Some Issues in the Management of the Educational Process

M. S. Aleinikov, T. Yu. Aleinikova

(Presented by the section of the Faculty of Automation and Electromechanics of the methodological conference of TPI)

At present, questions of improving the quality of training of specialists graduating from a higher educational institution are being given enormous importance.

It is known a priori that the quality of specialist training depends on the qualifications of the teachers, the material and technical support of the educational process, the general preparation of the secondary-school graduate who has entered the higher educational institution, the student’s striving to obtain the maximum of knowledge, i.e., on his independent work and academic discipline, by which is meant the student’s attendance of compulsory classes. Considering the student as the “object of control,” one may propose the following scheme for controlling this “object” (Fig. 1).

Fig. 1.

The “object of control” is in state \(C\) (a first-year student with his level of general-education preparation); it is acted upon by the input signal \(X\) (a group of teachers) and the disturbance \(Z\) (illness, living conditions, shortage of textbooks and teaching aids, imperfection of the educational process, etc.). After some time the “object” passes into state \(C_1\) (transfer to the next year of study), and at the output of the “object” we have the quantity \(Y\) (the student’s academic performance, his moral character, political tempering). By repeating many times (over the course of five years of study) the control process, they strive to obtain the desired \(C_{\text{ж}}\) and \(Y_{\text{ж}}\), i.e., to obtain an engineer meeting the requirements of society. Note: by \(X\), \(Y\), \(Z\) is meant an aggregate of influences. In group instruction, by \(C\) is meant the aggregate of states of an individual member of the group.

Since a student studies not alone, but is in a group of students, the control scheme presented in Fig. 1 should be considered as applied to the student group and should take into account all pri-

existing internal links in this group. Taking internal links into account, the control scheme becomes extremely complex. Still more complex control systems are the faculty and the institute. Thus, in managing the educational process we are dealing with a very complex control system—so complex that the system does not lend itself even to an approximate mathematical description.

In their work, instructors, heads of subdivisions and public organizations, and the rector’s office of the institute adopt various decisions on managing the educational process, relying mainly on their own experience and intuition and being guided by the legislation in force.

For the purposes of formalizing problems of managing the educational process, it is very important to study the processes of intuitive decision-making for achieving a stated goal under conditions of some poorly defined situation. In recent years a scientific field has developed that is called “artificial thinking.” “Artificial thinking” includes the processes of recognizing images and situations, learning, and constructing conjectures. All these processes are observed, to one degree or another, under conditions of intuitive decision-making [1].

It is obvious that applying the method of “artificial thinking” for purposes of managing the educational process in an institute, i.e., for constructing an automated control system (ACS) for the educational process, requires the broad use of computing technology. Under the conditions of the Tomsk Polytechnic Institute, application of an ACS to the educational process as a whole is at present impossible, since there is no mathematical support or technical equipment. However, the institute has a subsystem of the ACS of the educational process, which includes optimization of curricula and programs, preparation of class schedules, distribution of teaching loads, and monitoring of students’ current academic performance and discipline. In order to ensure that the correct decision is made in managing the educational process, i.e., to develop a controlling influence for achieving the stated goal, it is necessary to have a mathematical description of the process. As noted above, it is impossible to obtain a mathematical description of the educational process. But it is possible to obtain a mathematical description of certain interrelated processes.

We have attempted to obtain a mathematical dependence of the average student’s average academic performance on preparation (academic performance in previous years) and attitude toward study (independent work and academic discipline).

The dependence of the performance of an “average” student was modeled by the expression:

\[ y=c(a_{01}+a_{11}x_1)(a_{02}+a_{22}x_2)(a_{03}+a_{33}x_3), \tag{1} \]

where \(y\) is the academic performance of the “average” student in the subsequent semester (averaged grade);

\(c\) is the academic performance of the “average” student in the semester under study;

\(x_1\) is the academic performance of the “average” student in previous years, including the grades received on entrance examinations;

\(x_2\) is the average daily workload of the “average” student in independent work, in hours, obtained from questionnaire data in the semester under study;

\(x_3\) is the number of absences of the “average” student in the semester under study.

Since (1) is used to predict the academic performance of each student according to the “average” student, then in calculating the coefficients

level (1), the averaging method was used, in particular the method of D. D. Brandon [1].

To obtain the mean values of \(c, x_1, x_2, x_3\), questionnaire data from a survey of each student on the amount of independent work, records of academic performance in previous years and in the semester under study, and data from the register of student attendance were used.

As a result of calculating the coefficients by D. D. Brandon’s method, the following equation was obtained:

\[ y = 3.34 + 0.465x_2 + 0.254x_1 - 0.105x_3 + 0.0354x_1x_2 - \]
\[ {} - 0.008x_1x_3 - 0.0146x_2x_3 - 0.00112x_1x_2x_3. \tag{2} \]

Using equation (2), we predicted the academic performance of the “average” student for two study groups. The prediction was made on the eve of the winter examination session of the 1970/71 academic year.

For the first group, the average grade calculated from equation (2) proved to be 4.12, and for the second, 4.2. The actual average grades based on the results of the examination session proved to be, respectively, 4.06 for the first group and 4.08 for the second.

Prediction of the academic performance of each student in the groups under consideration using equation (2) gives results coinciding with the actual grade for approximately 70 percent, while for 30 percent the prediction results differ significantly from the actual grade. This fact is explained by the circumstance that, in constructing the model, not all factors influencing academic performance were taken into account.

Thus, using Brandon’s method, it was possible to obtain an adequate model describing the dependence of students’ academic performance on such factors as the student’s prior preparation and his attitude toward study. An analogous model can be obtained for each student; for this it is necessary to have information about the state of the “object.”

The model for each and for the “average” student will have a variable structure, i.e., variable coefficients that change over time. By organizing the collection of the corresponding information about the factors influencing students’ preparation and its prompt processing, taking into account disturbances and student adaptation, it is possible at each specific moment in time to have an adequate model; by analyzing it, one can develop control actions on the study group and on each student in order to achieve the desired results.

Conclusions

1. Considering a group of students as a system (object), and teachers as a set of input actions, it is impossible to apply regular methods of studying the system in order to obtain a mathematical description of the system’s behavior. Only by applying the method of “artificial thinking” can one speak of constructing controls \(X_1, X_2, \ldots, X_n\) under conditions of the existence of disturbances \(Z_1, Z_2, \ldots, Z_n\), under which the socially required behavior of students \(Y_1, Y_2, \ldots, Y_n\) is achieved and transferred into the state \(C_1, C_2, \ldots, C_n\) [1].

2. Some processes in the education of students lend themselves to mathematical description. By using the mathematical model of these processes and introducing them into an automated control system, one can ensure the development of operational control actions for achieving the stated goal.

1. By applying the method of “artificial thinking” together with the method of mathematical modeling, it is possible to create flexible feedback in an automated control system for the educational process.

REFERENCES

1. A. M. Letov. Study of problems of management in the social sphere (based on materials from certain works by U.S. scientists). Avtomatika i telemekhanika, 1971, No. 1.

2. V. M. Ordyncev. Mathematical description of automation objects. Mashinostroenie, 1965.