PattERn REcognItIon: dEscRIPtIon oF modEs oF tEacHIng Boys agEd 7 tHRoWIng a small Ball at a vERtIcal taRgEt

The study purpose was to determine the possibility of using pattern recognition methods to study the impact of physical exercises modes on teaching primary school children throwing a small ball at a vertical target. Materials and methods. The study participants were boys aged 7 years (n=48). The paper relied on analysis and generalization of data of scientific and methodological literature, general scientific methods of theoretical level, such as analogy, analysis, synthesis, abstraction, induction, as well as general scientific methods of empirical level: observation, testing, experiment. results. The effectiveness of teaching boys aged 7 “throwing a ball at a vertical target” is positively influenced by 6-12 sets, 3 repetitions per set, rest interval of 60-180 seconds. The focus in choosing a teaching mode is on the number of repetitions per set. conclusions. A full factorial experiment method makes it possible to mathematically describe the process in some local area of the factorial space and to verify the regression model. Regression equations provide an opportunity to select the modes of performing for each exercise being studied. Discriminant analysis has made it possible to determine the modes of physical exercises in the process of motor skills development; to answer the question as to how significantly the modes of training differ by the effectiveness of motor skills development; what motor tasks most substantially influence the differentiation of classes; what class the object belongs to based on the values of discriminant variables. To select the most rational mode of performing exercises in the process of motor skills development in boys aged 7, the first and second discriminant functions can be used, with a focus on the most informative variables.

One of the methods for studying the peculiarities of motor skills development in children and adolescents is modeling.Modeling is an effective method to obtain new information on the possibility of current and final control through testing children's and adolescents' motor preparedness (Khudolii, & Ivashchenko, 2013, 2014;Lopatiev, Ivashchenko, Khudolii, Pjanylo, Chernenko, & Yermakova, 2017;Vlasov, Demichkovskyy, Ivashchenko, Lopatiev, Pitin, Pjanylo, & Khudolii, 2016).One of the statistical modeling methods is discriminant analysis, the data of scientific literature point to its effectiveness for the classification of children's and adolescents' functional and motor preparedness (Khudolii, & Ivashchenko, 2014;Milić, Milavić, & Grgantov, 2011;Ivashchenko et al., 2015;Khudolii et al., 2015).A full factorial experiment method makes it possible to mathematically describe the process in some local area of the factorial space and to verify the regression model.Regression equations provide an opportunity to select the modes of performing for each exercise being studied.To select the most rational mode of performing exercises in the process of motor skills development in boys, the first discriminant function can be used, with a focus on the most informative variables (Ivashchenko, Khudolii, Iermakov, Chernenko, & Honcharenko, 2018).
Therefore, it is relevant to study the peculiarities of motor skills development in primary school children.
The study purpose was to determine the possibility of using pattern recognition methods to study the impact of physical exercises modes on teaching primary school children throwing a small ball at a vertical target.

Study participants
The study participants were boys aged 7 years (n=48).

Study organization
The paper relied on analysis and generalization of data of scientific and methodological literature, general scientific methods of theoretical level, such as analogy, analysis, synthesis, abstraction, induction, as well as general scientific methods of empirical level: observation, testing, experiment.
The study used full 23 type factorial experiment plans (see Table 1).The motor modes of teaching boys aged 7 throwing a ball at a target were studied.The purpose of the FFE was to optimize the modes of teaching and to determine the peculiarities of motor skill development in boys aged 7 based on the analysis of regression equations.
During a pedagogical experiment, the researchers studied the influence of the number of sets (х1), the number of repetitions per set (х2) and rest intervals (х3) on the level of proficiency in exercises performance of boys aged 7.
When teaching throwing exercises, the study evaluated the level of proficiency during every class by the alternative method ("performed", "failed") and calculated the probability of exercise performance (p = n/m, where n is the number of successful attempts, m is the total number of attempts).
When teaching boys aged 7, the study used the method of algorithmic instructions.The next exercise ISSN 1993-7989 (print).ISSN 1993-7997 (online).Теорія та методика фізичного виховання.Том 19, № 3 was carried out after three successful attempts.Throwing a ball at a vertical target was taught.

statistical analysis
The study used well-known methods of analyzing the results of a full 2 k type factorial experiment (Khudolii & Ivashchenko, 2014;Ivashchenko, 2016).
The study materials were processed using the IBM SPSS 20 statistical analysis program.In the process of discriminant analysis, the researchers created a prognostic model for group membership.This model builds a discriminant function (or, when there are more than two groups -a set of discriminant functions) in the form of a linear combination of predictor variables, which ensures the best division of groups.These functions are built according to a set of observations, for which their group membership is known.These functions can continue to be used for new observations with known values of predictor variables and unknown group membership.
To determine the impact of the suggested modes of physical exercises for boys aged 7, a discriminant analysis was conducted.The study analyzed the influence of the number of sets, the number of repetitions per set and the rest interval on the level of proficiency in the following movements: 1. Throwing a ball against the floor; 2. Throwing a ball forward and up, feet shoulder width apart; 3. Throwing a ball forward and up, left leg forward; 4. Throwing a ball forward and up, left side to the throwing direction; 5. Throwing a ball at a 3 m distant target.
The study protocol was approved by the Ethical Committee of the University.In addition, the children and their parents or legal guardians were fully informed about all the features of the study, and a signed informed-consent document was obtained from all the parents.

Results
The results of factorial experiment are shown in Tables 2.
The analysis of regression equations showed that the level of proficiency in the first exercise "Throwing a ball against the floor" in boys aged 7 is influenced negatively by the number of repetitions per set (х 2 ) and positevely -by the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ) (see Table 2).The result in teaching depends on the number of repetitions per set (х 2 ) by 72.25 % and on the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ) -by 16 %.
The level of proficiency in the second exercise "Throwing a ball forward and up, feet shoulder width apart" is influenced negatively by the number of repetitions (х 2 ) and positevely -by the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ).The result in teaching depends on the number of repetitions per set (х 2 ) by 50.4 % and on the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ) -by 41.04 % The level of proficiency in the third exercise "Throwing a ball forward and up, left leg forward" is influenced negatively by the number of repetitions (х 2 ) and positevely -by the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ).The result in teaching depends on the number of repetitions per set (х 2 ) by 33.36 % and on the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ) -by 41.43 %.
There is a positive influence of the number of sets (х 1 ), the number of repetitions per set (х 2 ) and a negative influence of the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ) on the level of proficiency in the fourth exercise "Throwing a ball forward and up, left side to the throwing direction".The result in teaching depends on the number of sets (х 1 ) by 37.34 %, on the number of repetitions per set (х 2 ) -by 14.18 %, and on the relationship between the number of sets and the number of repetitions per set (х 1 х 2 ) -by 41.54 %.
Therefore, the effectiveness of teaching boys aged 7 years "throwing a ball at a vertical target" is positively influenced by 6-12 sets, 3 repetitions per set, rest interval of 60-180 seconds.The focus in choosing a teaching mode is on the number of repetitions per set.
To specify the impact of different modes of physical exercises on the level of proficiency, let us perform a discriminant analysis (see Tables 3-6).
The first canonical function explains 57.6 %, of the results variation, which indicates its high informative value (r=0.790)(see Table 4).The analysis of canonical functions proves a statistical significance of the first and second canonical functions (λ 1 =0.140; р 1 =0.001; λ 2 =0.373; р 2 =0.022).The first and second functions have a high discriminative ability and meaning in the interpretation of the general population (Table 4).
The structure discriminant function coefficients, which are the coefficients of correlation between the variables and the function, indicate that the functions are closely connected with the level of proficiency in vaulting preliminary exercises.The level of proficiency in exercises depends on teaching modes, and the level of proficiency in vaulting depends on the level of proficiency in preliminary exercises (Table 3).
The graphic material given in Fig. 1 shows the density of objects in each class and the distinct boundary between the classes, which indicates the possibility of choosing the mode of performing the exercise to successfully teach throwing a small ball at a vertical target (Table 6).

discussion
The study assumed that a full factorial experiment and discriminant analysis would make it possible to determine the peculiarities of motor skills development in boys aged 7. The obtained results show that the matrix for a full 23 type factorial experiment given in Table 1 can be used to study the effectiveness of the learning process.A full factorial experiment method makes it possible to mathematically describe the process in some local area of the factorial space around the point with the coordinates of the n-dimensional space and to verify the regression model.Regression equations provide an opportunity to select the modes of performing for each exercise being studied.
The study makes an assumption on the possibility of using a discriminant function to evaluate the effectiveness of different modes of physical exercises when teaching a series of throwing exercises.The verification of canonical functions proves their statistical significance, and the discriminant function equation provides an opportunity to select the best option for obtaining a positive effect when teaching a series of exercises.
The results obtained: • specify the conceptual approaches to planning the experiment in studying the learning process effectiveness and developing learning models in children (Khudolii, & Ivashchenko, 2013;Ivashchenko, 2016;Ivashchenko, Khudolii, Iermakov, & Harkusha, 2017); • regression models given in Table 5 provide an opportunity to select the best option for teaching each exercise and supplement the conclusions on the effectiveness of using a full factorial experiment (FFE) in physical education and sports research (Khudolii, & Iermakov, 2011;Khudolii, et al., 2016;Khudolii et al., 2015); • supplement the information on the use of a discriminant function in the classification of schoolchildren by motor activity (Milić et al., 2011;Gert-Jan de Bruijn, & Benjamin Gardner, 2011;Lulzim, 2013).As in the papers by Geoffrey D. Broadhead And Gabie E. Church (1982), Ivashchenko, Khudolii, & Miroshnichenko, (2016), Ivashchenko, (2016), Khudolii et al. (2015), the study observed a high discriminative and predictive ability of the obtained functions in evaluating children's and adolescents' motor preparedness.During the analysis, the study calculated canonical discriminant function coefficients (unstandardized) acting as factors of the given values of variables included in the discriminant functions.Based thereon, it is possible to classify the modes of exercises by the level of proficiency in physical exercises performance of boys aged 7, which is of practical value.
In order to select the mode of performing throwing exercises, let us plug the level of proficiency in each exercise, which ensures a positive learning effect, into the discriminant function equation: where Y is the function result, Х 1 is the level of proficiency in exercise 1, Х 2 -the level of proficiency in exercise 2, Х 3 -the level of proficiency in exercise 3, Х 4 -the level of proficiency in exercise 4, Х 5 -the level of proficiency in exercise 5.
Let us compare the obtained result (Y 1 = -1.587;Y 2 = 0.336) with the values of centroids for the first and second canonical functions (Table 4).The comparison shows that mode of training 4 (12 sets of 3 times per set, with a 60-second rest interval) is the most favorable for teaching throwing to boys aged 7. Consequently, the discriminant analysis allowed to answer the question as to the reliability of classification of physical exercises modes; as to how the level of proficiency in series of learning tasks influences the process of mastering the whole exercise; and what mode of performing exercises can be universal for teaching throwing exercises.

conclusions
A full factorial experiment method makes it possible to mathematically describe the process in some local area of the factorial space and to verify the regression model.Regression equations provide an opportunity to select the modes of performing for each exercise being studied.
Discriminant analysis has made it possible to determine the modes of physical exercises in the process of motor skills development; to answer the question as to how significantly the modes of training differ by the effectiveness of motor skills development; what motor tasks most substantially influence the differentiation of classes; what class the object belongs to based on the values of discriminant variables.
To select the most rational mode of performing exercises in the process of motor skills development in boys aged 7, the first and second discriminant functions can be used, with a focus on the most informative variables.

table 1 .
Matrix for a 2 3 type factorial experiment in studying the impact of different modes of repeating the exercise on the level of their performance proficiency