On Some Methods of Optimizing the Educational Process
Abstract Generated abstract
This paper argues that the accelerating growth of scientific and technical knowledge requires a more dynamic and scientifically managed educational process, especially in higher education. Using cybernetic concepts, it models learning as a self-organizing information system involving perception, processing, memory, reproduction, feedback, and teacher-student control relations. The authors discuss memory decay, repetition intervals, levels of knowledge reproduction, programmed instruction, and the possible use of sensors, control automata, computers, and network planning to regulate instruction. They propose that optimal curricula and teaching schedules are those that maximize the accumulation of processed, retained, and reproducible information while preserving necessary repetition and minimizing losses from incomplete assimilation.
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ON SOME METHODS OF OPTIMIZING THE EDUCATIONAL PROCESS
V. M. Razin, V. S. Shuvarikov
The modern era in the development of society is characterized by an exponential growth of scientific knowledge. Science is increasingly discovering the laws of nature and finding ever new ways of acting upon it. The regularities discovered by science can be used only if they are mastered by the people directly engaged in the sphere of material production. This task is solved by education. Therefore education must be regarded as a powerful means of linking science and production, as a means of obtaining the maximum quantity of products in the minimum time and with minimum expenditure.
The rapid growth of scientific information increasingly exceeds the capacity of production workers to assimilate it. The existence of an ever-widening gap in time between scientific discoveries and their assimilation in the sphere of material production leads to economic losses from the prolonged non-use of newly opened possibilities. Thus there arises the task of seeking ways to improve the system of education that would lead to the maximum reduction of this gap. The modern scientific and technological revolution, when professions change so rapidly that new processes and new products make previously attained mastery obsolete, gives particular urgency and significance to the formulation and solution of this task.
The specific character of the development of the sphere of education consists, first, in the economic necessity of qualitatively improving and accelerating the assimilation by students of a certain sum of knowledge previously accumulated by mankind, and, second, in the economic expediency of assimilating a certain sum of new knowledge discovered by science within a limited period of study. This creates great difficulties in organizing and managing the educational process. Under modern conditions, the system of education passes from the realm of statics into the realm of dynamics. What is required of it is continuous regulation of the content and methods of instruction in order to ensure rapidly changing conditions of production and further scientific and technological progress. All this urgently requires the development of methods for a scientifically grounded organization and management of the education system. In this respect, as Academician A. I. Berg notes, of the three spheres of human activity—science, education, and production—the most conservative sphere is education1.
At the present time, cybernetics—the science of control, which studies the organization and processes of perception, processing, storage, reproduction, and transmission of information in complex systems of various natures and reveals the common properties and laws of these processes—is finding ever broader application in various fields. From this point of view, education, as a complex functioning system, is a subject of investigation for cybernetics.
The basic element of the education system is the human being. In the course of his development, man acts upon nature in order to obtain consumer products necessary for his existence. In the process of acting, man registers, processes, and stores information about nature for the purpose of acting upon it more effectively subsequently. In other words, in the process of acting upon nature, man teaches himself. The process of self-instruction is a cybernetic self-organizing system.
The mechanism of this system is a closed loop of sequentially connected links: a control device (the brain), an executive device (a complex of functioning muscles), the object of control (nature), and a registration device (a complex of organs of sight, hearing, and touch). The control device is interconnected with a memory device (a complex of neurons).
The system functions as follows. The C. D. (control device) forms control information (commands) and sends them to the E. D. (executive device). Depending on the content of the commands, the E. D. acts upon the R. D. (registration device), which registers the properties and phenomena of the O. C. (object of control). The E. D. may also act upon the O. C. Then the R. D. also registers the results of this action. Information on the registration is sent to the C. D., where it is processed. The processing of information occurs as a result of the circulation of information along the C. D.—M. D. loop. The processed information is sent to the M. D. (memory device), where it is stored for a long time. The result of the processing is the next command formed by the C. D., which is again sent to the E. D. The further functioning of the system is analogous.
In the process of the system’s functioning, man produces the products of his labor in the form of material means, which are the result of the actions of the E. D., and knowledge, which is the result of information processing and is stored in the M. D. Man again includes material means and knowledge in the work of the system in order to obtain a larger quantity of the products of his labor. The functions of the E. D. may be called physical labor, and the functions of the R. D. and C. D.—mental labor, or the process of self-instruction. The process of man’s functioning in the system may be called self-organization, and the system as a whole—a cybernetic self-organizing system.
In the course of the functioning of the C. D. system, by processing information, it constantly optimizes the control commands formed in the process and thereby optimizes the functioning of the system as a whole. The content of the optimization of mental labor consists in the effort to register (perceive) the maximum necessary information about nature, to process (comprehend) the maximum amount of registered information, to preserve (memorize) the maximum amount of processed information, and to reproduce the maximum of stored information in the minimum time with the minimum expenditure of human energy.
Optimization of perception consists in creating favorable conditions for the simultaneous work of all registering organs.
The logical sequence of registering and transmitting information in the U. U. contributes to its more rapid processing by the control device. The results of the processing of information registered by the control device also depend on the amount of previously processed information stored in the U. P. The greater the volume of stored information, the greater the amount of registered information the U. U. can process. Therefore, optimization of information processing consists not only in creating favorable conditions for the work of the brain, not only in creating a logical sequence for registering information, but also in striving to preserve the maximum of previously processed information in the U. P.
A person’s U. P. has the property of constantly losing information transmitted to it for storage. Ferster, in the work “A Theory of Memory Constructed on the Principles of Quantum Mechanics,” obtained an analogue of memory on the assumption that the rate of change in the number of elements of processed and transmitted information existing at a given moment is proportional to the sum of the disappearing elements of information and the learning coefficient, which represents feedback of negative forgetting²). He obtained a mathematical dependence of the share of preservation of information registered and transmitted after processing on time in the form of an exponential tending at infinity toward a certain established share of preservation of transmitted information. The steepness and magnitude of the established share of preservation of transmitted information are characterized by the coefficients of forgetting and memorization, which are constant quantities for an individual memory device under definite conditions. One of the conditions for obtaining a lesser steepness and a greater magnitude of the established share of information preservation is an abrupt change in the content of the registered information periodically every 30–50 minutes. This is explained by the entry of new neurons into the process of information processing³).
It should be noted that the established share of preservation of transmitted information, obtained theoretically by Ferster, will in practice also decrease if an incomparably large interval of time is taken into account. It is natural to suppose that this decrease will be characterized by an analogous exponential curve derived by Ferster, but with incomparably less steepness.
Woodworth’s experiments made it possible to draw the important conclusion that, with repetition of the registration, processing, and transmission into the U. P. of lost information, the exponential tends at infinity toward an increased value of the share of preservation of transmitted information. With repeated repetitions, the value of the share of preservation of information tends toward unity. It is advisable to carry out repetitions at time intervals equal to 2–3 days. In this case, the increase in the share of preservation of information and the decrease in the means for repetitions as a function of time will be characterized by an exponential law. Moreover, the first 3–4 repetitions make it possible to obtain a value of the share of preservation of transmitted information up to 0.9, and the time of these repetitions will be approximately equal to the time of information processing during the first registration⁴).
Hence follows the conclusion that periodic repetitions are necessary for the registration, processing, and transmission into the U. P. of lost information. This will make it possible to preserve the maximum of initially registered informa-
²) S. Beer. Cybernetics and Management of Production. Moscow, 1965.
³) A. N. Luk. Memory and Cybernetics. Moscow, 1966.
⁴) R. Woodworth. Experimental Psychology. Moscow–Leningrad, 1950.
mation and, consequently, to accelerate and increase the volume of processing of information registered in the future.
It also follows from the foregoing that the existing method of assessing knowledge in higher education is not objective, since it does not make it possible to distinguish established knowledge from temporarily existing knowledge. For an objective assessment it is necessary to take into account the number and effectiveness of repetitions of the registration, processing, and transmission of lost information.
The formation and content of control commands also depend on the volume of information processed and stored in the M.D. and on the ability of the learner to reproduce it. There are three levels of reproduction of information from the M.D.: reproductive, when the stored information is reproduced completely without any assistance; recognitional, when the information is reproduced completely only after a sample of this information has been shown; facilitating, when the information is reproduced completely after a brief repetition of it2.
In higher education, knowledge is assessed mainly by the reproductive level of memory. Preserving processed information at this level is considerably more difficult and requires more time and resources from the learner. At the same time, instructional material in higher education also contains such elements of information that can be assessed at the recognitional and facilitating levels of reproduction, since these elements very rarely affect the content and formation of control commands. This will make it possible to obtain a reserve of time and resources for the registration, processing, and preservation of an additional volume of information.
In order to increase the effectiveness of physical labor, man uses various machines that increase the force and speed of the actions of his E.D. upon nature.
An analogous amplifier, an amplifier of the mental labor of learners, is the teacher. The teacher is also a complex self-organizing system, which differs from the learner’s system by the large volume of processed and stored information in the M.D. For the teacher, the object of control is the learner, who is a part of nature upon which it is necessary to act in order to obtain products of labor, and also to register the results of the action with the learner’s E.D. for the purpose of processing, preserving, and forming more effective control commands. For the learner, the C.O. is the teacher, who is likewise a part of nature with a purposefully acting E.D., the results of which the learner must register for the purpose of processing, preserving, and forming more effective control commands. If the teacher’s action on the learner is characterized as a direct connection, then the learner’s action on the teacher is a feedback connection. Considering the two types of action in unity, we obtain a more complex cybernetic system—the system of instruction.
The actions of the teacher’s E.D. can be registered simultaneously by several learners, which indicates the possibility of mass instruction. The actions of each learner’s E.D. can be registered with the aid of special sensors and control automata. With the aid of a computer, the registered information can be rapidly processed and supplied to the teacher’s C.D. In this case, the time for processing, preserving, and forming control commands for the teacher will be greatly reduced and will relieve the teacher’s M.D. of memorizing unneces-
…additional information, which resolves the question of the possibility of mass, effective instruction.
Taking into account the need to repeat information lost after its first registration, processing, and retention, it is useful to organize the management of instruction in such a way that, after the students’ first assimilation of one topic of the teaching material, the time needed for repetitions is planned; that is, instruction is carried out step by step.
Molibog, in his work Programmed Instruction3, relying on the experience of Belorussian higher educational institutions, concludes that repetitions should be consistently carried out, at certain intervals of time, through students’ stages of independent work, self-checking and consultation, and practical work. In this case the first perception (lectures) and the stages of repetition imitate the process of the movement of information within the learner, which consists in the registration, processing, retention, and reproduction of information.
The mathematical description of the learning process, and its possibility, shown in the work of V. I. Petukhov, Regulation Processes in Models of Learnability4, and in the above-mentioned work of Ferster, will make it possible to construct a model of the educational process both for the consecutive study of academic disciplines and for their parallel and consecutive-parallel study. The input quantity of the model is the speed of movement of the controlling information created by a device imitating the action of the teacher. The output quantity is the quality of the reproduction of information created by a device imitating the action of the learner. With the help of feedback, the quality of reproduction is stabilized by changing the input quantity—the speed of movement of information.
In connection with the constant growth of scientific and technical information, the learning process will be effective only if the speed of movement of information created by the teacher continuously increases. The limit of the increase in speed is the magnitude of the growth of scientific and technical information in the specialty being studied.
The increase in speed is proportional to the increase in the quality of the reproduction of information by learners. Therefore, the growth in the effectiveness of the learning process is conditioned by an improvement in the quality of the reproduction of information by learners, which depends on the content of the teacher’s controlling information, on the effectiveness of registration, processing, and retention by learners—some methods of optimizing which were set forth above.
With the aid of a model of the learning process one can obtain a graphical curve of the accumulation of the volume of processed, retained, and reproducible information of the learner over the period of study, for example, at a higher educational institution. This curve is a part of an exponential curve, since the learner had, before entering the higher educational institution, a certain volume of information, and after graduation the accumulated volume of information will increase. Ideally, the process of accumulating information may be represented in the form of a straight line inclined to the abscissa axis at a certain angle, characterizing the maximum possible speed of movement of the controlling information created by the teacher. With constant optimization of the learning process, the part of the exponential curve will approach the ideal straight line, i.e., decrease its steepness.
Let us provisionally call the product of time and the volume of information capable of reproduction real assimilation, and the product of time and the volume of information that could become capable of reproduction possible assimilation. Then the area between the exponential curve and the abscissa axis characterizes real assimilation, while the area between the ideal straight line and the exponential curve characterizes possible assimilation. The area of possible assimilation is formed at the expense of the time required for repetitions, and also at the expense of the results of incomplete processing of the recorded information. The limit of optimization will be the state in which the area due to incomplete processing of the recorded information disappears. In this case the exponential curve will divide the entire area into the area of real assimilation and the area of possible assimilation, determined only by the necessary time for repetitions.
If the time required for repetitions is reduced, the area formed by the results of incomplete processing of information is much larger than the area formed by the reduction in repetition time. This is explained by the fact that incomplete processing of once-recorded information entails incomplete processing of each subsequent logically connected item of recorded information. In this case, the unassimilated volume of information will grow continuously, increasing the area of probable assimilation and decreasing the area of real assimilation, which is highly undesirable.
If the topics of all academic disciplines that students must study are represented as operations with events of beginning and completion, as is done in network schedules, and if the logical sequence of study of these topics is found, then with the aid of a digital computer one can construct a set of network plans for the sequential-parallel study of the topics of all disciplines. With the aid of a model of the instructional process, one can, in a short time, obtain graphical curves of the accumulation of the volume of processed, retained, and reproducible information by students. The optimal network plan should be considered the one whose graphical exponential curve most closely approaches the ideal straight line of information accumulation. With the aid of the model, one can quickly test the influence of changes in the organization and management of the instructional process on the amount of instructional material assimilated by students, and also obtain a network plan taking the changes into account, which is especially important for educational institutions where the instructional process lasts 3–6 years.