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Executive Editor:Publishing house "Academy of Natural History"
Editorial Board:
Asgarov S. (Azerbaijan), Alakbarov M. (Azerbaijan), Aliev Z. (Azerbaijan), Babayev N. (Uzbekistan), Chiladze G. (Georgia), Datskovsky I. (Israel), Garbuz I. (Moldova), Gleizer S. (Germany), Ershina A. (Kazakhstan), Kobzev D. (Switzerland), Kohl O. (Germany), Ktshanyan M. (Armenia), Lande D. (Ukraine), Ledvanov M. (Russia), Makats V. (Ukraine), Miletic L. (Serbia), Moskovkin V. (Ukraine), Murzagaliyeva A. (Kazakhstan), Novikov A. (Ukraine), Rahimov R. (Uzbekistan), Romanchuk A. (Ukraine), Shamshiev B. (Kyrgyzstan), Usheva M. (Bulgaria), Vasileva M. (Bulgar).
Teaching science
The article deals with the pedagogical experiment of experimental proving the efficiency of the author’s mathematical model: dY = Σi [(∂Y/∂Хi )( ∂Хi /∂τi )]dτі (Хі – the factors functions of forming future music teachers’ competence ways; ∂Y/∂Хi  functions of factors importance; ∂Хi/∂τi – the speed of competence forming by the factors) [1]. The article is of interest for science.
Results and Interpretation
The pedagogical experiment in the form of a test task for students consisted of two parts: an establishing part (before teaching the practical course on forming professional competence by the means of music and computer technologies) and a forming one (after teaching students). The test task was the same and consisted of a musical dictation of a solo composition with choosing piano accompaniment for solo. The analyzing parameters are τi  the time of completing the test task; Vi – the speed of competence forming of future music teachers in courses; with a given parameter of ΔY – the newlyformed part of future music teachers’ competence that is shown in the test task. The author supposes that ∂Хi /∂τi of professional competence of future music teachers is proportional and is shown with the speed of completing the test task  Vi and taking into account that the factors parameters can be thought equal and take ∂Y/∂Хi = С, after evident changes the author gets the following model dY = СΣi (Vi )dτi for our experiment. Taking into consideration the increase dY, dτ quite insignificant regarding the functions on a quite limited interval of the function Y, that is real concerning the test tasks, as a result the author receives the following model: ΔY = СΣi (Vi )Δτi. Taking particular parameters: С = 1, when ΔY = 1, the simple average Vi equals V0 , the author gets such a model as: ΔY = V0 Σi Δτi. Thus, knowing the parameter of V0 (experimentally defined during studies) it is easy to calculate the time Σi Δτi of competing the test task by each student. Theoretical and experimental researches are shown in the table.
Students 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 

The establishing experiment 
Σi Δτi min 
45 
37 
32 
56 
49 
51 
43 
41 
59 
65 
45 
40 
50 
55 
56 
62 
The forming experiment 
Σi Δτi min 
39 
29 
30 
47 
36 
41 
27 
27 
33 
44 
27 
30 
44 
41 
39 
49 
V0 х102 min 1 
3,3 
3,1 
4,0 
2,6 
2,9 
2,4 
3,9 
3,8 
3,0 
2,4 
2,9 
2,9 
2,4 
2,5 
2,3 
2,0 

Model calculations 
Σi Δτi min 
30,3 
32,3 
25,0 
38,5 
34,5 
41,7 
25,6 
26,3 
30,3 
41,7 
34,5 
34,5 
41,7 
40,0 
43,5 
50,0 
The model efficiency was evaluated by Fisher criterion – comparing dispersion of test grades of both establishing and experimental (σ2est, σ2exp) on the level of importance 0,05. Using F criterion the author finds Femp = σ2exp / σ2est = 856 / 774 = 1,11. Using the table of F criterion with freedom levels equaling k =16  1 = 15 the author receives Fcrit = 2,3 , that increases Femp = 1,11, therefore, using the terms of statistic hypotheses it can be stated that the hypothesis about sampling similarities is accepted and the efficiency of the mathematic model competence forming of future music teachers was proved.
Сonclusion
Carrying out the pedagogical experiment the efficiency of the mathematic model of competence forming of future music teachers by the means of music and computer technologies was proved; the technologies lead to the improvement of professional competence level; it was proved by less time for task completing by the students who took part in the pedagogical experiment.
Platon Zavgorodniy THE PEDAGOGICAL EXPERIMENT TO PROVE THE MATHEMATICAL MODEL OF FORMING PROFESSIONAL COMPETENCE OF A FUTURE MUSIC TEACHER. International Journal Of Applied And Fundamental Research. – 2014. – № 2 –
URL: www.sciencesd.com/45724618 (14.12.2019).