The paper presents a formalized mathematical model for assessing the balance of educational program profiles in Ukrainian higher education institutions. The model is based on constructing a metric profile of program learning outcomes, which enables quantitative evaluation of program coherence and proportionality. The concept of a metric profile is introduced, and a method for calculating the balance coefficient of an educational program is proposed. A clustering approach for program learning outcomes is developed following the structure of the Computer Science Curricula 2023 (CS2023) framework, along with a normalization procedure for credit load comparison across programs. Examples of real educational programs are analyzed to demonstrate the model's applicability, including the use of radar (petal) charts for profile visualization. The proposed model provides a foundation for developing intelligent systems to support individual learning trajectories and can be adapted to various fields of higher education. educational trajectory, structural analysis of educational programs 1 ITS-2024: Information Technologies and Security, December 19, 2024, Kyiv, Ukraine ∗ Corresponding author. † These authors contributed equally.
The requirements of the labor market, the rigid framework of educational and professional
standards, and the needs of higher education students in choosing individual learning trajectories
necessitate the development of tools for multidimensional evaluation of the quality of educational
programs (EPs) and for the formalized comparison of their individual characteristics [
It should be noted that the diversity of educational programs (EduProgs) within a single specialty
creates significant challenges in transferring students between programs, even within the same
higher education institution (HEI), as well as in recognizing learning outcomes obtained through
academic mobility. Therefore, the establishment of a formalized mechanism for multidimensional
evaluation and comparison of EduProgs would make it possible to minimize losses during the formal
recognition of learning outcomes acquired outside the HEI [
The aim of this study is to develop a mathematical model that enables the formalization of criteria for evaluating and comparing EduProgs.
Higher education standards define the content of learning at each educational level for every specialty in terms of an integral competence, a set of general (GC) and special (SC) competences, the formation of which is achieved through the acquisition of program learning outcomes (PLOs) prescribed by the respective standard. It should be noted that in Ukraine, the structure of all higher education standards follows a unified model established by the Order of the Ministry of Education and Science of Ukraine No. 600 of June 1, 2016, “On the Approval and Implementation of the Methodological Recommendations for the Development of Higher Education Standards.”
Based on the approved higher education standards, higher education institutions develop unique educational programs (EduProgs) that differ in the structure of their educational components (EC), credit load, forms of final assessment, and the alignment of ECs with the program learning outcomes (PLO) and, consequently, with the competences defined by the standard. In addition to the sets of general (GC), special (SC) competences, and PLOs established by the standard, institutions may introduce additional components.
The model of the content of learning in the EduProg can be represented as a Knowledge Flow
Structure (KFS) [
Competency level (upper level): general competencies (GC1, GC2, GC3, etc.) are universal skills, knowledge, and abilities that are not tied to a specific specialty but are necessary for successful study, work, and personal development. For example, the ability to think abstractly and critically, the ability to work in a team, etc. They form the basis for interdisciplinary thinking, adaptation to change, and communication in modern society; special competencies (SC1, SC2, SC3, etc.) are knowledge, skills, abilities, and abilities that are directly related to a specific field of professional activity and provide students with indepth specialized knowledge and skills necessary to perform professional tasks and solve specific problems in the relevant field; competencies in their entirety form an integral competence, which is the main goal of this educational program. 2. Level of program learning outcomes (middle level): program outcomes (PLO1, PLO2, PLO3, etc.) are specific knowledge, skills, abilities, ways of thinking and other qualities that a student should acquire after completing the educational program. They are the criteria for assessing the success of the student's training (i.e., they must be specific and measurable), focus on what the student will be able to do in practice, and be useful for performing professional tasks in real life. 3. Level of educational components (lower level): educational components (EC1, EC2, EC3, etc.) or disciplines are the structural elements of the educational program that form the basis of the educational process and ensure the achievement of program learning outcomes and competencies. These are specific disciplines, practices, term papers/projects, qualification work aimed at developing the knowledge, skills, and abilities of students; educational components are the basis that ensures the formation of program learning outcomes through their content, which is determined by the discipline's work program; educational components are interconnected in a structural and logical diagram of the educational program - this is usually a graphical representation of the logical relationships between educational components, showing how one EC creates the basis for studying another. It allows you to understand the sequence of learning, demonstrating the logical relationship between individual disciplines and between disciplines and learning outcomes, and is used to plan the learning process.
Connections between levels: the level of educational components supports the level of program results (PR) through the implementation of relevant disciplines, courses, practices, etc; the level of program outcomes ensures the achievement of general competencies and special competencies, which ultimately form the integral competence of the educational program.
The upper and middle levels of the KFS are determined by the standards of higher education by specialty and level: first (bachelor's), second (master's) educational levels, and third (educational and scientific) level.
Thus, the standard of higher education in the specialty 122 "Computer Science" of the first (bachelor's) level of higher education [13] defines the integral competence, general competencies GC1-GC15 ( − ), special (professional, subject) competencies SC1-SC16 ( − ), the normative content of training in terms of learning outcomes ( − ) and the links between program outcomes and general and special competencies defined by the standard [13], which corresponds to the links between the upper and middle levels of the Knowledge Flow Structure in
The list of educational components and the logical connections among them, represented at the third (lower) level of the KFS in Fig. 1, are defined by the corresponding educational programs through their component lists. The descriptions of all educational programs also include a matrix of correspondence that maps the achievement of program learning outcomes to specific educational components, which corresponds to the relationships between the lower and middle levels of the
The European Credit Transfer and Accumulation System (ECTS) [14] represents a significant step toward the creation and implementation of formalized mechanisms that promote the standardization of approaches to the planning, evaluation, and quality assurance of educational programs, as well as the transparency and mutual recognition of academic results among higher education institutions across countries. ECTS provides a framework for quantifying students’ academic workload in the process of achieving planned learning outcomes and ensures the transparency and comparability of EduProgs, thereby facilitating academic mobility and the recognition of qualifications [15, 16].
The credit serves as the conventional unit for measuring a student’s academic workload, reflecting the amount of time required to achieve the program’s intended learning outcomes. One credit corresponds to 30 hours of student workload, including both classroom instruction and independent study. This system has long ensured a unified procedure for learning assessment across universities in different countries, allowing for the measurement and comparison of students’ learning outcomes and facilitating academic recognition and credit transfer among higher education institutions.
The Law of Ukraine "On Higher Education" establishes general requirements for educational programs and their volume in ECTS credits: bachelor's programs - not less than 180 and not more than 240 ECTS credits; master's program - 90-120 ECTS credits (for some specialties - not less than 60); Doctor of Philosophy (PhD) - 30-60 ECTS credits, with at least 25% of the volume of the educational program being its elective component. Thus, given that the formation of program outcomes defined by the Higher Education Standard can only be ensured by mandatory educational components of the EduProg, no more than 180 credits can be allocated for the formation of the EduProg at the bachelor's level for a 240-credit EduProg. Ideally, this credit volume should be evenly distributed among the planned learning outcomes.
Definition 1. The metric profile of an educational program is defined as a vector whose elements represent the number of credits allocated to the achievement of the respective program learning outcomes: =
, =
, where – is the number of program results.
To determine the metric profile of an educational program, it is necessary to transform the matrix of correspondence between program learning outcomes and mandatory educational components. This transformation replaces the binary relation between ECs and PLOs with an averaged value representing the number of ECTS credits allocated by each EC to the formation of a particular PLO. As a result, the matrix is represented in the following format: where
– is the average value of the number of credits allocated by the educational component i to form the program result ; and – are, respectively, the number of mandatory EC and PLO defined in the description of the educational program.
Thus, the elements of the metric profile of the educational program (1) are calculated on the basis of the matrix: : (1) (2)
A comparison of the balance coefficients of the metric profiles of different educational programs makes it possible to evaluate their balance, adaptability, and orientation. The generalized evaluation characteristics of EduProgs based on the analysis of their metric profiles are presented in Table 1.
It is evident that knowledge modeling cannot be fully represented by an additive model; however, the authors of this study rely on the model proposed by the Ministry of Education and Science of Ukraine (MES), which has been implemented across all higher education institutions in the country. Credits provide a convenient means of quantifying the contribution of each educational component to the learner’s body of knowledge, their influence on the formation of program learning outcomes, the level of student workload, and the achievement of the required competences defined by the educational program. Therefore, the determination of a program’s metric profile and its comparison with those of other educational programs can serve as an important instrument for modeling and evaluating educational program quality and for the formalized comparison of their individual characteristics, ensuring: an objective approach to program analysis, reducing the influence of subjective judgments; a simple mechanism with a high level of visual representation of the results in the form of graphs or diagrams to compare the programs of different educational institutions by a single measurable criterion; a simple and visual tool for tracking changes in educational programs based on the results of its implementation and monitoring; the ability to quickly respond to identified significant deviations already in the process of designing educational programs.
However, the comparison of programs by metric profile also has disadvantages: it does not take into account the integrity of the program, structural and logical relationships between disciplines, the level of achievement of PLO and their relevance (importance) for the labor market [17, 18]. The analysis should take into account that many professional competencies require an interdisciplinary approach (e.g., integration of statistics, machine learning and programming, etc.), so the comparison by individual PLO only ignores such interrelationships. In addition, the different number of learning outcomes and educational components for each individual PLO complicates their comparison, as it affects the distribution of credits and the alignment of components with program objectives. Evaluation characteristics of the EduProg based on the results of the metric profile analysis
=
, = ∑
− (3) (4) The balance of Indicates a more uniform distribution Indicates significant deviations from credit of credits among the program the mean, that is, the presence of allocation learning outcomes (PLOs), which clearly defined priorities or gaps, demonstrates that the program aims which may suggest either the to ensure equal development of all specialization of the program in PLOs without placing significant certain areas or insufficient attention emphasis on particular ones. to specific program learning This type of balance is characteristic outcomes (PLOs). At the same time, it of general or broad-based educational should be taken into account that a programs. high credit weight of an individual
PLO that considerably exceeds the average value may also reflect a strength of the program, where students receive advanced or in-depth training.
Program focus May indicate a more universal Indicates that the program has a and relevance program that ensures a balanced specific narrow specialization. to market development of skills. Such a program is oriented toward the needs This type of program is typical for training of highly specialized broad-based curricula aimed at professionals with in-depth preparing specialists with versatile knowledge in particular fields. professional competencies applicable The program has a clearer focus, across a wide range of occupations. although this may make it less The program is easier to adapt to adaptable to new labor market needs changes in labor market if the demand for other types of requirements, as it provides a baseline knowledge or skills changes.
in all areas.
Identification There is a risk of underperformance in There is a risk that the program pays of potential those PLO that received fewer credits insufficient attention to certain weaknesses of than others, which may affect the important areas (e.g., complex tasks the program overall competence of graduates in may be overlooked due to an attempt these areas. to distribute resources evenly).
It should be noted that the Ministry of Education and Science of Ukraine (MES) continues the reform of Ukrainian higher education in alignment with the European Higher Education Area (EHEA). As part of this process, new lists of specialties and updated approaches to the development of higher education standards by specialty have been introduced (Order of the MES of Ukraine No. 512 of March 27, 2025, “On the Approval of Methodological Recommendations for the Development of Higher Education Standards”). According to the approved recommendations, education standards will no longer include the normative content of training for students within educational programs in terms of program learning outcomes (PLOs) (with the exception of standards for regulated professions). Consequently, higher education institutions (HEIs), when developing their educational programs, will independently determine both the number and formulation of PLOs. This will significantly complicate the possibility of formalized comparison and assessment of the balance of EduProg metric profiles.
In view of this objective and comprehensive analysis, it is better to use a different approach to building a metric profile of the program, which provides a broader view of the program's balance, integration of knowledge and professional orientation.
In this study, the Computer Science Curricula 2023 (CS2023) [19] was used as a benchmark for comparing the profiles of educational programs in the specialty 122 “Computer Science.” This modern international standard reflects a consolidated vision of the structure, content, and competency framework of the computer science domain and serves as a conceptual foundation for the design and development of educational programs in this field. This choice was made due to several factors. On the one hand, its structure and content were developed taking into account global trends in the development of information technology, as well as the professional and social requirements for graduates. On the other hand, CS2023 provides a comprehensive, multi-level knowledge model that includes 17 Knowledge Areas and integrates both the knowledge-based and competency-based approaches. This makes it possible to compare educational programs both at the level of program learning outcomes (PLOs) and by generalized knowledge areas, which is consistent with the structure of educational programs in Ukraine.
The CS2023 standard distinguishes between “core” topics (CS Core), which must be included in every program, and “advanced” topics (KA Core), which may vary depending on the program’s profile. This approach is consistent with the logic of developing national higher education standards and allows for meaningful comparison regardless of the number or specificity of PLOs in a particular program.
Although there is no strict hierarchy among the 17 knowledge areas in CS2023, the authors of the document identify three competency areas, as well as a group of cross-cutting (general education) competences (Table 2), which serve as guidelines for constructing a holistic educational program profile.
Frequency SDF: Software Development Fundamentals, AL: Algorithmic Foundations, FPL: Foundations of Programming Languages, SE: Software Engineering AR: Architecture and Organization, OS: Operating Systems, NC: Networking and Communication, PDC: Parallel and Distributed Computing, SF: Systems Fundamentals, DM: Data Management, SEC: Security AI: Artificial Intelligence, GIT: Graphics and Interactive Techniques, HCI: Human-Computer Interaction, SPD: Specialized Platform Development SEP: Society, Ethics, and the Profession, MSF: Mathematical and
Statistical Foundations
In this study, an extended cluster model was applied to analyze educational programs (EduProgs). The model is based on the logical grouping of the CS2023 Knowledge Areas into six clusters (Table 3). According to the authors, this clustering offers several important advantages: it enables semantic generalization of the learning content by grouping domains that are similar in subject matter and professional orientation (for example, all topics related to algorithms, programming languages, and data structures are grouped into the Algorithmic & Programming Core cluster). the clusters facilitate the construction of graphical models (in particular, radar or petal diagrams), allowing for a visual representation of each program profile, identification of its strengths and weaknesses, and assessment of its balance and adaptability to labor market changes. the cluster structure enhances the interoperability of analysis results – it can be easily adapted for comparison among programs with different sets of PLOs, varying numbers of educational components, or differences in their formulation, as it operates at a higher level of abstraction. Programming Languages (FPL); Software Development
Architecture and Organization (AR); Operating Systems (OS); Networking and Communication (NC); Parallel and Distributed Computing (PDC); Systems Fundamentals (SF); Data Management (DM).
Applications and platforms
Specialized Platform Development (SPD); Graphics and
For a deeper analysis of the content structure of educational programs and their comparison with the international benchmark – Computer Science Curricula 2023 (CS2023) – this study conducted a classification of the program learning outcomes defined by the higher education standard for specialty 122 “Computer Science” according to the identified clusters. The results of this classification are presented in Table 4. Applications and platforms Artificial intelligence Algorithmic & Programming Core
PLO5, PLO9
PLO1, PLO2, PLO3, PLO6, PLO7, PLO8 PLO11, PLO15, PLO16 PLO10, PLO13, PLO14, PLO17
PLO4, PLO12
To perform the classification, a simplified expert (rule-based) approach was applied, which included the following steps: 1. Forming a list of key concepts characteristic of each cluster.
Comparison of key concepts with the wording of program results.
Conducting an expert evaluation of the domain content of each PLO to determine the most appropriate cluster for its classification.
Subsequently, the metric profile of the educational program was recalculated, taking into account the resulting classification of program results by the defined K clusters: = , k = 1, (5) where K is the number of defined clusters. Accordingly, each element of the metric profile is defined as the amount of ECTS credits allocated to achieve the relevant programmatic outcomes in the EduProg:
To improve the accuracy of inter-program comparison of the obtained results, the credit load values for each cluster were normalized. This approach makes it possible to standardize the measurement scale and ensure objectivity in the visualization and subsequent analysis of the balance of educational programs (EduProgs). The normalized value for each cluster was calculated by dividing the actual number of credits allocated to the corresponding cluster within each program by the maximum value of that cluster among all analyzed programs: = ⋃
, = 1, , = 1, , = ∑
, = ∑
, where K is the number of defined clusters, Q is the number of educational programs that are compared with each other.
This approach makes it possible to assess the relative saturation of each cluster within the set of programs, independent of the total volume or absolute ECTS credit indicators. It focuses attention on the structural priorities of programs and enhances the precision of analyzing their specialization, balance, and potential content disproportions.
For a comprehensive analysis of educational program profiles and the identification of their structural balance, it is advisable to apply visual methods of multidimensional comparison, among which the radar chart (petal diagram) is one of the most illustrative and analytically effective tools.
The radar chart allows for the simultaneous visualization of the distribution of intensity across key knowledge clusters within each program while preserving their structural arrangement. It enables the identification of both absolute and relative priorities in the content composition of a program. In the case of normalized values (as shown in Table 6), the radar chart also functions as a visual normalized profile, facilitating inter-program comparison regardless of the total ECTS credit volume.
To verify the hypothesis regarding the adequacy and sensitivity of the proposed formal model for assessing the balance of educational program (EduProg) profiles, a computational experiment was conducted. Within its framework, several bachelor’s EduProgs in the specialty 122 “Computer Science”, implemented by different higher education institutions (HEIs) of Ukraine, were analyzed. To illustrate the obtained results, examples of calculations are provided for three of these programs. In the following sections, these programs are referred to by the conventional identifiers EduProg1, EduProg2, and EduProg3. The initial calculation data for the selected programs are presented in
Where are the elements of the metric profile of the program P obtained by formula (2); t is the number of program results assigned to the corresponding cluster k. deviation of the credit dimension aimed at generating program results:
(the coefficient of balance of the EduProg metric profile) as the standard the relevant EduProg. program, but also to assess its balance.
(7) (8)
The metric profiles were constructed based on the matrices linking the program learning outcomes (PLOs) with the mandatory educational components (EduComps), followed by clustering according to CS2023, normalization of the credit load, and calculation of balance coefficients (standard deviations).
All calculations and visualizations (radar charts) were performed using Microsoft Excel, which ensured reproducibility of procedures and transparency of algorithmic steps. The obtained results were used to evaluate the structural balance of the programs, identify knowledge cluster priorities and deficiencies, and verify the consistency of the program profiles with the CS2023 core framework.
The graphical interpretation of the constructed metric profiles of the educational programs EduProg1-EduProg3 is presented in Figures 2, a) - c). Also in Figure 2, d) for comparison, generalized metric profiles of these EduProg are presented only taking into account the program learning outcomes (Р ), which are defined by the standard of higher education in the specialty 122 "Computer Science" of the first (bachelor's) level.
The results of the metric profile analysis for the selected educational programs (EduProgs) are presented in Table 6. The first part of the table shows the maximum, minimum, and average values of the credit load derived from the EduProg metric profiles, as well as the corresponding balance
coefficient. The second part of the table presents the total number of credits allocated for the formation of the standard program learning outcomes Р , along with the metric profile indicators and balance coefficient values calculated only for these PLOs.
Results of the analysis of the metric profile of the educational programs.
Results of the analysis of the metric profile of the educational programs clusters max 89,06 101,1 min 4,56 0
mid 30
27,75464 0,311701 30,01 32,704
0,323487
158 89,06 24,58 23,7 28,56 4,56 9,643 1 0,275 0,266 0,321 0,051 0,108 101,1 20,21 14,69 20,52 0 23,52 1 0,2 0,145 0,203 0 0,233 95,48 21,6 31,43 21,99 0 9,492 1 0 0,226 0,329 0,23 0,099
3 2 3,8 max min
mid 53,3 37,8 23,7 11,5 8,5 5,3 11 8,5 9,9 49 64 8 41 11 8 0,766 1 0,125 0,641 0,172 0,125
The classification of program learning outcomes according to the defined clusters was carried out for all PLOs specified in the educational programs (Table 7). Distribution of ECTS credits of different EduProg by clusters
The results of the analysis of the metric profile of clusters for the selected educational programs are presented in Table 9. The first part of the table provides the maximum, minimum, and average values of the credit dimension of the EduProg clusters based on their metric profiles, as well as the obtained values of the profile balance coefficient without normalization and with normalization of the credit dimension of the clusters taken into account. Normalized ECTS credit distribution across CS2023 clusters for three CS programmes
2 3 4 5 6 # 1 2 3 4 5 6 Applications and platforms Artificial intelligence
Foundations Algorithmic & Programming Core Software Engineering Systems & Infrastructure Applications and platforms
Artificial intelligence
CS Core 95,48 64 0 8 29,99 30,17 30,94343 22,23673 0,324151 0,347514
The radar charts, constructed based on the normalized values, make it possible to visualize the distribution of knowledge cluster weights within the structure of the analyzed educational programs (EduProg1, EduProg2, and EduProg3) (Figures 3–6).
The educational program EduProg1 is characterized by a relatively uniform distribution across the knowledge clusters. Four of the six clusters have values within the 0.25–0.32 range (Algorithmic Core, Software Engineering, Systems & Infrastructure, and AI), which indicates a tendency toward broad-based training. The highest values are observed in Foundations (1.0), Systems & Infrastructure (0.321), and Algorithmic Core (0.275), suggesting a high content density in the fundamental, infrastructural, and algorithmic components that form a solid basis for a universal educational trajectory. The moderate coverage of the AI domain (0.108) and the low representation of Application & Platforms (0.051) indicate potential areas for further program development.
The profile of EduProg2 demonstrates a distinct dominance in the Artificial Intelligence cluster (0.233) – the highest value among all analyzed programs. This allows EduProg2 to be interpreted as a program oriented toward training specialists in the fields of Data Science and Machine Learning (ML). At the same time, the considerably lower values in Software Engineering (0.145) and Algorithmic Core (0.200) indicate a less pronounced engineering component. The Application & Platforms cluster is completely absent, which may potentially limit graduates’ competences in UX/UI design, cross-platform applications, or interactive technologies.
The profile of EduProg3 shows the highest value in the Software Engineering cluster (0.329), which is almost twice as high as the corresponding values for EduProg1 and EduProg2. This provides grounds to position the program as engineering-oriented. The high values in Systems & Infrastructure (0.230) and Algorithmic Core (0.226) further confirm its technical training profile. At the same time, the low value in Artificial Intelligence (0.099) and the complete absence of Application & Platforms (0.000) indicate a lack of content in areas related to interactivity, UX, and modern interface design, which may affect the program’s adaptability to emerging challenges in digital product development.
For an objective assessment of the development directions of educational programs (EduProgs), it is appropriate to compare them with a reference model that reflects the recommendations of the international academic community. In this study, such a reference was represented by the core curriculum profile (CS Core) in accordance with the Computer Science Curricula 2023 (CS2023), which defines the fundamental knowledge and skills that should be ensured by any computer science program.
Table 6 and Figure 3(b) present the normalized CS Core profile across six knowledge clusters. According to this profile, the clusters with the greatest weight are:
Algorithmic & Programming Core - 1.0; Systems & Infrastructure - 0.641;
Foundations - 0.766.
Other clusters have smaller but still significant intensity – specifically Artificial Intelligence (0.125), Software Engineering (0.125), and Application & Platforms (0.172) – which together represent the minimum essential content for a modern, comprehensive computer science curriculum.
A comparison of real educational programs with this model shows the following:
EduProg1 is the closest to the CS Core: it covers all clusters and demonstrates high values in Foundations, Algorithmic Core, and Systems & Infrastructure – the three fundamental areas. This indicates a strong alignment with international benchmark recommendations EduProg2 exhibits significant deviations: the Algorithmic Core cluster has a low value (0.200) while AI shows a high emphasis (0.233), which does not correspond to the recommended balance of the core. This may indicate insufficient fundamental engineering training compared to the analytical component.
EduProg3, on the other hand, exceeds the benchmark values in Software Engineering (0.329) but completely lacks coverage of Platforms & UX, while AI is represented only minimally. The program is thus more technically specialized but less comprehensive in the area of digital technology applications. The paper presents a formalized approach to assessing the balance of educational programs (EduProgs) through the construction of a metric profile and its interpretation via a balance coefficient. The proposed model is based on the Knowledge Flow Structure (KFS) framework and enables the formation of a matrix of weighted relationships between educational components and program learning outcomes. This provides a means for quantitative evaluation of the distribution of credit load across learning outcomes.
The computation of the metric profile and the corresponding coefficient allows for the assessment of the uniformity of PLO formation, the identification of program priorities, and the detection of potential risk areas. The semantic grouping of PLOs according to the cluster model derived from the Computer Science Curricula 2023 (CS2023) ensures the possibility of comparing EduProgs even when they have different sets of PLOs. The constructed radar charts visually illustrate the distribution of knowledge and reveal the strengths and weaknesses of each program.
The developed mathematical model for assessing the balance of educational program (EduProg) profiles is grounded in the principles of mathematical modeling, cluster analysis, and data normalization, which are fundamental to the field of computer science. The model is universal and can be adapted to various specialties and educational levels, demonstrating both flexibility and crossdisciplinary applicability. It is particularly relevant for disciplines characterized by rapid technological change, such as information technology.
Within the framework of this study, Microsoft Excel was used to verify the hypothesis concerning the adequacy, sensitivity, and practical applicability of the proposed formal model for assessing EduProg balance. This tool enabled the implementation of algorithms for metric profile formation, CS2023-based clustering, normalization of credit load indicators, and calculation of balance coefficients, thereby ensuring automation of computations, algorithmic transparency, and reproducibility of results. The obtained calculations confirmed the validity of the hypothesis and demonstrated the analytical capability of the model to identify structural disproportions and patterns within educational program profiles. This provides a solid foundation for further software implementation of the model in the form of a specialized analytical application or an intelligent decision-support system designed for analyzing, comparing, and optimizing educational programs across different levels and specialties.
Beyond its analytical potential, the proposed approach can be applied to the development of an intelligent adaptive system for managing individual learning trajectories, personalizing curricula, detecting knowledge gaps, and enhancing the flexibility of educational programs.
For further development of the model, both cardinal and ordinal measurement scales may be employed. In particular, weighting coefficients of significance for all model components – competences, program learning outcomes, and educational components – can be defined using expert methods. The relative importance of these components can then be determined through ranking of alternatives, pairwise or multiple comparisons, and various clustering techniques for result aggregation [20, 21]. The authors have not employed any Generative AI tools.