Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ
The National Multi-subject Test has been prepared and conducted in Ukraine in online learning conditions for several years. Test results show a decline in schoolchildren’s performance in mathematics. The article presents a prototype of an intelligent training system for solving mathematical problems...
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The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2025
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Репозитарії
System research and information technologies| _version_ | 1867334453598093312 |
|---|---|
| author | Kulik, Anatoliy Zeleniak, Oleg Chukhray, Andriy Prokhorov, Oleksandr Yashyna, Olena Havrylenko, Olena Yevdokymov, Oleksandr Torzhkov, Andrii Zayarnyi, Oleksii |
| author_facet | Kulik, Anatoliy Zeleniak, Oleg Chukhray, Andriy Prokhorov, Oleksandr Yashyna, Olena Havrylenko, Olena Yevdokymov, Oleksandr Torzhkov, Andrii Zayarnyi, Oleksii |
| author_institution_txt_mv | [
{
"author": "Anatoliy Kulik",
"institution": "National Aerospace University “Kharkiv Aviation Institute”, Kharkiv"
},
{
"author": "Oleg Zeleniak",
"institution": "Olexandriya Multi-Profile Lyceum, Olexandriya"
},
{
"author": "Andriy Chukhray",
"institution": "National Aerospace University “Kharkiv Aviation Institute”, Kharkiv"
},
{
"author": "Oleksandr Prokhorov",
"institution": "National Aerospace University “Kharkiv Aviation Institute”, Kharkiv"
},
{
"author": "Olena Yashyna",
"institution": "National Aerospace University “Kharkiv Aviation Institute”, Kharkiv"
},
{
"author": "Olena Havrylenko",
"institution": "National Aerospace University “Kharkiv Aviation Institute”, Kharkiv"
},
{
"author": "Oleksandr Yevdokymov",
"institution": "National Aerospace University “Kharkiv Aviation Institute”, Kharkiv"
},
{
"author": "Andrii Torzhkov",
"institution": "SoftServe"
},
{
"author": "Oleksii Zayarnyi",
"institution": "National Aerospace University “Kharkiv Aviation Institute”, Kharkiv"
}
] |
| author_sort | Kulik, Anatoliy |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2025-07-25T15:56:08Z |
| description | The National Multi-subject Test has been prepared and conducted in Ukraine in online learning conditions for several years. Test results show a decline in schoolchildren’s performance in mathematics. The article presents a prototype of an intelligent training system for solving mathematical problems that should become an accessible test preparation tool. The system provides a solution to a wide range of mathematical problems in a step-by-step mode. The system is developed in accordance with the principle of rational management by diagnosis, which implies the presence of many diagnostic models. It allows for deep diagnostics of student errors. Artificial intelligence tools will make it possible to implement individual recommendations for each student, taking into account their level of preparation and learning goals. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2025.2.09 |
| first_indexed | 2025-07-27T04:04:09Z |
| format | Article |
| fulltext |
Publisher IASA at the Igor Sikorsky Kyiv Polytechnic Institute, 2025
Системні дослідження та інформаційні технології, 2025, № 2 125
TIДC
НАУКОВО-МЕТОДИЧНІ ПРОБЛЕМИ
В ОСВІТІ
UDC 004.8: 004.421.2
DOI: 10.20535/SRIT.2308-8893.2025.2.09
THE CONCEPT OF INTELLIGENT TRAINING SYSTEM FOR
UKRAINIAN SCHOOL FINAL STEM EXAM PREPARATION
A. KULIK, O. ZELENIAK, A. CHUKHRAY, O. PROKHOROV, O. YASHYNA,
O. HAVRYLENKO, O. YEVDOKYMOV, A. TORZHKOV, O. ZAYARNYI
Abstract. The National Multi-subject Test has been prepared and conducted in
Ukraine in online learning conditions for several years. Test results show a decline
in schoolchildren’s performance in mathematics. The article presents a prototype of
an intelligent training system for solving mathematical problems that should become
an accessible test preparation tool. The system provides a solution to a wide range of
mathematical problems in a step-by-step mode. The system is developed in accor-
dance with the principle of rational management by diagnosis, which implies the
presence of many diagnostic models. It allows for deep diagnostics of student errors.
Artificial intelligence tools will make it possible to implement individual recom-
mendations for each student, taking into account their level of preparation and learn-
ing goals.
Keywords: intelligent tutor system, National multi-subject test, math problems.
INTRODUCTION
The traditional education system was formed in the conditions of gradually in-
creasing volumes of information and focused on the formation of a certain critical
amount of knowledge, on the basis of which the necessary skills were formed. In
modern conditions of digitization and exponential increase in information load,
even a highly qualified instructor is not able to effectively adapt the educational
process to each pupil or student in the class (group), also taking into account the
need for inclusive education.
Intelligent Tutoring Systems (ITS) are effective tools of solving the problem.
At the same time, none of the developed ITS has yet approached the effect of in-
dividual learning described by the famous American psychologist B. Bloom: the
average success rate of a student who learns individually can be better than the
success rate of 98% of students who learn in a traditional way: one mentor for
thirty students.
Thus, the development of ITS is relevant for improving the efficiency and
quality of education, which allow to combine, within the requirements of the
modern educational system, the existing methodical and pedagogical experience
of leading mentors with an individual approach to the education of each of the
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pupils and students with different basic levels of training, motivation and peculi-
arities of perception information
The paper proposes the author’s scientifically based viewpoint at the tech-
nology of creating ITS in exact sciences for preparation for the National multi-
subject test (NMT).
LITERATURE REVIEW
The paper [1] proposes a taxonomy of artificial intelligence (AI) methods used in
digital tools for teaching mathematics. The taxonomy consists of four categories
that cover the entire range of such AI systems:
1. Information Extractors to denote AI technologies that take observations
from the real world (test, audio, images) and transform them into a mathematical
representation.
2. Reasoning Engine, which includes all software systems capable of auto-
matically solving a mathematically formulated problem.
3. Explainers, i.e., the field of explanatory artificial intelligence research that
deals with the development of artificial intelligence methods that produce inter-
pretable models and interpretable solutions.
4. Data-driven Modeling, where methods of intelligent data analysis and
machine learning are used to analyze this data and turn it into practical models.
In [2], an intelligent tutoring system for mathematics uses the author’s ITSB
tool with four modules — domain, learning, student, and user interface — coordi-
nated by the training module. The system collects personal and academic data,
tracks student progress, and adapts learning paths based on profiling and activity
monitoring.
In [3], an intelligent system teaches fractions multiplication and division via
adaptive dialogue, identifies errors in real time, and employs cognitive conflict,
problem simplification, and representative learning.
In [4], an AI-based system improves mathematics education strategies in un-
derprivileged regions by integrating rating scales, norms, improvement strategies,
and an intelligent assessment program. It diagnoses learner performance in batch-
es and automatically proposes targeted improvements.
Scientists of the National Aerospace University “Kharkiv Aviation Institute”
proposed their own approach to the creation of intellectual educational programs.
The article [5] discusses the technology of building intelligent computer programs
for learning algorithms. The subject area of study is an algorithmic tasks which
are characterized by properties of determinism, mass and efficiency. Develop-
ments are based on an approach to the rational control of objects in conditions of
partial uncertainty. Proposed information technology based on an approach to the
rational control of objects in conditions of partial uncertainty.
The process of step-by-step solution of algebraic equations is considered in
the article [6]. On the basis of the signal-parametric approach to diagnostics of
faults in dynamic systems the mathematical diagnostic models are created which
allow detecting classes of errors by comparing the results of Student’s calcula-
tions and the results of system calculations. The approach to the formalization of
the generation of problem situations applicable to the development of tutoring
programs consisting of many tasks is considered in [7]. The parametric generation
method proposed in the article allows getting the large quantitative variations in task
problem situations. Thereby, every learner will get a personal unique set of tasks.
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In [8], OnlineMSchool offers math problems of varying complexity and
online calculators that show step-by-step solutions.
In [9], IXL Learning provides interactive exercises, personalized recommen-
dations, and real-time diagnostics for math and language skills.
In [10], Khan Academy delivers free, self-paced courses across various sub-
jects, featuring thousands of videos, adaptive exercises, and progress tracking. Its
paid AI tool, Khanmigo, uses ChatGPT technology to serve as a personal tutor for
students and an assistant for teachers.
LearnBop [11] is a virtual system guiding children step-by-step through
math problems, pinpointing gaps in foundational knowledge. Uses images, graph-
ics, and video hints (via LearnZillion). Teachers can customize lessons, track pro-
gress, and assign interventions with the built-in LMS. Children enjoy the panda
mascots during lessons.
Mangahigh [12] is a web platform offering math games, tutorials, and tests
aligned with Common Core standards, covering fundamentals from counting to early
algebra and geometry. Learning adapts to the learner’s level, and wrong answers
come with explanations. More practice variety could further enhance skill depth.
GeoGebra [13] is a free program enabling students to create, visualize, and
manipulate mathematical models in algebra, geometry, and more. It has browser
and mobile versions, with a vast library of ready-made resources. Though there’s
a learning curve, its interactive approach helps students explore and understand
math concepts hands-on.
CueThink [14] introduces Thinklets: four-step solutions — Understand, Plan,
Solve, and Revise. Students view teacher assignments, create videos showing their
solutions, and share them with peers for feedback. Tools like markers and notebooks
support each step, fostering collaboration and deeper problem-solving skills.
WeBWorK [15] is a free Perl-based system (launched in 1995) for online
math homework, developed at the University of Rochester. Gives students imme-
diate feedback, encouraging multiple attempts. Distinguishes itself by integrating
LaTeX with Perl for flexible problem generation.
In turn, IMathAS [16] is an internet-based math assessment system generat-
ing algorithmic questions with numeric or symbolic answers. Includes learning-
control tools, shows math and graphs accurately, and accepts simple calculator-
style inputs..
WirisQuizzes is a tool for creating STEM assessments with equations,
graphs, or text answers, automatically graded. Random parameters help prevent
cheating. It integrates seamlessly with different systems, allowing dynamic ques-
tion generation in real time.
Recently, many math-focused educational resources have begun using gen-
erative AI (e.g., ChatGPT). While machine learning has advanced significantly,
including ChatGPT, it lacks a “true understanding” of math and can struggle with
structured computation. Though ChatGPT may generate plausible explanations, it
is often unreliable for precise answers. A solution involves connecting ChatGPT
to Wolfram|Alpha, whose computational “superpowers” rely on Wolfram Lan-
guage [17] for exact code and computations.
Another interesting study in the direction of the application of AI for math-
ematics was presented by the division of the Google company Deepmind. Al-
phaGeometry [18] solves complex geometry problems at near — Olympic gold
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medalist level, a notable breakthrough in AI. In testing with 30 Olympiad geome-
try problems, AlphaGeometry solved 25, compared to 10 by the previous best
system and 25.9 by the average gold medalist. AI often struggles with complex
geometry due to limited reasoning and training data. AlphaGeometry tackles this
by merging a neural language model’s predictive power with a rule-based deduc-
tion engine.
Thus, the possibilities of preparing for the NMT in mathematics are quite
powerful, schoolchildren and teachers can choose the tools at their discretion and
estimate the effectiveness of learning on trial tests that have been developed by
the Ukrainian Center for Education Quality Evaluation. On the other hand, we
will analyze the results of last year’s testing of Ukrainian students within the
NMT, using data from the official report [19].
The certification work contains tasks of various forms:
1. Tasks 1–15 with the choice of one correct answer (1 point).
2. Tasks 16–18 for matching, determining “logical pairs” (3 points).
3. Tasks 19–22 open form with a short answer (2 points).
The maximum number of points that could be obtained by correctly complet-
ing all the tasks of the certification paper in mathematics is 32.
The mathematics test was included in the main block of the NMT, the sub-
jects of which were mandatory for all test participants. Fig. 1 shows the distribu-
tion of mathematics test participants by the number of test points scored. The dia-
gram shows that the vast majority of participants scored less than 10 points,
which is a very low indicator for the possibility of further study at a university.
The share of competence tasks, namely: the task of constructing a pie chart
according to a known distribution, calculating the percentage of a number, classi-
fying a body formed as a result of the rotation of a geometric figure around an
axis, and the combinatorial task of determining the number of options using com-
binations and multiplication rules — was 23 % of all test tasks.
Fig. 1. Distribution of mathematics test participants by the number of test points scored
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The analysis of the results of the tasks of the certification work showed that
even the tasks for checking the level of formation of basic skills and abilities and
their application when solving standard problems cause difficulties for the par-
ticipants. The number of such tasks was two-thirds of the total number of certifi-
cation work tasks. For example, 48% of participants successfully coped with task
6 on the reproduction of facts (determining the zero of the function according to
the given graph). Problem 20 from combinatorics caused the greatest difficulties,
only 12.7% of those tested gave the correct answer.
The statistical indicators of the NMT tasks have slightly deteriorated com-
pared to the corresponding indicators of the VET tasks of previous years. Thus, in
2020, more than two-thirds of the participants completed the task of determining
the zero of the function according to the given figure, and in 2023, less than half.
In 2020, 60% of the test subjects completed a short-answer task to check the fi-
nancial literacy of participants, which involved finding percentages from a num-
ber, and in 2023, only 53.6% completed a similar task with choosing the correct
answer from five offered [20].
The analysis of the statistical indicators of the certification work revealed a
high distributive ability of the test tasks with an average score of 56.7, which
made it possible to single out the participants prepared for study in higher educa-
tion institutions.
The analysis of the results of the NMT in mathematics for the past year, as
well as the tendency of deterioration of performance indicators in previous years,
makes the task of improving the methodology of preparing for the NMT in math-
ematics with the help of intelligent computer training programs an urgent and im-
portant task.
THE LEARNING PROCESS FROM THE POINT OF VIEW OF CONTROL
THEORY
There are three classical control principles: impact control, disturbance control,
and deviation control. They allow you to achieve the goal in different ways.
Many destabilizing factors — well-being, mood, motivation, and a student’s
initial preparation — affect progress toward learning goals. We can’t effectively
manage these without identifying them through interaction with the student.
A different approach, the principle of control by diagnosis, is needed to address
these challenges.
Let’s consider the application of various control principles in the educational
process.
When teaching calculation skills (e.g., in math, physics, or chemistry), two
types of teachers illustrate how control principles are applied: Schematically, such
a learning process can be represented by the following diagram (Fig. 2).
LESSON
PROGRAM
Teacher STUDENTS
KNOWLEDGE
SKILLS
Errors
Errors
a
b
Fig. 2. Scheme of training control: a — regular; b — irregular
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Teachers (Fig. 2, b) follow formal procedures and schedules without deeply
checking each student’s work, feedback is irregular, only at control points or at the
end of class, quality and efficiency suffer because errors are not addressed quickly
Professional teachers (Fig. 2, a) provide ongoing, personalized feedback.
They regularly identify errors, clarify misunderstandings, and strengthen student
motivation. This “vector feedback,” or continuous monitoring and correction,
aligns with personalized training methods and achieves the highest efficiency and
quality of learning.
High efficiency and significant quality of skill training are achieved with in-
dividual training. With such training, the teacher has the opportunity to identify
“gaps” in knowledge, reasons for misunderstanding the theory, errors in the abil-
ity to apply theoretical knowledge in the practice of calculations, weak motivation
and a number of other reasons for imperfect ability to solve calculation tasks, as
well as to quickly increase the level of knowledge and the necessary skills to
overcome the difficulties found in the student. The learning control process in this
case is based on operational system diagnostics of the student’s knowledge and
skills (Fig. 3).
In such a learning process, the teacher has more opportunities to diagnose
the causes of errors made when solving the calculation task, as well as more op-
portunities to eliminate them with help the involvement of additional material that
is more accessible to this student with the help of an insightful explanation of the
causes of errors and ways to eliminate them. Diagnosing errors in this learning
process is a highly intellectual type of teaching activity that allows you to identify
weaknesses in the student’s training in the ability to acquire new knowledge and
use it in practical activities, in motivation.
Productive control of skill training is based on the use of the principle of di-
agnosis control [22].
Based on the results of the analysis of the above principles, and taking into
account the work created by Professor A.S. Kulik approach to the rational control
of objects in conditions of partial uncertainty was formed by the block diagram of
the system of rational control of education with the help of ITS, depicted in Fig. 4.
As shown in figure the 6 main blocks in the learning control system with the
help of ITS are the student diagnosis and modeling block (BDMO), as well as the
learning action selection block (BBBV). Through the feedback channel, the data
entered by the students in the IKOP are sent to the BDMO. In addition, as input
actions on the BDMO, the necessary KZU and reference data are required in the
ITS. BDMO affects BVOV by transferring the diagnosis, and even the model of
the student.
LESSON
PROGRAM
Teacher
STUDENTS
SKILLS
KNOWLEDGE
Errors
Diagnosing
Fig. 3. Scheme of rational training control
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PECULIARITIES OF THE COMPUTER IMPLEMENTATION
OF THE PRINCIPLE OF CONTROL BY DIAGNOSIS
The principle of control by diagnosis has been applied in various projects focused
on rational control of physical objects, using diagnostic models and knowledge
bases on emergency behavior. Its computer-based implementation for training
involves breaking down calculation tasks into stages, each producing intermediate
numerical results for verification. Since mistakes can occur at any operation, each
stage’s result is compared with a reference outcome. Errors are then diagnosed by
locating the incorrect operation and identifying the specific error. This step-by-step
diagnostic process relies on a detailed solution model, making a production knowl-
edge base and dichotomous tree structure ideal for implementing diagnostic control.
The consolidated structure of the curriculum, which implements the principle
of diagnosis control, can be presented graphically in the following way (Fig. 5).
The scheme presents the functionally necessary software modules for the
implementation of the principle of control based on the diagnosis. In the key
module — the diagnostic module, a step-by-step program for diagnosing the re-
sults of student problem solving is implemented.
The module receives data from the knowledge base (machine solution) and
the student’s solution. After diagnosing the student’s errors, it sends the results to
the resource control module, which provides explanations and guidance for cor-
Fig. 4. Block diagram of the system of rational control of training with the help of ITS
Fig. 5. Scheme of learning skills using the principle of diagnosis control
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rection. The student then recalculates the problematic stage, iterating until their
results match the correct solution. A control unit synchronizes all modules, and
upon completion, generates performance indicators and an assessment of the stu-
dent’s ability. This iterative process arises due to insufficient preparation and the
inevitable calculation errors.
A GENERAL APPROACH TO COMPUTERIZED LEARNING
The learning process is realized by a combination of internal and external cycles.
The process of problem solving forms an internal learning cycle.
The student receives a task. He can immediately go to the answer or
choose a step-by-step mode. In the step-by-step mode, he receives hints
previously created by the teacher and implements his solutions. In this, it
performs both calculations and symbolic or graphic transformations. If the answer
is correct, it is highlighted in green and the student can proceed to the next task. If
an incorrect solution is entered at the next step, the system issues the message
“Think!” without specifying what the error is. The student can correct the error
himself or ask for a hint. In the case of a repeated error, the input field is
highlighted in red, visualizing the incorrect component of the solution. At the next
error, built-in models are included to search for the cause of the error and generate
an individual prompt. If the student could not complete the task, he can request a
solution to this step. The correct solution is filled in by the system and highlighted
in orange, after which the Student is prompted to proceed to the next step. The
internal cycle is schematically presented in Fig. 6, 7.
New task
Do you have
answer?
Student’s answer
Correct?
Yes
Step mode
No
No
Yes
No
Increase
competencies
All steps
solved?
Decrease
competencies
Yes No
Congratulations!
Shall we continue?
Don’t give up!
Shall we continue?
Fig. 6. Internal cycle of solving the task
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Th e external cycle manages the learning process depending on the achieved
competencies and the results of solving tasks. It can be presented schematically in
the form of a Table 2.
T a b l e 2 . External cycle of task selection
Last task solved
Correct Incorrect
H
ig
h Suggest a high difficulty problem
or move on to the next section
Decrease the competency level
and suggest the next task
C
om
pe
te
nc
ie
s
le
ve
l
L
ow
Increase competency level and offer
a more complex task
Decrease the competency level and:
– offer work in demo mode;
– recall theoretical material;
– propose a simple task
The choice of the next task depends on the results of solving the previous
one and previously achieved competencies. If the student successfully coped with
the task, he is offered a more difficult task or a transition to the next chapter. If he
made a mistake, and before that he had a high level, another task is offered. If he
had a low level of competence and made mistakes again, he is offered a simpler
task, as well as an opportunity to familiarize himself with the solution of tasks in
a demonstration mode, that is, without evaluation. In addition, links to the theo-
retical material, which is desirable to repeat, are offered.
Based on the results of solving the problem, the student’s level of compe-
tence is assessed on a probability scale (the probability of mastering this compe-
tence ranges from 0 to 1). Initially, it is equal to 0.5. Successful decisions increase
this possibility, and mistakes decrease it. Achieving a level of 0.95 means master-
ing this competency.
Systematically modeling effective pedagogical activity, we will get three
modes of operation of ITS: demonstration, training and test (Fig. 8). Thus, first
the instructor explains the new material, demonstrating how new tasks for the stu-
dents are solved, then calls the students to the blackboard and formulates tasks
from the considered class of tasks, while helping the students in case of difficul-
Fig. 7. Step mode
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ties or wrong actions. Finally, to test the acquired knowledge and skills, the men-
tor gives homework or a control work, which the students solve independently,
without prompts.
In the second mode, the task is formulated by the program, and the learner
must complete it step by step. In case of mistakes or substitutions of the student,
the ITS can give him a hint. The student can also ask questions to the program.
In the third mode, the task is formulated by the program, and the learner has
to complete it. Unlike the previous mode, hints are not available. Also, the student
does not have the opportunity to ask the program questions.
In order to develop stable skills for solving mathematical problems, the stu-
dent must solve a number of problems of a certain class, which differ in condi-
tions and numerical parameters. This increases the degree of assimilation of com-
petencies, and also prevents memorization of answers to improve results when
retaking tests. For this, it is necessary to ensure:
1) a set of meaningful statements for individual classes of mathematical
problems (if possible);
2) the possibility of generating random numerical parameters for all classes
of tasks.
To store problem templates in the system, the LATEX format is used — the
data markup language and the TeX macro package, which is considered the de
facto standard for preparing mathematical and technical texts for publication in
scientific publications [109].
Fig. 8. Operating modes of education al programs
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When the task template is entered, the teacher will have several fields as-
signed to different areas on the student’s screen, which he can use to fill out in
LATEX format. Numerical parameters are generated according to the scenario
defined by the teacher.
For example, a hint template for one of the steps of a vector algebra task
looks like this:
step_21_2.Text_Sample ="We got the equation \n\n"+ \
"$\overrightarrow{{AB}}({task21.xab}; {task21.yab};
{task21.zab}) = \overrightarrow{{((({task21.xb})‐ xa;
{task21.yb}) – ya; ({task21.zb}) ‐ za)}}$ \n\n" + \
"Deduce from it equations for individual coordinate compo‐
nents in the form: \n\n"+ \
"$xab=xb‐xa$, \n\n"+ \
"$yab=yb‐ya$, \n\n"+ \
"$zab=zb‐za$, \n\n"+ \
"where $\overrightarrow{{AB}}(xab; yab; zab)$ ‐
coordinates of the vector $\overrightarrow{{AB}}$"
After its interpretation by the program and generation of numerical parame-
ters, we will get the prompt shown in Fig. 9.
By storing parameter-generation and calculation functions as scripts in the
database, the system can dynamically create a new, unique set of problems each
time a student takes the test. This not only prevents students from memorizing
fixed question sets but also promotes deeper understanding and problem-solving
skills through repeated exposure to varied task scenarios.
Thus, each time the student passes the test, he receives a unique set of tasks
generated just for him.
To increase the motivation of students in the programs, it is advisable to im-
plement the game principle. The prototype uses playful, step-by-step interaction
to keep students engaged. By “peeling the nuts” (solving each part of the problem
in sequence) and assembling correct answers like puzzle pieces, learners gain a
sense of exploration and achievement. Game elements such as immediate feed-
back, hints, and visual cues transform the learning process into an enjoyable ex-
perience.
Students have the option to either enter the final answer directly or work
through each stage of the solution. This approach fosters incremental learning:
students can pinpoint exactly where they go wrong and receive immediate guid-
ance on how to correct it. Over time, these targeted corrections reinforce strong
problem-solving habits.
Fig. 9. A hint for a step-by-step solution of the problem with generated numerical parameters.
A. Kulik, O. Zeleniak, A. Chukhray, O. Prokhorov, O. Yashyna, O. Havrylenko, O. Yevdokymov…
ISSN 1681–6048 System Research & Information Technologies, 2025, № 2 136
By tracking each step and offering just-in-time assistance, the system helps
students identify and rectify misconceptions before they become entrenched. This
ultimately leads to more stable competencies in arithmetic, algebraic manipula-
tions, and other targeted math skills.
In Fig. 10 shows screen forms of the process of step-by-step solution of one
of the NMT problems. The student has the opportunity to immediately enter the
answer, or to solve the problem step by step, peeling the “nuts”. At each step, he
assembles the correct answer, like a puzzle, by dragging the pieces of the answer
(correct or incorrect) into the corresponding fields. If necessary, he can get addi-
tional information.
In this way, the student in a playful way solves a number of tasks of a certain
class, forming and consolidating the relevant competencies.
CONCLUSIONS
We have presented an author’s vision of a modern Intelligent Tutoring System
(ITS) for exact sciences, particularly mathematics, aimed at preparing Ukrainian
schoolchildren for the National Multi-Subject Test. A functional prototype has
been developed to demonstrate how diagnostic control, real-time feedback, and
adaptive guidance can be effectively combined.
Our prototype employs structured knowledge bases, algorithmic problem
generation, and iterative error diagnosis. This design ensures that each step of
a student’s solution can be systematically monitored and corrected, demonstrating
a high level of scientific rigor in both pedagogy and software engineering.
Through an analysis of existing tools and research, we identified critical
gaps in personalized learning and feedback mechanisms within mathematics edu-
cation. The prototype addresses these gaps by incorporating specialized modules
for real-time assessment and targeted remediation.
Based on the prototype’s initial success, the future goal is to refine and de-
ploy the ICNP software throughout Ukraine. Further development will focus on
Cancel
Fig. 10. An example of a screen for a step-by-step solution to a mathematical problem
The concept of intelligent training system for ukrainian school final stem exam preparation
Системні дослідження та інформаційні технології, 2025, № 2 137
expanding the system’s capabilities, integrating additional educational resources,
and conducting large-scale trials to validate its effectiveness and scalability.
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10416498
Received 24.09.2024
INFORMATION ON THE ARTICLE
Anatoliy S. Kulik, ORCID: 0000-0001-8253-8784, National Aerospace University
“Kharkiv Aviation Institute”, Ukraine, e-mail: a.kulik@khai.edu
Oleg P. Zeleniak, ORCID: 0000-0003-0024-485X, Olexandriya Multi-Profile Lyceum,
Ukraine, e-mail: zlnk@ukr.net
Andriy G. Chukhray, ORCID: 0000-0002-8075-3664, National Aerospace University
“Kharkiv Aviation Institute”, Ukraine, e-mail: a.chukhray@khai.edu
Oleksandr V. Prokhorov, ORCID: 0000-0003-4680-4082, National Aerospace Univer-
sity “Kharkiv Aviation Institute”, Ukraine, e-mail: o.prokhorov@khai.edu
Olena S. Yashyna, ORCID: 0000-0003-2459-1151, National Aerospace University
“Kharkiv Aviation Institute”, Ukraine, e-mail: o.yashina@khai.edu
Olena V. Havrylenko, ORCID: 0000-0001-5227-9742, National Aerospace University
“Kharkiv Aviation Institute”, Ukraine, e-mail: o.havrylenko@khai.edu
Oleksandr O. Yevdokymov, ORCID: 0009-0008-9687-6344, National Aerospace Uni-
versity “Kharkiv Aviation Institute”, Ukraine, e-mail: o.yevdokymov@khai.edu
Andrii A. Torzhkov, ORCID: 0009-0005-0257-095X, “SoftServe”, Ukraine, e-mail: an-
drejtorzhkov94@gmail.com
Oleksii V. Zayarnyi, ORCID: 0009-0003-5208-3848, National Aerospace University
“Kharkiv Aviation Institute”, Ukraine, e-mail: o.zaiarnyi@khai.edu
КОНЦЕПЦІЯ ІНТЕЛЕКТУАЛЬНОЇ КОМП’ЮТЕРНОЇ НАВЧАЛЬНОЇ
СИСТЕМИ ДЛЯ ПІДГОТОВКИ УКРАЇНСЬКИХ ШКОЛЯРІВ ДО НМТ /
А.С. Кулік, О.П. Зеленяк, А.Г. Чухрай, О.В. Прохоров, О.С. Яшина, О.В. Гавриленко,
О.О. Євдокимов, А.А. Торжков, О.В. Заярний
Анотація. Уже кілька років підготовка та проведення національного мульти-
предметного тесту (НМТ) в Україні відбувається в умовах онлайн-навчання.
Результати тестування показують зниження успішності школярів у математи-
ці. Подано прототип інтелектуальної навчальної системи для розв’язування
математичних задач, яка має стати доступним засобом підготовки до тесту-
вання. Система забезпечує вирішення широкого кола математичних задач
у покроковому режимі. Систему розроблено відповідно до принципу
раціонального керування за діагнозом, що передбачає наявність багатьох
діагностичних моделей. Це дає змогу поглиблено діагностувати помилки
учнів. Інструменти штучного інтелекту дозволять реалізувати індивідуальні
рекомендації для кожного учня з урахуванням його рівня підготовки і цілей
навчання.
Ключові слова: інтелектуальна репетиторська система, національний мульти-
предметний тест, задачі з математики.
|
| id | journaliasakpiua-article-336168 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-09-17T09:26:03Z |
| publishDate | 2025 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/44/2e33b284d9a3cee77cdcec0409644344.pdf |
| spelling | journaliasakpiua-article-3361682025-07-25T15:56:08Z The concept of intelligent training system for Ukrainian school final STEM exam preparation Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ Kulik, Anatoliy Zeleniak, Oleg Chukhray, Andriy Prokhorov, Oleksandr Yashyna, Olena Havrylenko, Olena Yevdokymov, Oleksandr Torzhkov, Andrii Zayarnyi, Oleksii intelligent tutor system National multi-subject test math problems інтелектуальна репетиторська система національний мультипредметний тест задачі з математики The National Multi-subject Test has been prepared and conducted in Ukraine in online learning conditions for several years. Test results show a decline in schoolchildren’s performance in mathematics. The article presents a prototype of an intelligent training system for solving mathematical problems that should become an accessible test preparation tool. The system provides a solution to a wide range of mathematical problems in a step-by-step mode. The system is developed in accordance with the principle of rational management by diagnosis, which implies the presence of many diagnostic models. It allows for deep diagnostics of student errors. Artificial intelligence tools will make it possible to implement individual recommendations for each student, taking into account their level of preparation and learning goals. Уже кілька років підготовка та проведення національного мультипредметного тесту (НМТ) в Україні відбувається в умовах онлайн-навчання. Результати тестування показують зниження успішності школярів у математиці. Подано прототип інтелектуальної навчальної системи для розв’язування математичних задач, яка має стати доступним засобом підготовки до тестування. Система забезпечує вирішення широкого кола математичних задач у покроковому режимі. Систему розроблено відповідно до принципу раціонального керування за діагнозом, що передбачає наявність багатьох діагностичних моделей. Це дає змогу поглиблено діагностувати помилки учнів. Інструменти штучного інтелекту дозволять реалізувати індивідуальні рекомендації для кожного учня з урахуванням його рівня підготовки і цілей навчання. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2025-06-28 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/336168 10.20535/SRIT.2308-8893.2025.2.09 System research and information technologies; No. 2 (2025); 125-138 Системные исследования и информационные технологии; № 2 (2025); 125-138 Системні дослідження та інформаційні технології; № 2 (2025); 125-138 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/336168/324899 |
| spellingShingle | інтелектуальна репетиторська система національний мультипредметний тест задачі з математики Kulik, Anatoliy Zeleniak, Oleg Chukhray, Andriy Prokhorov, Oleksandr Yashyna, Olena Havrylenko, Olena Yevdokymov, Oleksandr Torzhkov, Andrii Zayarnyi, Oleksii Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ |
| title | Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ |
| title_alt | The concept of intelligent training system for Ukrainian school final STEM exam preparation |
| title_full | Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ |
| title_fullStr | Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ |
| title_full_unstemmed | Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ |
| title_short | Концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до НМТ |
| title_sort | концепція інтелектуальної комп’ютерної навчальної системи для підготовки українських школярів до нмт |
| topic | інтелектуальна репетиторська система національний мультипредметний тест задачі з математики |
| topic_facet | intelligent tutor system National multi-subject test math problems інтелектуальна репетиторська система національний мультипредметний тест задачі з математики |
| url | https://journal.iasa.kpi.ua/article/view/336168 |
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