The article contains a study of the principles of student's educational trajectory formation by using modern technologies in data analysis. There is a mandatory requirement to have the selective component (optional to a student) among the curriculum educational components. This rule is legislated in the laws «On Education» and «On Higher Education» of Ukraine as well as in the normative documents on accreditation of educational programs, defined by the Standards and recommendations on quality assurance in the European Space of Higher Education (ESG) and the National Agency for Quality Assurance of Higher Education. However, adherence to the principles of the individual educational trajectory formation is mostly formal and is reduced to offering students a non-coherent list of courses. On the one hand, this leads to the disorientation of a student, who cannot see the systemic perspective of his future profession in the initial list of study courses, and therefore cannot consciously choose the optimal set of optional courses. On the other hand, the unknown choice of courses by students leads to situational management of the educational process at the HEI. A large number of courses create significant difficulties in managing the selection process. To analyse the process of individual educational trajectory formation, the authors propose to use methods of data association and, in particular, the apriori algorithm for the formation of associative rules. The procedure of popular sets of elective courses formation, the configuration of associative rules of educational courses choice is studied. The characteristics of these rules quality are calculated. The example of the procedure implementation in analytical platform Deductor Studio is considered.
The prior goal of modern higher education is to prepare in HEIs competent specialists with a harmonious combination of personal and professional qualities, that are capable of self-development and self-realization in the future professional activity. In this regard, the orientation of the educational process towards the student becomes particularly relevant and valuable. It includes taking into account the individual opportunities and needs of the students. This orientation allows students to choose components of educational programs and to form an individual educational trajectory.
The educational trajectory determines the direction of the student in the educational space. Its existence is not a norm, but a fact of reality. Different scenarios for defining this trajectory are possible under different educational conditions. According to the traditional approach, the HEI defines a single trajectory of educational achievement results by students in accordance with the National standard. The more modern method offers several possible paths for groups of students with different capabilities. Both such approaches do not take into account the views of the student. Because of the goals, content, forms, methods, results are determined directly by the teacher. At the same time, a large proportion of students have a low level of motivation to achieve goals, as they do not see personal meaning in such educational activities. One way to overcome this problem in higher education is to form an individual educational trajectory.
Recognition of students' right to an individual educational trajectory is one of the progressive innovations of the «Law on Education». This law provides for «a personal way of realizing the student 's potential, is formed taking into account his abilities, interests, needs, motivation, opportunities and experience, is based on the student 's choice of types, forms and pace of education, courses of educational activities and their offered educational programs, educational courses and the level of their complexity, methods and means of education» [1].
The main tool for the realization of personal potential is in optional courses choice. According to the Law of Ukraine "On Higher Education" [2], students have the right to choose courses in the amount of at least 25% ECTS credits from the total educational program (paragraph 15, part 1, Article 62).
Requirements for individual educational trajectory are contained in the regulatory documents for the accreditation of educational programs defined by the Standards and Recommendations for Quality Assurance in the European Higher Education Space (ESG) [3] and the National Agency for Quality Assurance of Higher Education [4].
The authors of the article are experts of the National Agency for Quality Assurance of Higher Education and may argue that compliance with the principles of formation of individual educational trajectory in Ukrainian HEIs is mainly formal and is reduced to offering students to choose an unrelated list of courses. This leads to the disorientation of the students, who at the initial courses of study cannot see the systemic perspective of their future profession, and therefore cannot consciously choose the optimal set of optional courses. The unknown choice of courses by students leads to situational management of the educational process at the higher educational establishment. A large number of courses create significant difficulties in managing the selection process. System analysis of the process of the individual educational trajectory formation can be effectively carried out with the help of Data Science tools [5]. 2.
The theoretical and methodological justification for research is the fundamental principles of the system approach, analysis and synthesis of information, dialectical method in the justification of the use of information technologies.
In particular, the following scientific methods are used in research: association method – for combine courses into logical modules and create causal relationships between modules of optional courses; apriori algorithm – for the formation of frequent itemset sets of optional courses and a system of associative rules construction based on these sets; a graphic method – for creation of the formation scheme of frequent itemsets subsets of optional courses with various weights; a method of the quantitative analysis – for calculation of characteristics of support and confidence of associative rules and its sorting.
The information basis for the research is data on the content of the optional components of curricula set and results of course selection by students of the Faculty of Information Technologies of Kyiv National University of Trade and Economics. 3.
According to the National Strategy for the Development of Education in Ukraine for 2012-2021, the main direction of the educational space development is the introduction of the individualized learning concept [6]. Implementation of individualized learning is ensured by the determination of individual educational trajectory.
Basic concepts of individual educational trajectory are given, for example, in the work of I. Krasnoshchok [7]. Analysis of the advantages of its use in the educational process and review of the principles to construct an online information system supporting the student's educational trajectory is the subject of research by S. Sharov and T. Sharova in the article [8].
Various aspects of the information and communication technologies introduction in the educational process are constantly attracting the attention of many researchers.
Systematic studies of informatization of education and practical implementation of information and communication technologies in the educational sphere of Ukraine were conducted by Yu. Bykov, O. Burov, A. Gurzhii, M. Zhaldak and others in [9]. The needs of digital transformation, which require special flexibility from modern universities, the creation of a digital learning environment to support educational activities are discussed in the studies of O. Kuzminska, M. Mazorchuk, N. Morze, O. Kobylin [10]. The formation of competences in the field of information technologies was presented in the study by N. Morze and M. Umryk [11]. The development of innovative entrepreneurial universities in Ukraine on the platform of digitalization is assessed in [22]. The principles and structure of the information support system for the individual educational trajectories as an open modular portal were investigated by A. Bogdanov, I. Chepovoy, P. Ukhan, L. Yurchuk in [12]. It analyzes Tools for Mobility, Tools for Quality, Tools for Transparency, and Portals and Databases, which can be useful for building and implementing an individual educational trajectory. The formation of an integrated quantitative assessment of the HEI activity is proposed by V. Bykov, A. Biloshchytskyi, O. Kuchanskyi, Yu. Andrashko, O. Dikhtiarenkoand S. Budnik in [13].
The problems of big data processing are extremely pressing today. Scientists D. Dietrich, B. Heller, B. Yang tell how it is effective to use Data Science tools in almost all areas of human activity [14]. An associative analysis is one of the main components of Knowledge Discovery in Databases and its main component, Data Mining [15]. Practical implementation of associative rules in various fields of scientific research is represented by C. Zhang and S. Zhang in [16] and G. Bhavani and S. Sivakumari in [17].
The main purpose of the vast majority of management systems is the integrated management of HEI. Among the well-known foreign systems of automation it is necessary to assign such as MyEdu – University Automation Software [18], Eifell Corp Services and Custom eLearning [19], CyberVision University Management System [20].
In Ukraine, at the state level, there is no more than a single state electronic database on education, which is an integrated information and telecommunications management system. The Ukrainian software market offers its solutions for the automation of the educational process. The most famous is the Automated control system of the higher educational institution ACS "University", developed by the Research Institute of Applied Information Technologies of the Cybernetics Center of the National Academy of Sciences of Ukraine [21], Computer Systems Packages "Dean's Office", "COLLOQUIUM", "PS-Staff" of the private enterprise "Politek-soft" [22], Program Complex "ALMA-MATER" of the company "Direct IT" [23] and others.
None of the control systems described above contains a module for automating the process of choosing courses. As a result of the analysis, the authors found only a few attempts of a scientific approach to solving this problem.
A. Kravets and R. Al-Shaebi in the article [24] offer a method of automated formation of the individualized curriculum. A. Kardan with co-authors describes using a neural network approach for the process of student behaviour modelling in choosing courses [25]. I. Ognjanovic, D. Gasevicand S. Dawson created a model for predicting the student course choice [26].
These approaches do not use the logical relationships between the courses that the student must choose. However, this is a necessary condition for the formation of a high-quality curriculum for the training of highly qualified specialists. The educational program must have a clear structure; educational components should be a logically interconnected system and together enable the achieving of learning goals and outcomes.
The search for associative rules is a good tool for solving the problem of establishing relationships between courses and a systematic approach to building a quality logical and structural system of educational components.
The purpose of this research is to provide a tool for students for a conscious choice of courses, to analyze the frequent itemsets of optional courses in the formation of professional qualities of future specialists. Along it is also to replace inefficient situational management with a systemic approach in the management of the educational process at the HEI.
The large volumes of modern databases have generated a steady demand for new scalable data analysis algorithms. Systematizing the complex structure of big data has led to the emergence of affinity analysis, one of the most common methods of Data Mining. The purpose of this method is to investigate the relationship between events that occur together.
One popular method of knowledge discovery is the algorithms for associative rules finding. For the first time, the associative rules finding task has been proposed to find typical shopping patterns made in supermarkets, so it is sometimes also called market basket analysis.
Associative rules are now applied to solve problems in various areas: identifying sets of goods in supermarkets that are often bought together or never are bought together; identification of a part of clients who are positive about innovations in their services; determining the profile of visitors to the web resource. identification of a part of cases where new drugs cause dangerous side effects, etc.
The authors of the article aimed to embody the idea of affinity analysis and associative rules to optimize the educational process in the formation of the individual educational trajectory of the student. 5.
Although the National Agency for Quality Assurance of Higher Education promotes a wide selection of courses for students and claims not to limit their choice to separate blocks, the division of optional courses into logical units is a prerequisite for analyzing the structural and logical relationship between courses.
As initial data, we take the recommended optional courses of the professional training at the Faculty of Information Technologies at the Kyiv National University of Trade and Economic (Table 1). Once again, it should be stressed that there is no division of optional courses into blocks in the curricula of the Faculty of Information Technology. Courses are combined into logical units only as part of this study. According to the Regulation on the Organization of the educational process of students, the applicants choose educational courses for the next academic year in February. During the study, students are asked to choose one course from each logic unit. It should be noted that before the survey, students had the opportunity to familiarize themselves with presentations of optional courses to raise the consciousness of their choice.
A total of 100 faculty students enrolled in the second, third or fourth study years were interviewed. Such a sample is appropriate, as it takes into account not only the desire of students of junior courses to gain knowledge in certain areas of information technology in the future but also a certain experience of students of senior courses who have already studied some of the offered courses. Results of the courses selection among students of one of the groups of the Faculty of Information Technology are presented in Table 2. In this table, the ID is the serial number of the student who participated in the survey. Each row contains the results of the student-specific selection of six of the 24 courses offered in Table 1.
First, we find single-element course sets by presenting the transaction database from Table 2 in normalized form (Table 3). In this Table Uij – the course name with the course sequence number j belongs to the logical unit number i. At the intersection of the transaction row and the course, the column is 1 if the course is present in the transaction and 0 otherwise. The column amount will be the frequency at which each course appears in the selection results.
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prise Business analytics of an enterprise In the practical implementation of associative rule search systems different methods are used, which allow reducing search space to dimensions, providing acceptable computational and time costs, for example, Apriori algorithm [14-17]. The Apriori algorithm is based on the concept of frequent itemsets, i.e. sets with high frequency in a given number of transactions.
In the classic Apriori algorithm, a popular subject set is a subject set with support, equal to or greater than a given threshold. This threshold is called minimum support. However, the problem of establishing relationships between modules imposes limitations on the selection of single-element sets, which must contain courses from different logical units. Therefore, we form the set F1 of single-element subsets from the most frequent itemsets of each logical unit.
Next, we find two-element sets, forming all possible combinations from F1 two courses (Table 4). In the future, the most popular representative logical unit Ui will indicate the name of this unit. 2 U & 1 U 3 U & 1 U 4 U & 1 U 5 U & 1 U 6 U & 1 U 3 U & 2 U 4 U & 2 U 5 U & 2 U 6 U & 2 U 4 U & 3 U 5 U & 3 U 6 U & 3 U 5 U & 4 U 6 U & 4 U 6 U & 5 U 6 U & 5 U & 1 U 4 U & 3 U & 2 U 6 U & 3 U & 2 U 5 U & 4 U & 3 U 6 U & 4 U & 3 U 6 U & 5U U2&U3&U4&U6 & 3
U less than the minimum support threshold. So, the set F4 .
A graphical model of the formation of sets F1, F2 , F3 is presented in Fig. 1 U1
U2
U3
U4
U5
U6 U1 U5
U1 U6
U2 U3
U2 U4
U2 U6
U3 U4
U3 U5
U3 U6
U4 U5
U5 U6 U1 U5 U6
U2 U3 U4
U2 U3 U6
U3 U4 U5
U3 U4 U6
U3 U5 U6 all subsets F .
i If a subset f is a non-empty subset of Fi , then the association.
R : f Fi \ f , where Fi is the same subset without f , is considered. This procedure repeated for each subset f of Fi .
The associative rule consists of two sets of objects called a condition (antecedent, left-hand side – LHS) and consequence (consequent, right-hand side – RHS), which are signed as X Y : «If antecedent then consequent». Association rules describe the relationship between item sets, which is characterized by two main indicators – support S (support) and C (confidence).
Associative rule support S A B is the part of transactions that contain both antecedent and consequent. For example, for association A B support S A B means the fraction of the number of transactions containing antecedent A and consequent B to the total number of transactions.
Associative rule confidence С A B is a measure of the accuracy of a rule A B and is defined as the fraction of the number of transactions that simultaneously contain antecedent A and consequent B to the number of transactions that contain only antecedent A.
We form a set of associative rules for the set F3 .
For set U2 &U3 &U4 F3 U2 ,U3,U4 ,U2 &U3,U2 &U4 ,U3 &U4 . For set U2 &U3 &U6 F3 U2 ,U3,U6 ,U2 &U3,U2 &U6 ,U3 &U6 .
Because support and confidence give different evaluations of the quality of an associative rule, it is often the product S C of these two quantitative characteristics that are used to rank associative rules by priority (Table 8).
When we formed the set F1 of single-element frequent itemsets, we change the traditional scheme of the Apriori algorithm and set the task of identifying links between logical units. This approach is primarily related to the complexity of analyzing associative rules for all courses. In the case of a large number of transactions and a large number of courses, it is appropriate to use associative rule generation and processing software.
Such popular systems as Microsoft Power BI [27], R [28], RapidMiner [29], Deductor [30] and others have Associative rule tools. Next, we briefly describe the process of processing associative rules in the analytical platform Deductor Studio [31].
Deductor Studio uses a special unit «Associative rules» that implements the Apriori algorithm to solve such problems. When configuring the unit, it is possible to set minimum and maximum values of support and confidence of associative rules, calculate additional characteristics of the importance of rules (lift, leverage, improvement), create various visualizers (diagram, rule tree, OLAP cube).
The results of the survey of 100 students are processed. The Deductor system allowed the formation of 1,123 frequent itemsets with a capacity of up to five courses (Fig. 2) and found 8,594 associative rules (Fig. 3).
The formation of an individual educational trajectory is one of the main conditions identified in the guidelines for quality assurance in the European Space of Higher Education (ESG). A large number of courses creates significant difficulties in managing the choice process and often leads to situational management of the educational process in the HEI. The existing automation systems implement the complex management of a higher education institution and do not contain a module for automating the process of choosing academic courses.
As a systematic approach to manage the process of an individual student curriculum forming, we propose an algorithm based on the use of associative rules.
As a result of the Apriori algorithm using, we identified the associative rules of communication between educational courses chosen by the students together. The manual mode processing of 20 transactions revealed 18 popular course sets and 26 associated associative rules. The application of the Deductor system to process 100 transactions allowed the formation of 1,123 frequent itemsets and the identification of 8,594 associative rules. The number of rules that should be used in the management of the learning process depends on the minimum support threshold set, the confidence or their production.
The use of associative rules makes it possible to build logical links between different units of courses, to form an individual educational trajectory of the student and to develop a better strategy for managing the educational process of the HEI. It helps students to enhance their backround and knowledge by giving them the solid logical system of courses. This approach helps the HEI's management to be objective in the funds' allocation and staff management.
Obviously, the proposed approach requires further software development, which
can be more effectively implemented using business intelligence tools such as Python,
R, Microsoft Power BI.
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