The stimulation of students’ cognitive activity, maximal visualization and updating the learning material, individual studies optimization are to be considered as the main functions of modern elearning process [1, 3, 4, 7]. Elearning various elements are the fundamental parts of high school educational process. However the elearning effectiveness is still to be questioned. And the whole number of research directions of elearning efficiency studies is taken nowadays [2, 5, 8]. Thus, earlier researchers have pointed out the usage of electronic didactic materials as the factor of students’ progress in studies and stimulation of students’ cognitive activities [6]. But the elearning contribution into generation and development of students’ skills is still questioned, especially if we talk about the aspect of mathematical abilities for analysis and synthesis.
The problematic importance is caused by the fact that mathematical skills, especially the abilities for analysis and synthesis, are to be considered as the fundamental part of successful professional activities which is highly important while searching for scientific methods, analysis and interpretation of research results. That is why we determined the purpose of our research as studying of elearning role as an instrument of medical students’ mathematical abilities development.
We chose the clinical psychology faculty students of medical university as an object of our research as development of students’ analytical skills and mathematical abilities to synthesis is extremely important while searching for scientific psychological methods, analysis and interpretation of psychological research results.
We can point out several tasks of our research:
– to study clinical psychology students’ analytical skills and mathematical abilities to synthesis at the initial stage of mathematics elearning;
– to analyze clinical psychology students’ analytical skill and mathematical abilities to synthesis at the final stage of mathematics elearning.
Materials and methods of research
Testing of 30 firstyear and secondyear clinical psychology students was carried out. The firstyear students were tested as the starters of mathematics elearning. The secondyear clinical psychology faculty students were involved into mathematical elearning testing after passing the mathematical course examination.
The experiment was held in constant conditions for both groups of students: the research was held at 11 a.m. in the academic auditory. The research duration was about 20 minutes. The clinical psychology students performed the testing independently without using any electronic devices. The testing was built on the basis of Atmhauer intelligence structure test including the scale of mathematical abilities determination.
The subject was to be guided in each task condition and structure initially. That was a highly important element of successful testing. To estimate the different elements in the structure of the task, systematize them and define their hierarchy. The high level of analytical skills was demanded for these operations.
Except analytical skills the mathematical task conditions analysis required the high level of students’ mathematical abilities to synthesis development, since the separate elements are to be united into the complexes. To answer the question, clinical psychology faculty students had to find the mathematical relations and functional associative nets between different elements of a problem.
So, the successful solution of the test task was the indicator of the developed mathematical abilities of the examinee to analysis and synthesis.
Results of research and their discussion
The examination results of clinical psychology faculty students’ analytical skills and mathematical abilities to synthesis at the initial stage of mathematics elearning are represented in the Table 1.
Table 1
Mathematical abilities development level to analysis and synthesis of clinical psychology faculty students
Level 
The initial stage of mathematics elearning 
Final stage of mathematics elearning 
High 
7 % 
13 % 
Average 
29 % 
38 % 
Lowaverage 
29 % 
44 % 
Low 
35 % 
5 % 
35 % of the firstyear medical university students, starting mathematics elearning showed the low analytical skills level. 58 % of examinees showed an average and lowaverage levels of mathematical abilities development. 7 % of the initial mathematics elearning students showed the high level of abilities to analysis and synthesis (Fig. 1).
Fig. 1. Level of clinical psychology students’ analytical skills and mathematical abilities to synthesis development at the beginning of mathematics elearning: 1 – results of research and their discussion low level of mathematical abilities development (35 % студентов); 2 – lowaverage levels of mathematical abilities development (29 % студентов); 3 – average levels of mathematical abilities development (29 % студентов); 4 – high levels of mathematical abilities development (7 % студентов)
As table 1 claims, after elearning mathematics course of clinical psychology faculty students their analytical skills underwent essential changes. The number of low level mathematical abilities students decreased considerably: from 35 to 5 %. The number of the students showing a high abilities development level to analysis and synthesis was almost twice enlarged. 13 % of such students appeared among secondyear examinees in comparison with 7 % of the first year students. Positive analytical skills development level dynamics was also observed among the average level students. This concrete group showed the 9 % extension at the end of the math elearning course in comparison with the initial stage: from 29 to 38 % (Fig. 2).
Fig. 2. Level of clinical psychology students’ analytical skill and mathematical abilities to synthesis development at the final stage of mathematics elearning: 1 – low level of development of abilities (5 % of students); 2 – lowaverage level of development of abilities (44 % of students); 3 – average level of development of abilities (38 % of students); 4 – high level of development of abilities (13 % of students)
The low average level to the analysis and synthesis students number was also increased. The number of such students was enlarged nearly by 1,5 times: from 29 to 44 %. Common growth of students groups with high, average and low average levels of analytical skills happened due to transition of 30 % of low abilities level group to the higher values of mathematical abilities, which undoubtedly shows the active influence of math elearning on students’ analytical skill and mathematical abilities to synthesis generation and development (Fig. 3).
The testing results comparison separately on each task offered to examinees shows that after mathematics elearning course the students cope with test tasks much more surely due to the higher abilities level development to synthesis and analysis. The Tables 2 witnesses the fact, that after mathematics elearning in the majority of questions (14 tasks from 20 that constitutes 70 % of number of questions), the students’ analytical skill and mathematical abilities to synthesis appeared much higher, than at the initial stage mathematics elearning.
Fig. 3. Comparison of clinical psychology students’ analytical skill and mathematical abilities to synthesis at the initial stage and at the final stage of mathematics elearning: 1 – high level of development of abilities; 2 – average level of development of abilities; 3 – lowaverage level of development of abilities; 4 – low level of development of abilities
Table 2
The testing results comparison separately on each task offered to examinees
The task number offered to examinees 
The number of examinees coped with test tasks surely (%) 

1 year – students at the initial stage of mathematics elearning 
2 year – students at the final stage of mathematics elearning 

1 
100 
100 
2 
79 
75 
3 
79 
81 
4 
50 
75 
5 
79 
81 
6 
79 
50 
7 
86 
94 
8 
86 
81 
9 
36 
38 
10 
21 
44 
11 
50 
63 
12 
50 
38 
13 
79 
63 
14 
21 
44 
15 
14 
44 
16 
43 
50 
17 
21 
38 
18 
14 
25 
19 
29 
75 
20 
14 
13 
More than 80 % of students who passed math elearning course showed excellent result in five tasks from twenty offered that has constituted 25 % of all questions, in comparison with the initial stage students who were able to perform only 15 % rate. As a result of elearning course the number of the students who had exact answer in six tasks from 20 (which is 30 % of all questions) became as much as twice larger in comparison with mathematics elearning initial stage students. The number of tasks which were answered correctly by less than a half of the initial stage mathematics elearning students was at the 60 % average (twelve tasks from twenty offered).
The correlation from 21 to 45 % of the right answers can definitely be seen in 25 % of tasks comparing initial stage and the end of the elearning course. The final stage students of mathematics elearning were not able to beat the initial stage students results only in three tasks from twenty (15 % of quantity of questions), showing the same result. The comparison of testing results to the academic progress proves that the high level of analytical skills and mathematical abilities to synthesis allows the students to master the training material much better (Table 3).
Table 3
The comparison of testing results to the academic progress
The testing results & result of the exam 
The testing results & average mark during the academic year 

valid 
30 
30 
Spearmen 
0,589732 
0,577140 
pvalue 
0,000604 
0,000841 
All above proves the effectiveness of elearning usage in aspect of mathematical abilities development to the analysis and synthesis.
Competently organized elearning course in discipline “Mathematic” develops students mathematical abilities to synthesis, allows to generate and improve their analytical skills, transferring about one third of students to higher mathematical abilities level, provides strong discipline knowledge formation, and guarantees the professional competence of the modern specialist in the field of clinical psychology.
So, without any doubt the various elearning elements usage throughout educational process of high school is necessary and reasonable, especially, keeping in mind a fact that variety of forms and methods of elearning allows to develop the students’ cognitive activity.