Modeling: ratio between means of teaching and motor training in junior school physical education classes

Material and Methods The study involved 32 boys who were 8 years old at the beginning of the experiment. They were randomly divided into four groups of eight people each. A pedagogical experiment was conducted using a 22 full factorial design. The study recorded the following indicators: number of repetitions required to teach exercises; grade for a unidirectional movement coordination exercise (test 1); grade for a multidirectional movement coordination exercise (test 2); error in time accuracy of performing the squat thrust (test 3); error in time accuracy of 5 jumps on marks in 5 s (test 4); error in assessing muscular effort with visual control (test 5); vestibular stability, error (test 6). The obtained experimental material was processed statistically using statistical analysis software packages (SPSS 20). Results According to the logistic function analysis, the achievement of an optimal result in differentiating temporal characteristics of movement requires 8.5 months, strength characteristics of movement – 8 months, movement coordination – 8 months, vestibular analyzer stability – 10 months. It takes 3 to 5 months to obtain positive increases in testing results in boys aged 8-9. The ratio of time allotted for strength training (ST) and coordination training (CT) to teaching motor actions (TMA) varies as 1:4 (ST: TMA) and 1:4.5 (CT: TMA). Conclusions: The ratio of time allotted for strength training, coordination training, and teaching to the time of the main part of the class ranges between 14.3-23.5% (strength training), 17.1-23.5% (coordination training), and 53.0-68.6% (teaching). As exercises become more complicated, the time allotted for strength and coordination training increases.

It was found that the effectiveness of motor skills development is influenced both by the mode of exercises [22][23][24] and the content of teaching [25][26][27].
Studies of motor skills development used a factorial experiment to examine the structure of the educational process [28,29], modeling [30,31], the logistic function ORIGINAL ARTICLE analysis to determine the duration of training and motor abilities development in children and adolescents [30,31]. Researchers established the effectiveness of using the modeling method to obtain new information about the patterns of motor skills development.
However, there are few studies aimed at investigating the ratio between means of teaching and motor training in junior school physical education classes. Most studies focus on the structure of motor fitness [1,10], modes of exercises during training [28].
Thus, the problem of determining the ratio between means of teaching and motor training in junior school physical education classes is relevant and requires further research.
The purpose of the study was to determine the ratio between means of teaching and motor training in junior school physical education classes.

Participants
The study involved 32 boys who were 8 years old at the beginning of the experiment. They were randomly divided into four groups of eight people each. The children and their parents were informed about all the features of the study and gave their consent to participate 03 in the experiment.
Research Design A pedagogical experiment was conducted using a 2 2 full factorial design (Table 1). Strength and coordination training was carried out by means of basic gymnastics. The boys were taught the forward roll and the straddle vault over side vaulting buck. The study recorded the level of proficiency in the exercises p = m/n, where m is the number of successful attempts, n is the total number of attempts. For strength development, the combined method according to the first variant was used. Exercises at one place are performed in the following order: dynamic effort method, maximal effort method, isometric effort method, repeated effort method. For movement coordination development -repeated method, in the process of teaching -method of algorithmic instructions.
The study recorded the following indicators: number of repetitions required to teach exercises; grade for a unidirectional movement coordination exercise (test 1); grade for a multidirectional movement coordination exercise (test 2); error in time accuracy of performing the squat thrust (test 3); error in time accuracy of 5 jumps on marks in 5 s (test 4); error in assessing muscular effort with visual control (test 5); vestibular stability, error (test 6).
Testing methods Test 1. Grade for a unidirectional movement coordination exercise, points.
The tests were evaluated on the following scale: 10 points -mistake-free performance of the test; 9.5 pointsone mistake was made (no coordination between arm and leg movements, one of the movements was forgotten); 9 points -two mistakes were made; 8.5 points -three mistakes were made.
General instructions and remarks. The teacher shows and performs the test once according to distribution, after which the students perform the test to the count for a grade.
Test 3. Error in time accuracy of performing the squat thrust 3 times in 3 s.
Test procedure. The test participant assumes the squat position. At the "Go" command, the participant begins to rhythmically perform the exercise.
Result. Time of performing the exercise. The error in time accuracy of performing the exercise is analyzed.
Test 4. Error in time accuracy of 5 jumps on marks in 5 s.
Test procedure. At the "Go" command, the test participant performs 5 jumps on marks, the distance between the marks is 50 cm.
Result. Time of performing the exercise. The error in time accuracy of performing the exercise is analyzed.
Test 5. Standing long jump at half strength, error in %. This test was performed to assess muscular effort with visual control.
Equipment. Non-slip surface with a line and marking in centimeters.
Test procedure. The test participant toes the line, with a two foot take-off and arm swing jumps as far forward as possible, then repeats the jump at half strength.
Result. The distance of the maximum-effort jump and the distance of the jump at half strength were recorded in centimeters. The error in % was analyzed.
General instructions and remarks. The test is carried out in accordance with the rules for standing long jump competitions. Take-off and landing places must be at the same level. Test 6. Walking in a straight line after three 360º turns, error cm.
This test was performed to assess vestibular stability. Test procedure. After three turns of 360° each, stand with the back against the wall and walk 4 m in a straight line.
Result. Deviation from a straight line in centimeters.
1. The analysis of change in the results of strength and coordination fitness in the groups of factorial design showed that this process can be described using growth models: Table 1 PEDAGOGY Y = A/(1 + 10 (a m + bx) ) + C (1) where Y is the effectiveness of teaching motor actions, Х is the number of training sessions held since the beginning of teaching the motor action, А is the distance between the upper (A-C) and lower (C) asymptotes, C is the lower asymptote, the point where the training begins; а, b are the parameters that determine the slope, bending, and inflection point of the logistic regression line.
2. The regression equation coefficients of the logistic function vary depending on the mode of training. Their change can be described by the following equation: where Y is the effectiveness of training process; х 1 is the time allotted for strength training; x 2 -for coordination training.
3. The following formulas were used to determine an optimal result and time of its achievement: 4. To determine the similarity between experimental and theoretical points, analysis of variance was performed.
Correlation coefficient, Fisher criterion were calculated.
5. Computational experiment. To determine an optimal ratio of time allotted for strength and coordination training, a computational experiment was conducted. Its essence is to create an array of data on 120 training modes and analyze the two-dimensional distribution. The computational experiment was conducted in two stages: 1. Based on the regression equations: Y = b 0 + b 1 x 1 + b 2 x 2 + b 3 x 1 x 2 , where х 1 is the time allotted for strength training; х 2 -for coordination training, an array of data was created Y [i, j], where i is the counter of variants of training modes, j is the counter of analyzed parameters (increase in the result, time of achieving the result, time for strength, coordination training, technical training).
2. Analysis of the two-dimensional distribution of an increase in the result, time of achieving an optimal result, time for strength, coordination training, and teaching movements.
The obtained experimental material was processed statistically using statistical analysis software packages (SPSS 20).
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 informedconsent document was obtained from all the parents.

Results
The analysis of the study results is given in Tables 2-6. Math analysis of the logistic function made it possible to conclude about a similarity between experimental and theoretical points ( Table 2). The change in the ability to coordinate unidirectional and multidirectional movements is most influenced by variants of training 1 and 4. The boys of group 4 achieve a maximum result in 7.5 months, and the boys of group 1 -in 15 months (Table 3).
The change in the error in differentiating temporal characteristics of movement is positively influenced by variants of training 1, 3 and 4. Group 3, where maximum attention was paid to coordination training, shows the greatest speed in achieving a maximum result ( Table 3).
The boys of group 3 show a higher result in less training time in differentiating muscular effort and in vestibular stability. It is noteworthy that achieving a similar result when using only the means of technical training takes twice as much time (Table 3).
According to the logistic function analysis, the achievement of an optimal result in differentiating temporal characteristics of movement requires 8.5 months, strength characteristics of movement -8 months, movement coordination -8 months, vestibular analyzer stability -10 months. Thus, when planning physical education lessons during the 2 nd and 3 rd grades of training, it is necessary to allocate time for strength, coordination training, and teaching movements. The main means of developing motor abilities is basic gymnastics.
The analysis of the computational experiment showed that the increases in the results are normally distributed with a certain degree of assumption, and the arithmetic mean and the root mean square are the most important characteristics of the sample. The optimal step of increase is a value equal to M ± s, because the probability of achieving this result is the highest (Table 4). Table 5 shows the ratio between the means of strength, coordination training and teaching in the class of boys aged 8-9 years.
It takes 3 to 5 months to obtain positive increases in testing results in boys aged [8][9]. The ratio of time allotted for strength training (ST) and coordination training (CT) to teaching motor actions (TMA) varies as 1:4 (ST: TMA) and 1:4.5 (CT: TMA).
The process of teaching the most difficult movements for this age was similarly analyzed. Based on the computational experiment, it was determined that the results of training are normally distributed, and the arithmetic mean and the root mean square are the most important characteristics of the sample ( Table 6). Table 7 shows the ratio between the means of strength and coordination training when teaching movements to boys aged 8-9 years. It is noteworthy that as exercises become more complicated, the time allotted for strength and coordination training increases, but these indicators do not reach maximum values adopted in the experiment. The ratio of time allotted for strength training, coordination training, and teaching to the time of the main part of the class ranges between 14.3-23.5% (strength training), 17.1-23.5% (coordination training), and 53.0-68.6% (teaching).

Discussion
An assumption was made about the possibility of using factorial designs and analysis of the logistic function to assess the effectiveness of different structures of physical education classes in junior school. The study established the effectiveness of the algorithm of computer modeling of the structure of physical education classes.
During the analysis, the study determined the structure of the main part of the class, which ensures the effectiveness of motor abilities and motor skills development.
The obtained data supplement the information on the factors that influence the effectiveness of motor skills development [14][15][16]; on the technique of pedagogical control in the process of motor skills development [17][18][19]; confirm the information that the conditions for motor skills development are one of the factors that determine the effectiveness of teaching schoolchildren [1,[10][11][12].
In addition, the study supplements the data on the effectiveness of using factorial designs in studying the patterns of motor skills development [28,29]. Also, the results of the study confirm the effectiveness of using the logistic function to determine the duration of training and motor abilities development in children and adolescents [30,31].
The results of the study can be used to plan strength and coordination training, and teaching basic gymnastics exercises in junior school physical education classes. The data given in Tables 5 and 7 are recommended for planning. The main method of strength development is the combined method according to the first variant. Exercises at one place are performed in the following order: dynamic effort method, maximal effort method, isometric effort method, repeated effort method. The development of strength and movement coordination is seen as a condition for successful motor skills development.

Conclusions
The logistic function analysis showed that the achievement of an optimal result in differentiating temporal characteristics of movement requires 8.5 months, strength characteristics of movement and movement coordination -8 months, vestibular analyzer stability -10 months. When planning physical education lessons during the 2 nd and 3 rd grades of training, it is necessary to allocate time for strength, coordination training, and teaching movements. The main means of developing motor abilities is basic gymnastics.
The ratio of time allotted for strength, coordination training, and teaching to the main part of the class ranges between 14.3-23.5% (strength training), 17.1-23.5% (coordination training), and 53.0-68.6% (teaching). As exercises become more complicated, the time allotted for strength and coordination training increases.

Acknowledgement
The study was carried out in accordance with the plan of research work of the Department of Theory and Methodology of Physical Education of H. S. Skovoroda Kharkiv National Pedagogical University.

Conflict of interest
The authors declare no conflict of interest.