 33), and that the ideas introduced can then be revisited repeatedly, “building upon them until the student has grasped the full formal apparatus that goes with them” (p. 13). The ideas introduced earlier in the curriculum facilitate more effective and more efficient learning later on, particularly when what is introduced earlier is structure—i.e., “the fundamental ideas in whatever subject is being taught” (J. S. Bruner, 1960, p. 18). Bruner wrote that, “an understanding of fundamental principles and ideas appears to be the main road to adequate transfer of training” (J. S. Bruner, 1960, p. 25). He also described how more complex acts can be realized by orchestrating smaller component acts previously learned into an integrated sequence (J. S. Bruner, 1964, p. 2). He described how transfer could be specific or non-specific (J. S. Bruner, 1960, p. 17) and cited the acquisition of language as one of the great facilitators of subsequent learning since “once the child has succeeded in internalizing language as a cognitive instrument, it becomes possible for him to represent and systematically transform the regularities of experience with far greater flexibility and power than before.” (J. S. Bruner, 1964, p. 4) and provides “a progressive release from immediacy” (J. S. Bruner, 1964, p. 14).

Vygotsky marked language as a means by which practical tasks are solved (Vygotsky, 1978, p. 26) and by which thought is organized (p. 89). However, he said, only after a certain level of internal development is reached does it become possible to master “cultural methods” (Vygotsky, 1994b, p. 8). In regards to the zone of proximal development (Vygotsky, 1978, p. 86), what makes one child able to do more with assistance than another is that which he has obtained through prior experience which can now be brought to bear in solving a problem with assistance. As an example, Vygostky described arithmetic operations as extending the zone of proximal development and providing a basis for highly complex thinking:

The major consequence of analyzing the educational process in this manner is to show that the initial mastery of, for example, the four arithmetic operations provides the basis for the subsequent development of a variety of highly complex internal processes in children’s thinking. (Vygotsky, 1978, p. 90)

In social cognitive theory, Bandura described sequence in terms of the availability of component skills pre-requisite to a more complex performance (Bandura, 1977b, pp. 27-28). Learner’s who possess the component skills can easily integrate them to produce new patterns. Thus, what is learned through observational learning depends on prior development (p. 29). It is also true that self-efficacy is built on previous successes  (Bandura, 1977a, p. 202), and that “first learning has certain advantages over later learning, since there is less interference from contradictory habits” (Fuller, 1962, p. 67).

In situated learning the newcomer’s task is one that requires less time, effort and responsibility that the task of a full participant (Lave & Wenger, 1991, p. 110). But, as time goes on, and prior experience accumulates, the apprentice takes on more and more of the workload (p. 69). More advanced tasks become possible by leveraging learned skills and experience.

Sequence is implied in activity theory under the principle of historicity. It can be assumed that models proposed as solutions to inner contradictions (Engestrom, 2010, p. 7) are constructed based on the leverage of prior experience. Thus, any given solution is possible, in part, only because of previously accumulated knowledge and experience.

Collins et al. (1991) caution that in establishing learning sequences for students, care should be taken to do so in a way that “preserve[s] meaningfulness of what they are doing” (p. 15). They recommend that tasks should be structured with global skills being taught before local skills to provide a conceptual model of the overall task that then provides context for any subcomponent of that task they are asked to perform. They also recommend the sequencing of tasks in order of increasing complexity, meaning at each stage, “more and more of the skills and concepts necessary for expert performance are required” (p. 15).

Table 5 summarizes the local principles from the theories reviewed that are subsumed by the universal principle of sequence.

 

Table 5

Principles of Learning Subsumed by the Universal Principle of Sequence

Theory Group   Local principles
 

Behavioral

   

Aristotle:

The linking of ideas similar, contrary, or contiguous

Central concept is key to accessing related ideas

 

Thorndike:

Associative shifting

Assimilation

Partial activity or prepotency of elements

Influence of prior experience

Associative polarity

Response availability

Order of bond formation and effect of the formation of one bond upon the condition of other bonds

 

Pavlov:

Prior experience sets the stage for association

Higher-order conditioning

 

Watson:

Individual acquisitions as building blocks of behavior

The integration of separate movements to form new unitary activities

Positive effects of prior learning on new learning

Positive effects depend on similarity between the old habit and the new habit to be learned

Movements displayed in a novel situation will be those gained from a past habit organization

 

Skinner:

One trial learning

Establishing a discriminative response to the sound of the food magazine prior to introducing the lever response

The law of chaining

Shaping

 

Hull:

New learning occurs only when existing responses do not reduce need

The fractional anticipatory goal reaction

Convergent habit-family hierarchy mediate transfer of reaction from one situation to a second which may be totally different

 

    Guthrie:

Recency principle

New situation response based on familiar parts of the situation

Learning a skill requires learning many associations

Forgetting requires active unlearning

 

Estes:

In each trial, the probability of a certain response is modeled as the relative portion of active stimulus elements in the stimulus condition that are already conditioned to that response

Response subclass hierarchy

 

 

Cognitive   Ebbinghaus:

Savings in number of repetitions when learning a derivative list created by skipping members

Increased number of repetitions required when learning a list created by permutation of previous list

Slight savings when learning a known list in reverse:

 

Tolman:

Previous knowledge acquired through latent learning applied when needed to accomplish a goal-oriented task

 

Kohler:

Preference to using existing knowledge and skills

Generalized use of the box

 

Cognitive Information Processing:

Interference and serial-position curve

Retroactive interference

Proactive interference

Automaticity

Stages of L1 language acquisition: a building sequence of development

Pattern recognition: recognizing environmental stimuli as exemplars of concepts already in memory

 

Ausubel:

The most important single factor influencing learning is what the learner already knows

Availability in learner’s cognitive structure of specifically relevant anchoring ideas

Extent to which anchoring ideas are discriminable from both similar and different concepts in the learning material

Stability and clarity of anchoring ideas

Acquisition of new information is highly dependent on the relevant ideas already in cognitive structure

Progressive differentiation

Importance of prior consolidation of more particular habit exemplars

Stability of anchoring ideas

Sequential organization of subject matter

Advance organizers

After junior high school age, we require less empirical and nonverbal contact with data on which verbal constructs are based

With increasing age concepts are learned through assimilation more than formation

Concept acquisition sequencing

Representation learning: representing known concepts with culturally designated signs or symbols

Forms of meaningful learning: subordinate, superordinate, combinatorial, and assimilation

Acquiring information results in a modification of both the newly acquired information and the specifically relevant aspect of cognitive structure to which the new information is linked

Adequately established subsumers

Rote learning

Positive transfer attributable to carry over of general elements of strategy, orientation, and adaptation

Prior learnings are not transferable until overlearned

Gradual acquisition of a coding principle to facilitate solution of a given class of problems

Prior learning helps to circumvent limitations of memory and process of storing information

 

Schema Theory:

The schemata a person already possesses are a principal determiner of what will be learned from a text

More significant than the structure that is in some sense contained in a text is the structure the reader imposes on the text

Acquisition of schema: accretion, tuning, and restructuring

 

 

Constructive   General:

Endogenous constructivism: the construction of new knowledge from old

Synthesizing new experiences into what we have previously come to understand

Structuring curriculum around primary concepts

A repertoire of previously learned thinking and reasoning strategies enables achievement of complex goals

Generalization and transfer

 

Piaget:

During first 18 months cognitive substructures are developed that will be foundation of intelligence for all later learning

Through sensori-motor activity the broad categories of action are constructed (object, space, time, causality)

Sensori-motor knowledge is reconstructed at the perceptual level

Assimilation: reality data are treated or modified in such a way as to become incorporated into the structure of the subject

Accommodation: adjusting to the environment

The semiotic function appears at end of sensori-motor period

Search for causality of previously experienced phenomena

Consistent succession of stages

Intellectual development is connected to, and builds on, organic biological growth

Consistent succession of stages

Intellectual development is connected to, and builds on, organic biological growth

 

Bruner:

Spiral curriculum

Cumulative constructionism, or the use of previously acquired information in guiding further discovery

Integration of smaller units into larger units

Language makes possible the representation and transformation of regularities of experience with greater flexibility and power

Importance of learning structure of a subject

Specific and non-specific transfer

Continual deepening through progressively more complex forms

 

 

Human   Biological Motivation:

First learning has advantage over later learning due to less interference from contradictory habits

 

Self-Efficacy:

Self-efficacy built on previous success

 

 

Social

 

  Vygotsky:

Language and the use of tools provide the rudiments of solving practice tasks

Transfer through similar elements

Zone of Proximal Development – what makes one child able to do more with assistance than another is that which he has obtained through prior experience which can now be brought to bear in solving a problem with assistance

Progressive utility of language

Learning creates the ZPD

Example of arithmetic operations providing basis for highly complex thinking

Internal development a pre-requisite to master cultural methods

Rich psychological experience

 

Bandura:

Availability of component skills pre-requisite to complex performance

Attention, retention, motor, and motivational subfunctions pre-requisite

 

Situated learning:

Learning progresses from learning simple to more complex tasks

 

Activity theory:

Implied: new models proposed in the third step of the cycle of expansive learning are generated based on previous experience

 

Cognitive apprenticeship:

Sequence without sacrificing significance

Global before local provides conceptual model of target skill or process

Increasing complexity

     


[1] Based on the interpretation given by Ross (Ross & Aristotle, 1906, p. 273).

[2] Cf. Watson’s principle of recency (Watson, 1914, p. 262).

[3] Note the similarity between Guthrie’s position and the common present day belief that it is better to learn to do something right the first time, than to have to unlearn a bad habit later. Guthrie (1938, p. 60) suggested three methods for breaking old habits: the threshold method, the fatigue method, and the incompatible response method.

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