179 Software System for Formation the Composition of Academic Groups (Subgroups) Based on the Diffusion- Like Model Natalia Porplytsya, Serhii Dubovyi Department of Computer Science, Ternopil National Economic University, UKRAINE, Ternopil, 8 Chehova str., email: ocheretnyuk.n@gmail.com, dubovyj.sergij@gmail.com Abstract: In this paper, the method of forming a laboratory (practical) classes on individual disciplines can be composition of academic groups (subgroups) in an educational divided into subgroups. In this case, such a division is usually institution was developed. The method based on a diffusion-like carried out in alphabetical order. Such an approach is model of the dissemination of knowledge potential. The completely unreasonable, since it does not take into account application of this method ensures the formation of academic the assessments received by students for related disciplines in groups (subgroups) in such a way as to maximize the coefficient of distribution of knowledge potential within each of the formed accordance with the structural-logical scheme specialty. groups (subgroups). Software system, which implements the Therefore, it is important to develop a method for forming specified method, is also considered. a composition of academic groups (subgroups) in an Keywords: diffusion-like model, knowledge potential, educational institution, in such a way as to ensure the academic group. maximum effectiveness of the educational process. To construct this method expedient to use a diffusion-like model І. ACTUALITY OF THE PROBLEM of the propagation of the knowledge potential, which Student academic group is a kind of small group, with its simulates the transfer of knowledge between students by stages of transformation into a collective, with parameters of analogy with the crystallization process of the solid body development and criteria of formation. Constant studying of from the melt at the outlet from the heat [7, 8]. In addition, the level of development and knowledge of each student and it’s need to develop the software module for the the team of the academic group enables to effectively develop implementation of this method. the educational process in a higher educational institution, taking into account the changes that the student’s team II. MODELING OF THE COMPOSITION OF undergoes in general and each member in particular, to ACADEMIC GROUPS AND SUBGROUPS BY correct the content and methodology of this process [1-5]. APPLICATION OF THE KNOWLEDGE POTENTIAL The initial formation of academic groups is based on the DISTRIBUTION COEFFICIENT level of knowledge of each entrant, which usually reflects as the average rating point for the implementation of During the formation of the composition of academic certification works on selected external subjects of external groups, we will take into account the calculated coefficient of independent testing (EIT). distribution of the knowledge potential calculated for them External independent testing (EIT, formerly also External [8], that is, the higher this value is the better. It is important to testing, ET) - entrance exams for higher education in note that the possible maximum value of this coefficient is Ukraine. The complex of organizational procedures (first of unknown in advance. In addition, the distribution of all - testing) aimed at determining the level of educational compositions to academic groups or subgroups is carried out achievements of graduates from secondary schools when they in such a way as to ensure the highest and virtually equivalent enter higher education institutions [6]. At the same time, the values of these coefficients for all formed academic units. division of students into groups (subgroups) in educational Then the task of finding such a distribution of student institutions, usually carried out on the basis of the average compositions can be equationted in the form of a multivariate rating point without taking into account its detail that is, the discrete optimization problem. compliance of competing subjects of EIT chosen specialty. At the same time, we will examine all possible variants of An applicant may receive a high score from the “Ukrainian the composition of the academic groups, which in turn shows language and literature” and at the same time and a low from that this task is extremely complex and belongs to the NP- the “Mathematics” at the entrance to the technical specialty, complex class. For each combination, the value of the where his level of knowledge plays an important role in the coefficient of distribution of the knowledge potential of the field of mathematics. In addition, in other cases, the group will be compared, which will be based on the level of formation of academic groups from the list enrolled to study knowledge of each student, taking into account the individual entrants can be carried out in alphabetical order, without characteristics of each discipline and specialty. considering at the same time the level of knowledge of So, determination of the coefficient of distribution of the k k applicants, which does not provide in the future the known potential will be calculated C n times, where C n - maximum effectiveness of the educational process. Further, number of combinations from n to k; k – number of students during the studing process, formed training groups for in the academic group (subgroup); n – total number of ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 180 students; m – required number of groups (subgroups). It will The formation of subgroups of students from groups in the be received C k sets of coefficients of distribution first semester of the first year will also be based on the results n of the EIT. Thus, the equation for determining the coefficient 𝑏𝑏𝚤𝚤 = 𝑏𝑏1 … 𝑏𝑏𝑚𝑚 , i = 1...k which knowledgeable potential ���⃗ of distribution of the knowledge potential of the formed we will store, for further determination of the "best" subgroup A j , g , m +1 will look like: according to the following criteria: j ���⃗ ⎧𝑏𝑏1 → 𝑚𝑚𝑚𝑚𝑚𝑚, 𝑏𝑏1 ∈ 𝑏𝑏𝚤𝚤 ; A j , g ,m +1 = ∑ ϕ j ,k ,m +1 − ϕ j ,k ,m where ⎪ … j =0 ⎪ 𝑏𝑏𝑚𝑚 → 𝑚𝑚𝑚𝑚𝑚𝑚, 𝑏𝑏𝑚𝑚 ∈ ���⃗ 𝑏𝑏𝚤𝚤 ; ϕ j ,k ,m +1 − ϕ j ,k ,m = f j ,k ,m + (1) ⎨|𝑏𝑏1 − 𝑏𝑏2 | → 0, 𝑏𝑏1 , 𝑏𝑏2 ∈ ���⃗ (4) ⎪ 𝑏𝑏𝚤𝚤 ; + D j ,k ,m ∑ σ k ,k ,k (ϕ j ,k ,m − 2ϕ j ,k ,m + ϕ j ,k ,m ), ⎪… 1≤ k < k < k ≤ k j ⎩|𝑏𝑏1 − 𝑏𝑏2 | → 0, 𝑏𝑏𝑚𝑚−1 , 𝑏𝑏𝑚𝑚 ∈ ���⃗ 𝑏𝑏𝚤𝚤 ; f j ,k ,m - source of knowledge, D j ,k ,m - coefficient which For example, when dividing students into two subgroups characterizing the ability k-agent j-group redistribute k information (knowledge) at the time m (analog of diffusion will be implemented C n /2 comparisons of the distribution coefficient)[7]. coefficients of the knowledge potential of the formed It should be noted that for the use of equation (4), the subgroups As can be seen from expression (1), as a result of student's marks with the EIT, which are calculated in the 200- the test, an option is chosen for which the difference in the point system, should be converted into 100-point system. It is knowledge potential among the groups formed will be the known that the minimum passing point of the EIT is 100 smallest, and the value of the knowledge potential will be points, while the minimum score required for passing the greatest. One of the options for introducing generalized discipline at the university is 60 points. We will make the potential K j -group 𝜑𝜑𝑗𝑗,𝑚𝑚 . There is a representation of it in the appropriate proportion for transfer of points from the 200- form of some function from 𝜑𝜑𝑗𝑗,𝑘𝑘,𝑚𝑚 , in particular, in the form point system to 100 points, which is represented by the equation: of a generalized arithmetic mean: 1 𝑘𝑘𝑗𝑗 60 * c , 𝜑𝜑𝑗𝑗,𝑚𝑚 = ∑𝑘𝑘=1 𝑎𝑎𝑗𝑗,𝑘𝑘 𝜑𝜑𝑗𝑗,𝑘𝑘,𝑚𝑚 (2) x= (5) 𝑘𝑘𝑗𝑗 100 where α j,k – some weight factor. where с – EIT score for a subject. In the initial iteration of the use of the method that is, the formation of a composition of academic groups of students of the first year will determine the knowledge potential of each student based on the results of the EIT. In this case, each item will be given a coefficient of importance that corresponds to the chosen specialty. Thus, the knowledge potential of a particular student will look like: 𝜑𝜑𝑗𝑗,𝑘𝑘,𝑚𝑚 = ∑𝑡𝑡𝑖𝑖=1 𝑧𝑧𝑖𝑖 𝑝𝑝𝑖𝑖 (3) where - coefficient of importance of an object, - subject score, а t – number of subjects. The sum of the coefficients of importance ∑ti=1 zi = 1. To form a composition of subgroups for the subject, you should introduce the notion of the source of knowledge, which will be the lecturer who will conduct practical classes. Depending on the qualification, each lecturer will be assigned the appropriate efficiency factor, which will characterize him as a source of knowledge. Table one shows the adequacy of the efficiency coefficients for the qualifications obtained. Fig. 1. A fragment of the structural-logical scheme of the related TABLE 1. CONFORMITY OF THE POINTS FOR THE disciplines of the specialty "Software Engineering" CALCULATION OF THE QUALIFICATIONS After forming a set of all possible combinations of the Obtained Level of Efficiency formed groups (subgroups), we calculate the value for them qualification qualification coefficient A j , g ,m +1 (on initial iterations j,m and then determine the Lecturer trainee 1 60 Lecturer 2 65 best combination by the equation (1). The time spent on Lecturer, Ph.D. 3 80 forming all possible combinations of the subgroup depends Senior Lecturer, Ph.D. 4 90 on the number of groups (subgroups) and the number of Docent, Ph.D. 5 100 students in these groups (subgroups). Reduction the timing of these operations may be the subject of a study in the future. ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 181 Note, during the program implementation of equation (1), it z1 = 0,5 - the coefficient of the importance of discipline is advisable to select several "best" combinations of groups (subgroups) and give the user the opportunity to select the "Object-oriented programming", z 2 = 0,25 - "Algorithms "optimal" combination. Formation of subgroups of students and data structures", z 3 = 0,25 - "Fundamentals of in all subsequent semesters will be carried out on the basis of programming". Student's points for the above-mentioned the results of previously studied adjacent disciplines, asking them with the coefficients of importance, based on the disciplines will be, for example, p1 = 75 , p 2 = 77 , structural-logical scheme of the specialty. For example, in p3 = 86 accordingly. Then, according to equation (3), his Figure 1, a fragment of the structural-logical scheme of knowledge potential in relation to the discipline ".NET adjacent disciplines for the specialty "Software Engineering". Technology" will equal: The equation for determining the knowledge potential of a 𝜑𝜑𝑗𝑗,𝑘𝑘,0 = 0,5 ∗ 75 + 0,25 ∗ 77 + 0,25 ∗ 86 = 78,5 subgroup based on the results of related disciplines corresponds to equation (4). The equation (3) will be used to Now we can equationte an algorithm for the determine the knowledge implementation of the proposed method for forming the For example, the formation of subgroups for the discipline composition of academic groups (subgroups) with the use of ".NET Technology" will be based on the results of previous a diffusion-like model, whose block diagram is shown in related disciplines, where, according to the equation (3) Figure 2. Fig.2. Algorithm for the implementation method for forming the composition of academic groups (subgroups) with the use of a diffusion- like model III. SOFTWARE REALIZATION groups, as well as other data necessary for the functioning of the system are stored in RDBMS MySql. The software system of forming the composition in Consider functional details of system. After launching the academic groups based on a diffusion model is developed program, the user will be given full access to the entire using an object-oriented approach and .NET technology, functional system. The "Form groups" function gives the user programming language С#. Student data, lists of formed the ability to form groups of first-year students based on the ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 182 results of external testing. In this case, each item will be The logical and conceptual description of the functionality given a coefficient of importance that corresponds to the of the system for the function "Form subgroups", is reflected chosen specialty. in the sketch of the form, which is presented in Figure 3. The logical and conceptual description of the functionality Once the groups and sub groups have been formed, the system for the function "Form groups" is reflected in the user will be able to save them or form them again, having sketch of the form, which is presented in Figure 2. previously changed the parameters. IV. CONCLUSION The paper analyzes the existing methods of forming the composition of academic groups (subgroups) and shows that they are not effective, because they do not take into account the influence of the interaction of students between groups and the lecturer on the effectiveness of the educational process. It is shown that for constructing the method of forming the composition of academic groups it is expedient to use the diffusion model of the process of dissemination of knowledge potential. A new method is proposed for the formation of composition of academic groups based on a diffusion-like model using the coefficient of distribution of the knowledge Fig. 3. Program’s window for forming a composition of groups potential of the group as the main comparison parameter. The function "Form subgroups" is similar to the "Form REFERENCES groups" function, but in this case, possible combinations will be formed as a result of division of the group into subgroups. [1] I. M. Avdeeva, “Innovative communicative technologies The division into subgroups will be carried out for a specific in the work of the curator of the academic group”. Kyiv, discipline, taking into account the results of previously Ukraine: Professional, 2007, 304 p. 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