A Model of School Learning
by John B. Carroll - 1963
The primary job of the educational psychologist is to develop and apply knowledge concerning why pupils succeed or fail in their learning at school, and to assist in the prevention and remediation of learning difficulties. A conceptual model is presented here that seems to have the advantage of comprehensiveness combined with relative simplicity.
THE PRIMARY JOB of the educational psychologist is to develop and apply knowledge concerning why pupils succeed or fail in their learning at school, and to assist in the prevention and remediation of learning difficulties.
This job is inherently difficult because behavior is complex and has a multiplicity of causes. To deal with it, educational psychologists have evolved a number of concepts which they find useful in classifying the phenomena of behavior. Textbooks in the field are commonly organized around such concepts as maturation, individual differences, learning, thinking, motivation, and social development. These are useful categories, but because they overlap or refer to different levels of organization in the subject matter, it is difficult to build them into an integrated account of the process of school learning. What is needed is a schematic design or conceptual model of factors affecting success in school learning and of the way they interact. Such a model should use a very small number of simplifying concepts, conceptually independent of one another and referring to phenomena at the same level of discourse. It should suggest new and interesting research questions and aid in the solution of practical educational problems. With the aid of such a framework, the often conflicting results of different research studies might be seen to fall into a unified pattern.
Many such formulations, perhaps, are possible. A conceptual model will be presented here that seems to have the advantage of comprehensiveness combined with relative simplicity. The model is amenable to elaboration, but for our immediate purposes, we will leave aside any such elaborations.
SCOPE OF THE MODEL
We need first to define learning task. The learner's task of going from ignorance of some specified fact or concept to knowledge or understanding of it, or of proceeding from incapability of performing some specified act to capability of performing it, is a learning task. To call it a task does not necessarily imply that the learner must be aware that he is supposed to learn or be aware of what he is supposed to learn, although in most cases it happens that such awarenesses on the part of the learner are desirable.
Most, but not all, goals of the school can be expressed in the form of learning tasks or a series of such tasks. Teaching the child to read, for example, means to teach him to perform certain acts in response to written or printed language. Examples of other learning tasks taught in the schools can be multiplied at will: learning to spell all the words in common use, learning to perform certain operations with numbers, learning to explain or otherwise demonstrate an understanding of the subject matter of biology, learning to speak a foreign language, learning to perform in competitive sports, and learning to carry out certain responsibilities of a citizen. Some of these tasks are very broadly defined, such as learning to read printed English, but we can also consider narrowly defined tasks like mastering the content of Lesson 20 in a certain textbook of French, or even mastering a certain grammatical construction covered in that lesson. The model presented here is intended to apply equally well to all such tasks, no matter how broad or narrow. It is required, however, that the task can be unequivocally described and that means can be found for making a valid judgment as to when the learner has accomplished the learning taskthat is, has achieved the learning goal which has been set for him.
It will be seen that as many as possible of the basic concepts in the model are defined so that they can be measured in terms of time in order to capitalize on the advantages of a scale with a meaningful zero point and equal units of measurement. An effort is made to provide for a mathematical description of the degree to which a learning task is achieved. Although the model applies only to one learning task at a time, it should be possible in principle to describe the pupil's success in learning a series of tasks (e.g., all the work of the fifth grade) by sum-mating the results of applying the model successively to each component task.
The model is admittedly oversimplified. The assumption that the work of the school can be broken down into a series of learning tasks can be called into question. In actual school practice, the various tasks to be learned are not necessarily treated as separate and distinct, and the process of teaching is often organized (whether rightly so or not) so that learnings will take place "incidentally" and in the course of other activities. Nevertheless, a conceptual model requires certain simplifying assumptions, and the assumption of discrete learning tasks is a useful one to make.
The model can be regarded as applying even to those educational goals ordinarily formulated in terms of "transfer"that is, the ability to apply in a "new" situation something learned previously. The concept of the learning task is defined to include the attainment of that degree of competence which will make "transfer" essentially as automatic as demonstration of performance in the original setting. "Transfer," correctly viewed, is a term in a metalanguage which states the conditions under which particular learnings occur or manifest themselves. Thus, when we say that "learning which occurred in situation A transfers to situation B," we are really saying that "something learned in situation A also manifested itself in situation B, there being sufficient commonality between the two situations to elicit the learned performance in both."
The model is not intended to apply, however, to those goals of the school which do not lend themselves to being considered as learning tasks. Such, for example, are those goals having to do with attitudes and dispositions. Educating a child so that he has tolerance for persons of other races or creeds, respect for parental or legal authority, or attitudes of fair play, is thought to be largely a matter of emotional conditioning or of the acquisition of values and drives. Learning tasks may indeed be involved in the cognitive support of such attitudes (as where the child learns facts about different races or creeds), but the acquisition of attitudes is postulated to follow a different paradigm from that involved in learning tasks. Perhaps the distinctions made by Skinner (6) are of use in this connection: We could say that whereas learning tasks typically involve "operants," the attitudinal goals of education typically involve "respondents."
OVERVIEW OF THE MODEL
Briefly, our model says that the learner will succeed in learning a given task to the extent that he spends the amount of time that he needs to learn the task. The terms of this statement, however, require special definition, explication, and interpretation if the statement is to be properly understood.
First, it should be understood that "spending time" means actually spending time on the act of learning. "Time" is therefore not "elapsed time" but the time during which the person is oriented to the learning task and actively engaged in learning. In common parlance, it is the time during which he is "paying attention" and "trying to learn."
Second, there are certain factors which determine how much time the learner spends actively engaged in learning.
Third, there are certain factors which determine how much time a person needs to spend in order to learn the task. These factors may or may not be the same as, or associated with, those which influence how much time he spends in learning.
The major part of this article is devoted to a presentation of the factors conceived as determining the times needed or actually spent in the course of a learning task and the way in which these factors interact to result in various degrees of success in learning. Four of these factors are convenient intervening variables or constructs which may, in turn, be regarded as functions of still other factors or variables; one, however, is in principle a directly manipulable and measurable factor ("opportunity").
This model of school learning should not be confused with what is ordinarily called "learning theory," that is, with the exact scientific analysis of the essential conditions of learning and the development of systematic theory about this process. Rather, the model may be thought of as a description of the "economics" of the school learning process; it takes the fact of learning for granted. The five factors or variables in the model will be presented under two headings: (1) determinants of time needed for learning, and (2) determinants of time spent in learning.
TIME NEEDED IN LEARNING
Aptitude. Suppose that a randomly selected group of children is taught a certain learning task by a teacher (or teaching device) with the best possible teaching techniques. Suppose further that each child is willing to stick attentively with the learning task for the number of minutes, hours, or days required for him to learn it to the specified criterion of success, and that each child is in fact given the opportunity to do this. Common experience, as well as abundant research evidence, suggests that the amounts of time needed by the children even under these ideal conditions will differ widely. Let us think, then, of the amount of time the pupil will need to learn the task under these conditions as the primary measure of a variable which we shall call his aptitude for learning this task. In ordinary parlance, learners who need only a small amount of time are said to have high aptitude; learners who need a large amount of time are said to have low aptitude. Some learners, it may be, will never learn even under these optimal conditions; we may say that these learners would need an indefinitely large (or an infinite) amount of time to learn the task.
It will be noted that this variable is measured in the opposite direction from the usual way of measuring aptitudethe shorter the time needed for learning, the higher the aptitude.
Furthermore, it will be noted that the measure of aptitude is specific to the task under consideration. Aptitude may be regarded as a function of numerous other variables. For one thing, it may depend upon the amount of prior learning which may be relevant to the task under consideration. A learner who has already progressed far towards the mastery of a task may not need much time to complete his learning. On the other hand, aptitude may also depend upon a series of traits or characteristics of the learner which enter into a wide variety of tasks; whether these traits can be accounted for solely on the basis of generalized prior learnings, or whether they reflect genetically determined individual" characteristics, is of no immediate concern here. It may be useful, however, to conceive that a learner's estimated needed time, at, for learning a given task, t, may be written as a mathematical function of a series of basic aptitudes, symbolized with Greek letters and subscripts, minus the amount of time, sty saved by virtue of prior learnings relevant to the task. Thus:
The exact form of this formula would vary for different tasks. Presumably, the basic aptitudes α1, α2, . . . , αn could be measured with considerable exactitude by appropriate tests.
Ability to understand instruction. We find it useful to postulate as a variable separate from those we consider under "aptitude" the ability to understand instruction, since this variable (in contrast to pure aptitude variables) is thought of as interacting with the method of instruction in a special and interesting way. The ability to understand instruction could be measured, one would suppose, as some combination of "general intelligence" and "verbal ability"; the former of these two would come into play in instructional situations where the learner is left to infer for himself the concepts and relationships inherent in the material to be learned, rather than having them carefully spelled out for him, while the latter would come into play whenever the instruction utilized language beyond the grasp of the learner. The way in which ability to understand instruction is postulated to interact with the type of instruction will be explained after we introduce a third variable affecting time needed for learning, the quality of instruction.
Quality of instruction. One job of the teacher (or any person who prepares the materials of instruction) is to organize and present the task to be learned in such a way that the learner can learn it as rapidly and as efficiently as he is able. This means, first, that the learner must be told, in words that he can understand, what he is to learn and how he is to learn it. It means that the learner must be put into adequate sensory contact with the material to be learned (for example, one must insure that the learner will adequately see or hear the materials of instruction). It also means that the various aspects of the learning task must be presented in such an order and with such detail that, as far as possible, every step of the learning is adequately prepared for by a previous step. It may also mean that the instruction must be adapted for the special needs and characteristics of the learner, including his stage of learning. All these things may be summarized in what we call quality of instruction. This variable applies not only to the performance of a teacher but also to the characteristics of textbooks, workbooks, films, teaching-machine programs, etc.
Now, if the quality of instruction is anything less than optimal, it is possible that the learner will need more time to learn the task than he would otherwise need. Some learners will be more handicapped by poor instruction than others. The extent of this handicap is conceived to be a function of the learner's ability to understand instruction. Learners with high ability in this respect will be able to figure out for themselves what the learning task is and how they can go about learning it; they will be able to overcome the difficulties presented by poor quality of instruction by perceiving concepts and relationships in the teaching materials which will not be grasped by those with lesser ability.
For the purposes of this conceptual model, we shall say that the amount of time actually needed by a person to learn a given task satisfactorily is a function not only of aptitude (as defined previously), but also of the quality of instruction in so far as it is less than optimal. And the amount of additional time he will need is an inverse function of his ability to understand instruction.
We could, of course, apply Occam's razor and get rid of both of the two preceding variables by conceiving that a change in the quality of instruction causes an essential change in the learning task itself. In this case, we would deal only with a learner's aptitude for learning a given task, subscripted with the quality of instruction attached to it. Such a modification of our model seems undesirable, however, for one would tend to lose sight of instructional quality as one of the important manipulable variables in educational psychology.
TIME SPENT IN LEARNING
Time allowed for learning ("opportunity"). It may come as a surprise to some to be told that the schools may allow less than adequate time for learning any task, but second thought will make one realize that this is very often the case. It is partly a consequence of the very large amount of material that the schools are expected to teach; the available time must somehow be distributed among many things. And it is partly a consequence of the very great variation that exists in the amounts of time that children need for learning, even under a good quality of instruction, and particularly when the instructional quality is such that many children of lower ability to understand instruction require much more time than they might otherwise need.
The school responds to differences in learning rates (for that is what differences in aptitude are) in many ways. Sometimes the policy of the school is, in effect, to ignore these differences; a certain amount of time is provided for everybody to learn, and no more. (For example, at some military academies, study time is prescribed and scheduled uniformly for all cadets.) At the opposite extreme is the case where each student is allowed to proceed exactly at his own rate; private instruction in music or foreign languages and self-instruction by teaching machine or other means are approximations to this case. The middle position is occupied by learning situations in which there is some kind of "ability grouping": Pupils are assigned to different groups, classes, or curricula on the basis of estimated learning rates.
Even when there is some constraint upon the amount of time "officially" provided for learning, teachers and instructional programs vary in the amount of time they allow for learning. Some programs present material at such a rapid pace that most students are kept under continual pressure; only the apter students can keep up with this instruction, while the others fall back or out, sometimes never to get caught up. In other programs, the instruction is paced for the benefit of the slower student. The faster student is fortunate if the teacher takes appropriate steps to "enrich" his instructional content; but this will not always happen, and it is undoubtedly the case that many fast learners lose some of their motivation for learning when they feel that their time is being wasted or when they are not kept at the edge of challenge.
Obviously, failure to allow enough time for learning produces incomplete learning. If a person needs two hours to learn something and is allowed only one hour, and if we assume that learning proceeds linearly with time, the degree of learning is only 50 per cent. Probably one of the most aversive things which a school can do is not to allow sufficient time for a well-motivated child to master a given learning task before the next is taken up. Children meet such frustrations by indifference or the more extreme avoidance reactions and are, in any case, handicapped in undertaking the next task.
The time the learner is willing to spend in learning ("perseverance"). The term perseverance is used here, rather than persistence, because of the somewhat pejorative connotations of the latter. Nevertheless, the concept is similar to what Paul Brandwein describes in the following passage:
The characteristics grouped under the Predisposing Factor... include a spectrum of traits which the writer places under the head of Persistence. This is defined as consisting of three attitudes. (1) A marked willingness to spend time, beyond the ordinary schedule, in a given task (this includes the willingness to set one's own time schedules, to labor beyond a prescribed time, such as nine to five). (2) A willingness to withstand discomfort. This includes adjusting to shortened lunch hours, or no lunch hours, working without holidays, etc. It includes withstanding fatigue and strain and working even through minor illness, such as a cold or a headache. (3) A willingness to face failure. With this comes a realization that patient work may lead to successful termination of the task at hand (1, pp. 9-10).
But the variable of perseverance applies not only in the case of the "gifted student" and not only in the case of long durations of effort, but also to all other learners and also to learning tasks which require only short times for mastery. That is, in the general case, a learner who (in view of his aptitude, the quality of the instruction, and his ability to understand the instruction) needs a certain amount of time to learn a task may or may not be willing to persevere for that amount of time in trying to learn. It is not a matter of his predicting how long he will be willing to learn: we simply postulate that there is a certain time over and above which he will not continue active learning of a task, and this time may lie anywhere on the scale from zero to infinity. The learner may not be motivated to learn at all, or he may regard the task as something too difficult for him to learn; in either case, he may spend no time at all in trying to learn. He may start to learn and later become distracted or bored, or he may lose confidence in his ability. He may go far toward mastery and then overestimate his achievement, thus prematurely terminating his efforts to learn. He may, of course, be so highly motivated that he would be willing to spend more time than he needs in order to reach a specified criterion of mastery. Nevertheless, for the purposes of our conceptual model, it will be assumed that the learner will never actually spend more time than he needs to master the task as defined, that is, that he will stop learning as soon as he has mastered the learning task. (In this way we avoid, for the present, the necessity of incorporating a concept of "overlearning" in the model.)
This variable, which may be called perseverance-in-learning-to-criterion, is thus measured in terms of time, and if it is not sufficiently great to allow the learner to attain mastery, it operates in our conceptual model to reduce the degree of learning. Assume, as before, that learning proceeds as a linear function of time. Then if a child needs two hours to learn something, is allowed one hour, but will persevere only thirty minutes, the degree of learning is only 25 per cent. Perseverance-in-learning is measured only in terms of the amount of time the child is actively engaged in learning; a child who is actively engaged in learning for various periods totaling only thirty minutes during an hour is presumably not paying attention to learning for the other thirty minutes, and this time is not counted.
Perseverance-in-learning is itself a function of many other variables which will not be separately treated in this conceptual model. It is a function partly of what is ordinarily called "motivation" or desire to learn. But there are many reasons for desiring to learn a given thing: To please the teacher, to please one's parents or friends, to get good grades or other external rewards, to achieve self-confidence in one's learning ability, to feed one's self-esteem, to avoid disapprovalall these can operate in place of or in addition to any incentives for learning which may derive from the intrinsic interest or perceived utility of the thing being learned. And there are probably just as many reasons which one may adopt (consciously or unconsciously) for not learning: to avoid the responsibilities which learning brings, to avoid the exertion of learning, to behave consistently with one's image of oneself as a non-learner, or to avoid wasting time on learning tasks of no perceived importance.
Perseverance-in-learning may also be a function of what are ordinarily called emotional variables. One may desire to learn but be unable to endure frustrations caused by difficulties in the learning task or distractions from external circumstances. It may also interact with the quality of instruction; poor quality of instruction may reduce perseverance-in-learning even beyond the toll it takes in wasted minutes or even weeks.
THE COMPLETE MODEL
It will be noticed that the model involves five elementsthree residing in the individual and two stemming from external conditions. Factors in the individual are (1) aptitudethe amount of time needed to learn the task under optimal instructional conditions, (2) ability to understand instruction, and (3) perseverancethe amount of time the learner is willing to engage actively in learning. Factors in external conditions are (4) opportunitytime allowed for learning, and (5) the quality of instructiona measure of the degree to which instruction is presented so that it will not require additional time for mastery beyond that required in view of aptitude.
Three of the factors are expressed purely in terms of time. If ability to understand instruction corresponds to a combination of general and verbal intelligence, it can be assessed in relative terms by currently available measuring devices. The most elusive quantity in this model is that called quality of instruction, but both it and the ability to understand instruction are interconnected with temporally measurable variables in such a way that by appropriate experimental manipulations, they could eventually be indexed in terms of time. Temporarily, let us put quality of instruction on a scale from 0 (poor) to 1 (optimal), and ability to understand instruction on a standard score scale with mean = o and σ = 1.
The five factors can be worked into a tentative formula which expresses the degree of learning, for the ith individual and the tth task, as a function of the ratio of the amount of time the learner actually spends on the learning task to the total amount he needs. Thus:
The numerator of this fraction will be equal to the smallest of the following three quantities: (1) opportunitythe time allowed for learning, (2) perseverancethe amount of time the learner is willing to engage actively in learning, and (3) aptitudethe amount of time needed to learn, increased by whatever amount necessary in view of poor quality of instruction and lack of ability to understand less than optimal instruction. This last quantity (time needed to learn after adjustment for quality of instruction and ability to understand instruction) is also the denominator of the fraction. It is not necessary or worthwhile here, however, to pursue the detailed mathematical formulation, which has been given elsewhere (3).
As an illustration of the usefulness of this model in clarifying other educational concepts, let us see how it provides a framework for interpreting the notion of "underachievement" as criticized by Henry Dyer (4). While we are at it, let us also look at the notion of "overachievement." It is our contention that these terms are useful and salvageable if properly defined.
Underachievement and overachievement, like underweight and overweight, are ordinarily taken with reference to some norm or baseline of expectation. The underachiever does poorer than we expect him to, and the overachiever does better than we expect him to. The issue is this: Upon what do we base our expectation? The approved manner of doing this is to make predictions from those tests or other measurements which in fact yield the best predictions of success, and statistical theory tells us how to make best use of these predictors (i.e., by making our predictions along a regression line). There is, however, a paradox here. Suppose our predictions were perfect: Then there would be no "underachievers" and no "overachievers." An unlikely eventuality to be sure! Nevertheless, our intuitive rejection of the case of perfect prediction lends credence to the following analysis of what we mean by "underachievement": Underachievement is a situation in which there is a discrepancy between actual achievement and that expected on the basis of a certain kind of evidenceevidence concerning the "capacity" or "aptitude" of the individual to achieve in a particular context. Such evidence is recognized as being quite distinct from evidence concerning other factors in achievement, e.g., "motivation," "opportunity for learning," etc., and these latter factors would not figure in forming our expectations. Instead, we would hope to gather as much evidence as possible concerning the "capacity" or "aptitude" of the individual, defined as his learning rate when all other factors are optimal.
ACHIEVEMENT AND EXPECTANCY
With reference to the conceptual model presented earlier, our expectation of an individual's achievement in a given learning task would in the strictest sense be that which he would attain when he spends all the time he needsthat is, when the ratio of the time spent to the time needed is unity. Anything less than this is, to some degree, underachievement. From this point of view, all learners are underachieves unless they are superhuman beings in an ideal world. Perseverance sometimes flags; the quality of instruction is seldom optimal, and time allowed for learning is not always sufficient.
Let us, therefore, strike some sort of average for perseverance, instructional quality, and opportunity for learning. Our expectation of the degree of learning will be somewhat less than unity because, on the average, individuals will spend less time in learning than they need. And we may gauge underachievement and overachievement with reference to this expectation. In effect, this is what we do by the customary regression techniques based on aptitude measures, although in a less precise way than might be done if we were able to measure each of the components of achievement as stated by the model. In the framework of the model, however, underachievement is now seen to be a state of affairs which results whenever perseverance is less than some "reasonable value," whenever the quality of instruction is poor, whenever time allowed for learning has not been sufficient, or whenever some combination of these conditions has occurred. "Over-achievement," contrariwise, may occur when there is an especially favorable combination of attendant events: high perseverance, instruction of high quality, or ample opportunity for learning.
We have a feeling about the relative amenability of different factors in achievement to manipulation or treatment: "Aptitude" is regarded as relatively resistant to change, whereas it is the hope of the psychologist that he can readily intervene to modify "perseverance," "quality of instruction," or "opportunity for learning." To some extent, this feeling is justified not only by logic but also by research findingsby the research on the apparent constancy of the IQ, on the effect of various instructional variables, etc. On the other hand, if aptitude is largely a matter of prior learnings, it may be more modifiable than we think, whereas, conversely, some kinds of clinical findings suggest that motivational characteristics of the individual may be much harder to change than one might think. These considerations, however, need not detract from the basic utility of the concepts of underachievement and overachievement. The concept of "underachievement" does not automatically imply the possibility of remediation any more than the concept of illness does. Some patients never get well, and some underachievers remain underachievers.
BABIES AND BATHWATER
Henry Dyer (4) has drawn attention to possible dangers in the concept of underachievementfor example, the dangers of making predictions from unreliable or invalid predictors, of assuming that ability is innate or fixed, of making unwarranted inferences from school marks, and of overlooking determinants of school performance which are external to the pupil. Nevertheless, in suggesting that we Mil the notion of underachievement, it would seem that he wants to throw out the proverbial baby with the bathwater. The concepts of underachievement and of overachievement are meaningful from both a statistical and a clinical point of view, as shown by the many fruitful studies of "underachieving" groups of students (e.g., 5). Careful attention to the elements of the conceptual model presented here will afford a safeguard against misuse of the concepts: Aptitude must be estimated by relevant and reliable measures (in actuality, all of them measures of past performance); the degree of learning must be accurately appraised, and the possible role of instructional variables must be considered. Above all, the variable which we have called perseverance must be validly assessed; the most direct evidence concerning it, our model would suggest, would come from observations of the amount of time the pupil actively engages in learning.
Before leaving this topic, let us consider another way in which the term "overachievement" is sometimes used. When a person is designated as an over-achiever, it is often implied that his achievements derive more from his perseverance than from his aptitude or his intelligence. In terms of our model, this can occur when the learning task can be broken down into a series of subtasks of varying difficulty with difficulty roughly gauged in terms of average learning time. Because of his great perseverance, the overachiever masters to a criterion more of the easy taskstasks which are within the compass of his aptitudethan the student of average perseverance. While he may fail to learn some of the more difficult tasks, the net result may be a high score on an achievement testa score considerably higher than predicted from aptitude measures. This concept of overachievement is distinctly different from the concept of overachievement suggested previously; responsible users of the term must clearly state which of these meanings they intend.
Our conceptual model could lead, it would seem, to almost endless possibilities for research. It should provoke renewed effort to develop measures of each of the basic variables included in the model. The measurement of aptitudes is a fairly well advanced art, although the exact ways in which these aptitudes are relevant to school learning tasks remain to be worked out. The same remark may be made about the measurement of ability to understand instruction. But measurements of perseverance and of instructional quality are practically nonexistent. It should be intriguing to attempt to provide a general way of measuring opportunity to learn, that is, the actual time available to individual students to learn in view of the pacing of instruction; for it is our hypothesis that variations in the pacing of instruction have remained largely unrecognized in pedagogical discussions.
Research is also needed on the interactions of the several variables in the model. Is the model correctly put together? To what extent are the variables interdependent? For example, how does instructional quality affect perseverance? In what way is the degree of learning a function of the ratio of the amount of time spent in learning to the amount of time needed? Are we correct in postulating an interaction between instructional quality and ability to understand instruction such that pupils low in the latter ability suffer most from poor instructional quality?
One of the most exciting possibilities suggested by the model is that of being able to state parameters for different types of learning by learners of varying characteristics under stated instructional conditions. Perhaps ultimately such parameters could be tied back to the data of pure learning theory. One of the bolder hypotheses implicit in the model is that the degree of learning, other things being equal, is a simple function of the amount of time during which the pupil engages actively in learning. Psychologists have paid little attention to this variable of pure time in human learning. A recent experiment by Bugelski (2) is one of the few to consider time factors in the field of paired-associate learning; and interestingly enough, it supports the hypothesis that more parsimonious descriptions of learning may be obtained by use of time as a variable rather than, say, number of trials.
What is important to emphasize is that this conceptual model probably contains, at least at a superordinate level, every element required to account for an individual's success or failure in school learning (at least in the learning tasks to which the model applies). The explication and refinement of these factors and the exploration of their interactions constitute a major task of educational psychology. Its other major task is to account for those types of school learning (e.g., attitudinal and emotional conditioning) to which the present model is not intended to apply and for which a separate model might well be constructed.
1. Brandwein, P. F. The gifted student as future scientist. New York: Harcourt Brace, 1955.
2. Bugelski, B. R. Presentation time, total time, and mediation in paired-associate learning. J. exper. Psychol., 1962, 63, 409-412.
3. Carroll, J. B. The prediction of success in intensive language training. In Glaser, R. (Ed.) Training research and education. Pittsburgh: Univer. Pittsburgh Press, 1962. Pp. 87-136.
4. Dyer, H. S. A psychometrician views human ability. Teach. Coll. Rec., 1060, 61, 394-403.
5. Goldberg, Miriam, et al. A three-year experimental program at DeWitt Clinton High School to help bright underachievers. High Points, 1959, 41, 5-35.
6. Skinner, B. F. Science and human behavior. New York: Macmillan, 1953.