TEACHING MACHINES

Yu. K. Petrov, V. M. Razin

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

At the beginning of our article we shall try to answer the question of how a machine can teach, and not simply teach, but teach optimally, i.e., as quickly as possible depending on the individual abilities of the learner. Let us consider how a machine built by the English scientist Pask works for teaching operation on a perforator. A perforator is a keyboard device for punching coded holes in a paper tape; by means of the coded holes, information is entered into a digital computer. Below are the impressions of a specialist in the field of cybernetics who himself was trained on Pask’s machine [1].

“Before you is a perforator with blank keys, since you must learn to work ‘blind.’ Before your eyes there is also Pask’s machine, connected to the perforator; on the machine you see a small window and a row of red lamps arranged in the same order as the keys of the perforator. The digit ‘7’ appears in the window. For you this is a command to press the ‘7’ key. But you do not know which key it is. Look at the lamps: one of them lights up brightly, indicating to you the position of the ‘7’ key, which you now find and press. Next, another digit appears in the window, another lamp lights up, and so on. Gradually you begin to remember the arrangement of the digits on the keyboard, and in this way your reactions become faster. Meanwhile the machine evaluates your reactions and constructs its own probabilistic model of your learning process. This model takes into account, for example, that you now type the digit ‘7’ without any delay, while the digit ‘3,’ for some unclear reason, constantly causes you difficulty. The machine detects this and takes it into account in constructing the model, reporting the result to you through a feedback circuit. Digits that present difficulties for you appear with ever-increasing frequency among the otherwise random presentation of digits. At the same time they are held for a longer time, as if saying to you: ‘Do not hurry.’ Conversely, digits that present no difficulty for you change at a much greater speed, i.e., the speed of digit presentation is a function of the state of the learning process. The system of red signal lamps behaves in an analogous way, since as you learn where the digit ‘7’ is located on the keyboard, the light stimulus gradually weakens. The teacher, as it were, gives you fewer and fewer hints toward the correct answer. Soon, provided that you continue to improve your knowledge of the arrangement of the dig-

“7,” the signal lamp corresponding to this digit stops lighting up altogether. The lamp corresponding to the digit “5” also lit up more and more dimly as you learned the position of this digit better and better. But unexpectedly a complete gap in your knowledge has been discovered—the digit “5” is not being guessed by you at all. Your teacher notices these new errors, and the digit “5” is presented to you again at a slower pace and with particular insistence, while the red optical signal again lights up with its former brightness.”

The process of instruction consists of a series of successive elementary acts. In each act of instruction the machine communicates a certain amount of information to the learner and asks a question; by answering it, the learner informs the machine about the degree to which the material has been mastered. The machine analyzes the learner’s answer and proceeds to the next elementary act of instruction. As a result of such a mutual exchange of information, the person masters the material, while the machine changes the order in which the information is presented so that poorly mastered material is presented more often and in greater detail, and well-mastered material less often and in less detail. Thus one may speak of mutual learning, or mutual adaptation, of the teaching machine and the person. In many machines the degree of correctness of the answer is communicated to the student after each elementary act of instruction. An evaluation of the work stimulates the student’s efforts; therefore it is recommended that it be communicated to the student as often as possible. In the present example, the evaluation of the correctness of the actions is given at the end of the instruction and in negative form: the prompting lamp goes out.

When one moves to machine instruction, many different problems arise.

The subject of instruction is programmed. In other words, it is divided into portions corresponding to the elementary act of instruction, and a control question is prepared for each portion of knowledge. Such work is useful not only in machine instruction, but also in compiling programs for any course.

In teaching machines, the presentation of information to the learner is carried out by various means: by means of cards, projection devices, magnetic recording, in the form of a television image, etc. In the example given, the digit that the operator must punch is illuminated, and a lamp indicating the position of the key to be struck lights up.

The input of the learner’s answer into the machine constitutes an independent problem and is the main difficulty in designing teaching machines. An ideal teaching machine should “understand” the learner from spoken words or determine the correctness of the answer he has written. At present, work is being carried out both in the Soviet Union and abroad on entering information into a machine from typewritten text and from speech, but reliably operating devices do not yet exist. The difficulty lies in the ambiguity of representing such information. For example, the letters even of printed text, not to mention handwritten text, have different configurations and printing defects; and any thought constituting a correct answer may be expressed in the most diverse verbal and grammatical forms. If the machine is not able to understand a human being, then perhaps it is simpler to teach the human being the “language” of the machine? It is difficult to call effective a method of instruction in which the student is obliged to master information that does not constitute the subject of instruction; nevertheless, at the present level of development of applied cybernetics, it is necessary to proceed to some extent along this path as well. In computers, information is stored and processed in binary discrete form. In such

form the machine is able to perceive it “without translation.” In the example given, information is entered in binary form. Each key can be in two states: pressed and not pressed; therefore no input problems arise. Let us note that in this example the pressing of a key is also the subject of instruction. In other cases the pressing of a key is not the subject of instruction, yet the keys still have to be entered. For entering an answer into the machine, the method of choice is widely used: together with the problem several answers are entered, one of which is correct, and the student is asked to press the button with the number of the correct answer. The problem of ambiguity is bypassed here in a somewhat unexpected and, at first glance, not entirely acceptable way, since the correct answer is communicated to the learner. True, it is masked, hidden among the incorrect answers. It should be noted that with skillful programming this masking is quite successful. Figure 1 gives an example of such a question with answers [2]. In this example the correct answer is \(i=-3a\). The choice system can also be used for answers in verbal form.

Most universal digital computers have input of information in numerical decimal form. Therefore, those courses for which all correct answers to questions can be given in an unambiguous numerical form can already now be converted to a machine version of instruction; in this case the need for a choice system disappears. Especially easy to convert to a machine version are those instructional courses in which the answer is given in binary form, i.e., in the “language” of digital computers. On the basis of Pasck’s machine, for example, one can organize the training of programmers in the command system of the “Minsk-1” electronic digital computer or of any other electronic digital computer. There are 101 such commands on the “Minsk-1” electronic digital computer, and memorizing them is quite difficult. The operation of the teaching machine can be described as follows. The machine issues commands in verbal form and prompts the machine code in binary form. In response to the task, the learner enters the digital code of the program into the machine. In the process of adaptation, in the general random stream of commands the machine begins to issue more often the commands that are poorly learned; by the end of successful instruction the prompt disappears.

Determine the magnitude of the current \(i\).

Answers:

1. \(-5a\)
2. \(-3a\)
3. \(1a\)
4. \(3a\)

Fig. 1.

Let us turn to the question of how a teaching machine adapts to the abilities of the student. In Pasck’s machine the subject of instruction is the development of a sum of independent conditioned-reflex movements, brought to automatism, which must arise in response to a random stream of digits. Such a random stream of digits is the information entered into the machine. The machine has a device for issuing tasks in random order. In the machine there are capacitors that are recharged in jumps by a small amount with each correct answer and slowly discharge exponentially through large resistances. If the student makes an error, the capacitors discharge quickly. As the charge of a capacitor increases, the brightness of the prompting lamp decreases, the duration of the pause for the corresponding movement decreases, and the number of corresponding questions decreases.

In many courses, the performance of subsequent assignments depends on assimilation of all the preceding material. In these courses the program is constructed so that portions of the material are issued in a definite sequence. The machine can be adapted to the learner in the following way: judging from the learner’s answers, the machine records which part of the preceding material has been poorly assimilated; the poorly assimilated material is then issued to the student again. For example, if to the question in Fig. 1 the student answers \(i = 1a\), then the machine gives the learner that part of the material in which the rules for denoting currents by arrows are described.

Sometimes, in order to take into account different abilities to perceive the subject of instruction, programs are built according to branched parallel systems, so that each portion of the material is composed in several variants. The machine begins to issue the material in the minimum amount, gradually increasing it until the student answers the question. In this way the machine “determines” the learner’s abilities. The next portion of the material is issued to the learner in an amount corresponding to his abilities. The tendency toward an optimal, or time-minimal, learning process may be expressed by the fact that with each step the volume of material is somewhat reduced.

The functions of adapting a teaching machine to the learner’s abilities are performed especially well with the aid of general-purpose digital computers. To adapt an electronic digital computer for instruction, it must be supplemented with devices for input and output of information. Converting any course into a machine version requires the joint efforts of at least three specialists: a pedagogue-methodologist to program the instructional material, a specialist in radio engineering and computer technology capable of designing and interfacing the auxiliary devices with the machine, and a programmer to compile the program that determines the sequence in which the instructional material is issued to the learner. Work has been carried out on developing instructional courses on a digital computer [2]. The instructional course was programmed according to a branched program. As a result of statistical processing of material on the instruction of many people, the volume of material that is successfully assimilated by the majority of students was determined. Instruction in courses developed in this way was conducted by the ordinary lecture method; the duration of training was shortened and performance improved. If such work is conducted at a high methodological level and the results are introduced on a broad scale, the quality of teaching can be raised considerably.

A complete transition to instruction with the aid of digital computers does not seem effective to us, at least at the present level of development of computer technology. On the one hand, owing to its very high speed, a single teaching machine based on a general-purpose electronic digital computer can serve many students; of course, for this it must be equipped with an appropriate number of input-output devices. Let us recall that such devices include tape recorders or a projector and are, in themselves, fairly complex technical devices. The machine can serve each student optimally in accordance with his individual characteristics. The possibility of such individual service consists in a continuous exchange of information between the learner and the machine. It is impossible to organize a continuous exchange of information in the lecture method of instruction; therefore the machine method of instruction appears more effective. As the practice of using teaching machines shows [2], with machine instruction the duration is shortened.

training, and academic performance improves. On the other hand, a modern universal digital computer has about 10 service personnel, and this number will apparently have to be increased in order to service the terminals. To this must be added the labor costs of manufacturing the computer and the terminals. If we assume that 25 people are being taught on the machine simultaneously, it follows that approximately one person is working for each student. Of course, if one teacher is assigned to each student, the effectiveness of teaching increases beyond comparison with either machine or lecture instruction. Let us add that programmed textbooks are published for the independent study of courses. In such a textbook, the material is printed on one side of the page and an assignment is given. The student completes the assignment and turns the page. On the opposite side of the page an instruction is printed. If the answer is correct, the student is invited to proceed to the next assignment. If the answer is incorrect, the instruction directs the student to the corresponding material for repeated study. Thus, the textbook contains a program compiled for machines. There is evidence [2] that the effectiveness of instruction by means of programmed textbooks is no worse than by means of teaching machines.

Teaching machines with an analog mechanism of adaptation, to which Pask’s machine also belongs, are simple in design, inexpensive, and do not require constant servicing. Such machines have found wide application in military conditions and in production [2], where weapons and technological procedures often change and it is necessary to retrain service personnel quickly.

The simplest teaching machines operate according to an unbranched program, and the answer is entered into the machine by means of selection. In the simplest tutors, the order in which the material is presented remains unchanged, and after each assignment a signal indicating the correct answer is given. In the simplest examiners, a random order of presenting questions may be used, and after several answers a grade is given at the end of the examination. Such machines are manufactured in many institutes of the Soviet Union and may find wide application in the practice of teaching students, in secondary school, and even in everyday life. The effectiveness of such machines is determined mainly by the skill with which the programs are composed; therefore, the best methodologists must be involved in programming, and mass production of programmed courses must be organized, which, apparently, is possible only if the cottage-industry production of small teaching machines is replaced by the serial production of standardized models.

A standard machine must be universal, i.e., adapted to instruction according to any program. The following method of instruction by means of small machines may be proposed. Courses are issued on motion-picture films. Each frame contains the instructional material, an assignment, several answers, including the correct one, and, in encoded form, the number of the correct answer. The student places the film in a device of the simplest filmoscope type, views the frame and, after completing the assignment, determines the number of the correct answer and presses a button. The device is supplied with a decoder of the correct answer, which is actuated by the button and lights a lamp with the number of the correct answer. The student compares his answer with the correct one, draws conclusions, and advances the frame. If the frame advance and the decoder are made manual and based on semiconductor devices, such an apparatus can be very simple and inexpensive. In film courses, stereoscopic

scopic images, which are especially useful in studying such subjects as stereometry in secondary school and descriptive geometry at an institute. The aesthetic aspect of this question should be taken into account, and color film courses should be produced whenever possible and necessary.

At the Department of Mathematical and Computing Instruments and Devices, the students themselves are constructing an automatic assignment machine for the practical study and testing of film courses. The device operates according to the scheme of the simplest tutor. A film course consisting of 15 question-and-answer items is inserted into the device. The device is equipped with a printing unit which, for each question, records the number of the correct answer, the number of the button pressed by the student, and the time spent by the student on the answer. It is assumed that the machine will operate without constant service personnel, while the quality and assimilation of the material can be judged from the printed information.

With the broad introduction of small teaching machines and appropriate organization, some practical classes can be assigned for independent study. It is advisable to concentrate film courses in an institute-wide film library with a reading room equipped with the simplest machines. Assignments based on film courses can be issued by the lecturer. Work on the assignment is completed by a credit test with the aid of a machine examiner. The lecture material should end with an ordinary examination. Moreover, if one question is added to the lecture questions in which the student sets out the logic of the solution of one of the problems from the film course, it will be possible to avoid cases of formal memorization of the numbers of the correct answers.

In conclusion, let us note that the use of teaching machines is effective in itself, but the special benefit of introducing machines into the teaching process lies in attracting public attention to teaching methodology and to the teaching process itself.

REFERENCES

1. S. T. Beer. Cybernetics and Management of Production. Fizmatgiz, 1963.
2. Experience in the Use of Machines for Teaching in the USA. Foreign Radio Electronics, No. 9, 1962.