On technical aspects of external and internal motivation

Annotation: The article discusses the student’s personality in the light of the theory of automatic control, where external and internal motivation is a controlling and disturbing influence. The technical aspects of motivation are considered, possible methods of increasing students' motivation are proposed.

One of the problems of current education is the low level of student motivation. It is no secret that most of the graduates of prestigious (and not only) universities go to work not in their specialty. The main reason, according to the authors, lies in the fact that during the course of study, the student was not sufficiently interested in the subject of study. As a result, the level of his internal motivation, after leaving the school, is not enough to get a job where the knowledge gained could be useful.

Consider motivation as a force pushing a student to increase their own level of development. Suppose there is a course of information of a certain volume and a certain duration, which a student must master. Imagine that a student is at a certain current level of knowledge, and the task of the teacher is to increase the level of knowledge of the student to a certain “height” $$$h$ for a certain time $$$t$ (picture 1).

Figure 1: The effect of different forces on the student
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Conditionally, you can compare the task with the body lifting along an inclined plane (we will assume the friction on the surface is zero). The student at this moment there are two forces:

1. Strength of motivation $$$F_m$ whose task is to ensure that the student has reached a higher level of knowledge;
2. Strength of degradation $$$F_d$ which will determine the student’s desire to return to the current level of development. We assume that the force of degradation is constant and does not depend on the level of student knowledge

Inclined plane has some angle $$$\ alpha$ , depending on which will be necessary to lift the power of motivation. Express the required strength of motivation:

$$

$$F_m = F_d '= F_d sin \ alpha (1)$$

Thus, the required strength of motivation increases with increasing angle of inclination. With an absolutely vertical plane, the strength of motivation will be equal to the strength of degradation.

On the other hand, the student is required to undergo some training, which is inversely proportional to the slope value:

$$

$$x = \ frac {h} {sin \ alpha} (2)$$

This path is the entire program necessary for mastering. Since the program must pass for a certain time (for example, a semester), we express the required speed of passage of the material:

$$

$$x = \ upsilon t \ rightarrow \ upsilon = \ frac {h} {t} \ cdot \ frac {1} {sin \ alpha} = \ upsilon_0 \ cdot \ frac {1} {sin \ alpha}$$

Where $$$\ upsilon_0$ - the basic rate of passage of the material, with $$$\ alpha = 90 ^ o$ .

Consider the limits of change in the speed and strength of motivation:

$$

$$\ lim_ {F_m \ to 0} \ upsilon \ to \ infty, \\ \ lim_ {F_m \ to F_d} \ upsilon \ to \ upsilon_0$$

It is known that the product of speed and force is power. In this case,

Figure 2: Graphs of the rate of study of the material and motivation on the angle of inclination
This is the power that is required to study the subject:

$$

$$P_m = F_m \ cdot \ upsilon = F_d \ cdot sin \ alpha \ cdot \ upsilon_0 \ cdot \ frac {1} {sin \ alpha} = \ upsilon_0 \ cdot F_d = const (5)$$

From (5) it can be concluded that with constant program complexity and a given time for studying it, the power required for studying will be the same for any difficulty in mastering its elementary part.

Consider the student’s learning opportunities. To do this, we introduce the following concepts:

$$$C_I$ - inertia training. It determines how inert the student is to the new information.
$$$\ lambda$ - coefficient of saturation, showing the student's ability to understand new information. Consider a simplified case where a student applies a uniform effort to master information throughout the entire period of study. Then, you can use the differential equation of order 1 and write:

$$

$$P_C - \ lambda h = C_I \ frac {dh} {dt} (6)$$

The qualitative solution of this differential equation is the function of the aperiodic link of the 1st order [1].

$$

$$h (t) = h_ {us} (1 - e ^ {\ frac {-t} {T}}) (7)$$

Figure 3: Transitional Learning Process $$$P = const$

Where $$$h_ {us}$ - the level of knowledge in the steady state at the applied power of the student $$$P_c$ , $$$\ tau$ - learning time constant. It is known that $$$T = \ tau$ the process will reach $$$1-e ^ {- 1} = 63 \%$ from the value in steady state. Behind $$$T = 3 \ tau$ the process is considered to be steady, as the current value has reached 95% of the steady state. Thus, full mastering of the subject is possible if the level of the program being mastered is lower than the maximum possible level of mastering the program by a student - the so-called saturation level, when, regardless of the energy expended, new information is no longer perceived. When approaching the level of saturation, the rate of assimilation of new knowledge gradually decreases. It is proposed to set the program level at 63% of the maximum in order for the program to be mastered during $$$T = \ tau$ . Since this section of the curve (Figure 3) is almost linear, during the entire period of time the program is mastered in equal parts, which means that the student will learn all the lesson material both at the beginning of the training period and at the end. Provides a constant rate of development of the subject.

Consider the case of preparation for the exam, when a student at an accelerated pace repeats or learns the program. To do this, we introduce the characteristic $$$K_p$ - retraining rate. This coefficient determines the student's ability to quickly store large amounts of information before testing knowledge. By solving a second order differential equation $$$a \ cdot y ^ {''} + b \ cdot y ^ {'} + c \ cdot y + d$ will be:

$$

$$h (t) = (1-e ^ {\ frac {-t} {\ tau}}) + (K_P sin (3 \ cdot \ tau \ cdot t)) \ cdot e ^ {\ frac {-t} {\ tau}} (8)$$

Figure 4: Transitional learning process with retraining

The obtained characteristic correlates with the student’s actual behavior during the session — when memorizing material during intensive preparation for the exam, depending on the student’s level of education, exceeds the saturation level — an overshoot process occurs, the value of which is determined by the retraining factor. After a while, a temporary decline occurs - some of the material is forgotten. Subsequently, the material is gradually y and the level of knowledge returns to normal.

Consider a student as a trained person from the point of view of the automatic control system [2].


Figure 5: Learned personality with a teacher

The subconscious of the person being taught adapts to changes, using the mechanism of adaptive regulation and external disturbing influences — by the teacher, the media, the party, the network, another person, etc. (Figure 5). With their help, one can replace the consciousness and subconsciousness of the overwhelming majority of members of the information society. Let us enlarge this model to the type of single-loop control system with soft feedback (Figure 6).


Figure 6: The enlarged management system of the trainee's motivation

In the initial state, the input signal of the control system is supplied $$$M_0$ - a certain level of self-motivation. With the help of the subconscious, acting as a regulator with a transfer function $$$W_P (P)$ the signal arrives at the power element (consciousness) with the transfer function $$$W_m (p)$ , which, as shown above, is close to a second-order aperiodic link. At the output of the power element, a signal of motivation to action appears directly. Through the feedback link signal $$$M_ {os}$ enters the adder. The task of the regulator is to minimize the error. $$$\ xi = M_0 - M_ {OS}$ between the driving force and the feedback signal. The system enters static mode. Consider two possible variants of external disturbance (Figure 7):

Figure 7: Possible options for the external motivation of the person being trained

1. The motivation signal is added to the self-motivation signal. Below it will be shown that this option is correct;
2. In the second case, the motivation signal is supplied outside the control system and, at the first approximation, does not affect its state. In practice, such an impact leads to a change in the parameters of the result of motivational activity, which in turn can affect your own level of motivation. In simple terms, the competition between two individuals begins.

Let us consider in more detail the first case. It is technically impossible to apply external motivation to the same input as the internal one. It is necessary to consider this process from a different point of view (Figure 8):

Figure 8: Impact of extrinsic motivation on self-motivation

External motivation supplied to the input of the system controls the regulator of its own motivation. Thus, one of the tasks of the teacher is the selection of parameters and ways to enhance self-motivation. It is the impact on self-motivation that is one of the most effective methods of programming a trained personality.

Consider an example:

Trained personality gets a job. On the one hand, the employer is interested in the employee working as intensively as possible and trying to find a way to stimulate the result of the work (according to the employee, money if it is a bonus wage system). On the other hand, money for an employee is not the final goal of the work. The main goal of the employee is the appearance of his own apartment, gaining personal independence, a sense of self-sufficiency. Then, in the scheme $$$work \ rightarrow money \ rightarrow flat$ in matters of employee motivation, money is the extra point of the motivational impact scheme, and the scheme is simplified to $$$work \ rightarrow apartment$ . Unfortunately, as a rule, the worker himself may clearly not know his true goals. This situation is a breach in the security system - it allows you to change a person's goals by influencing. These vulnerabilities are widely used in social engineering. The correct method of programming is a joint search for the true goals of a person without modifying it - often with the involvement of a full-time psychologist. After the trainee has determined her own goals for herself, the control system begins the process of self-reprogramming and the psychoanalytic archetype from the trainee is transformed into a self-sufficient personality [3].

Speaking about student motivation, let's continue the scheme:

$$

$$knowledge \ rightarrow cum \ rightarrow job \ rightarrow money \ rightarrow flat (9)$$

Where the intermediate link is a diploma, work, money. For a more general case:

$$

$$types of knowledge \ rightarrow types of goals (10)$$

First of all, it is necessary to find out the goal pursued by the student: perhaps he wants to become a scientist, engineer or a famous person. This can be done with the help of thematic testing (Olympiad, testing "Kangaroo", vocational guidance testing before entering universities) or with the help of a student with a psychologist. On the other hand, there are some kinds of knowledge that may be useful in one way or another. It is necessary to convey to the student the connection between his goal and a set of knowledge.

Based on the data obtained, it is possible to organize an individual training program, however, such a program has its drawbacks. First of all - high complexity - in fact, a certain motivating effect is required to be applied to each student [4]. One of the simple solutions is to break up a large group of students into smaller groups, where the goals of the group members in one form or another can be brought together under a single meta-goal. In one group, there are students “students-analysts” who are strong in heuristic analysis, in the other group - “students-creators”, etc. This kind of diversification of knowledge is useful because, although the student studies the general program, he is also a narrow specialist in some his area of ​​interest. In the future, expertise in a narrow area will help the student achieve his goal.

1. Bessekersky V.A., Popov E.P. The theory of automatic control systems / V.A.Bessekersky, .P. Popov. Ed. 4th, pererabot. And add. - SPb., Profession, 2007. - 752. - (Series: Specialist)
2. Tsyganov V.V. Adaptive mechanisms and high humanitarian technologists. Theory of humanitarian systems. - M .: Academic project; Alma Mater, 2012. - 346 p.
3. Brushlinsky A.V. Psychology of thinking and problem-based learning. M., 1983
4. Verbitsky, A.A. Active Higher School Education: A Contextual Approach / A.A. Verbitsky - M .: Higher School, 1991. - 205 p.