**4.6 Rules and methodology of modeling of dependence of prognostic competence general level depend on selected teaching model and frequency of application of prognostic activity**

Every person at least once a day makes plans for the next day. Therefore, as a very low frequency of predictive activity, we will take 7 times. If on each pair 2–3 problems of predictive nature are solved, then about 50 prediction problems will be solved. This frequency is taken as a very high level of the frequency of predictive activity. Conventionally, we distinguish the following frequency levels (once a week): very low (FX), low (F), below average (E), medium (D), above average (C), high (B), very high (A). The method is trimf.

We will designate prediction learning models as follows: lack of special prediction learning – FX, non-systemic prediction learning – F, semiotic educational model – D, simulation educational model – B, social educational model – A. Method – trimf. The range is from 0 to 100 conventional units.

The creative level of the development of predictive competence will be estimated at 100 points (A), productive – 75 points (B), reproductive – 60 points (D), formal level – below 60 points, but above 20 (F). The type of membership function is gaussmf.

We have made 16 rules of fuzzy logic. Some of them are presented below:


#### **4.7 Forecasting technology**

Forecasting is a stepwise process. The developed system of organizational and pedagogical conditions for each stage of forecasting is presented in the table format (**Table 2**).

## **5. Results**

The result of modeling in the format of 3D projections of multidimensional dependence of general level of prognostic competence are presented in **Figure 2**. The projections onto the 2D plane are shown in **Figures 3**–**6**.

We see the complex nature of the dependence at all intervals. Competence is an integrative quality of a person, therefore it is more correct to interpret it according to the totality of all known factors, and not to look for the dependence of only some indicators on others.

The dependence of the formation of competence on the cognitive component has a stepwise nature, i.e. on a number of intervals, it practically does not depend

#### **Figure 2.**

*The dependence of the final value of the level of formation of predictive competence on the level of formation of motivational and activity components.*

#### **Figure 3.**

*The dependence of the final value of the level of development of prognostic competence on the level of formation of the cognitive component.*

on external conditions and efforts of both students and teachers, but in the middle of the range, the level of competence is extremely dependent on cognitive efforts, quantitative characteristics dialectically turn into qualitative ones, so teachers should be as attentive as possible.

The dependence of the formation of competence on the activity component (**Figure 4**) is of the most complex nature, and advice can be given at each section of the level of formation. So, in the section from 30 to 50%, there is a maximum increase in qualitative changes with an increase in the number of solved prognostic problems, but then the slope angle decreases, although in any case the more we do prognostics, the greater the positive effect is observed. Every effort must be made to go from 90–100%.

#### **Figure 4.**

*The dependence of the final value of the level of formation of predictive competence on the level of formation of the activity component.*

#### **Figure 5.**

*The dependence of the final value of the level of formation of predictive competence on the level of formation of the motivational component.*

Motivation for forecasting also has a "stepwise" effect: a low level of motivation is identical to its absence, it is impossible to distinguish between the level of motivation "above average" and "high". There is a dichotomy: the student is motivated - he learns to forecast, not motivated - he is not taught.

As in the previous graphs, we see a stepwise level of dependence of futurological skills on sociability. The student is able to form the skill of forecasting only in communication: with the teacher and classmates.

The result of modeling of development of prognostic competence depend on the most factors is presented on **Figures 7**–**11**.

#### **Figure 6.**

*The dependence of the final value of the level of formation of prognostic competence on the level of formation of the communicative component.*

Pedagogical factors have the most important influence on the level of competence formation. Transitions from reproductive to productive, and from productive to creative are not possible without a mentor, although within these levels the teacher can have only minimal influence. Since there is a "plateau" on the graph.

Forecasting can be taught to almost any student, but for a qualitative transition to a new level of proficiency in futurology, you need to create a special psychological climate, so without a mentor it is difficult to independently learn predictions.

**Figure 7.** *The dependence of the formation of prognostic competence of pedagogical factors.*

**Figure 8.** *The dependence of the formation of prognostic competence of psychological factors.*

**Figure 9.** *The dependence of the formation of prognostic competence of socio-economic factors.*

A low level of socio-economic security means a poor skill in the formation of predictive competence, and any minor improvements in the economic component significantly improve futurological skills. However, with an average level of social security, there is an insignificant plateau, at which an increase in the economic wellbeing has practically no effect.

As indicated in the previous modeling, in **Figure 4**, the activity has a significant improvement in predictive skill at all intervals. Thus, the two different models confirm each other.

Up to the achievement of a productive level of prognostic competence by a student, all teaching methods are equally effective, but in further training,

**Figure 10.** *The dependence of the formation of prognostic competence on the frequency of application of prognostic activity.*

**Figure 11.** *Dependence of the formation of the prognostic competence of the technique used.*

the selection of the correct individual trajectory for teaching foresight skills is extremely important, because any minor changes in the teacher's behavior model can lead to synergistic changes ("bifurcation point") in learning outcomes. One should "sensitively" feel all the changes in the student's achievements, because the dependence has a rather complex non-linear character.
