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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Designing a matrix training for teacher professional development in a digital environment</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Oksana V. Ovcharuk</string-name>
          <email>ovcharuk@iitlt.gov.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nataliia V. Soroko</string-name>
          <email>soroko@iitlt.gov.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Oksana Ye. Kravchyna</string-name>
          <email>kravchyna@iitlt.gov.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Institute for Digitalisation of Education of the NAES of Ukraine</institution>
          ,
          <addr-line>9 M. Berlinskogo Str., Kyiv, 04060</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <fpage>53</fpage>
      <lpage>60</lpage>
      <abstract>
        <p>In the 21st century, a digital society is rapidly evolving, driven by the influence of artificial intelligence and other information and communication technologies (ICTs). As a result, education requires technical updates and significant methodological modernisation in the teaching and learning processes. The emergence of tools like ChatGPT, Copilot, Canva AI, Google Gemini, and others is changing the role of teachers, the methods and sources of knowledge and the forms of interaction between participants in the educational environment. The paper examines approaches to the professional development of teachers in a digital environment through artificial intelligence. The paper aims to present the Matrix, which ensures the conduct of teachers' training with the possible revision of options and addition of necessary topics. The Matrix serves as a planner for professional development, utilising AI tools. The levels along which the teacher moves towards acquiring the necessary competencies using AI are identified: knowledge, skills, soft skills, activity, and result. A practical sample of the realisation of the 1st level of AI use in the introductory stage is presented. We propose the use of matrix learning, which has received positive feedback from teachers, as it anticipates their needs and the flexibility of learning. The Matrix presented in this paper is aimed at developing teachers' competence in using AI at three levels - familiarisation, use, and transformation - which ensures gradual training and practice of teachers in using AI in the classroom.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;educational environment</kwd>
        <kwd>teacher training</kwd>
        <kwd>matrix</kwd>
        <kwd>teacher professional development</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>Modern teachers are involved in the use of digital technologies and solving complex tasks that are posed
to them by circumstances that afect the educational process, namely the transition to distance and
remote forms of interaction with students and colleagues, the need to use those means of organising
learning that are not always updated and modern, and the need to quickly adapt to the needs of students
and their parents. This is particularly evident, especially in Ukraine, where the ongoing conflict has
disrupted education systems, with many schools having been destroyed or closed, especially in occupied
territories. Therefore, considerable attention is paid to teachers’ support and professional development
today. The needs for the professional development of teachers lie in the need to use modern educational
digital resources and tools that contribute to the formation of key competencies in students, particularly
critical thinking, and the development of soft skills that contribute to their successful learning. Recently,
teachers have been paying attention to the possibilities of using artificial intelligence as a tool that helps
them organise the educational process and complements the range of possible tools for diversifying
forms of learning.</p>
      <p>The professional development of teachers is a complex task, and that is why it is necessary to
pay attention to matrix learning, which is becoming a popular approach to planning, organising and
implementing teachers’ professional development today. This approach is justified because matrix
learning enables teachers to determine and plan their development process independently, be flexible,
and choose the necessary work opportunities. The reform of the New Ukrainian School involves
changing approaches to student education and developing a new generation of teachers who can be
independent, competent, and motivated in performing their professional tasks.</p>
      <p>This article proposes the Matrix model for teachers’ professional development, which can be used
equally by teacher training institutions and teachers themselves to upgrade their use of AI in professional
contexts.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Literature review</title>
      <p>
        The development of matrix training for teachers is the subject of works by M. Korsager, B. Reitan,
M. Gaare Dahl, and others [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], who investigate the professional development of math and science
teachers through the use of a matrix, representing a framework. This matrix contains methods for
enactment, which can help teachers to realise the theory in practice. S. M. Wilson proposes a systemic
approach to reform to enhance the efectiveness of professional development for science teachers. She
identifies the top five characteristics of efective professional development: duration, active learning,
collective participation, coherence, and content focus [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. J. Crowell asserts that a successful teacher
has the necessary resources and tools to provide students with the best learning experience. She
emphasises that efective teacher professional development should go beyond a one-time training
session for science teachers. Instead, it should incorporate a comprehensive professional development
matrix that includes all the essential components for positively impacting student learning. These
components include the science curriculum, strategic planning, leadership reform, community building,
and educational sustainability programs [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. The authors A. Brandão, L. Pedro, and N. Zagalo consider
teachers’ professional development using integrative artificial intelligence as a key trend in modern
education. In their work, the authors guide teachers on the safe and ethical use of artificial intelligence
by reviewing relevant practices and literature. They emphasise the importance of fostering literacy in
generative AI, developing critical and creative thinking skills, and considering humanistic, ethical, and
social factors [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. The works of V.Slyusar, Y.Kondratenko, A.Shevchenko, and T.Yeroshenko address
the key aspects of the artificial intelligence development strategy for mobile technologies. The authors
propose how to use the set of mobile technologies, devices, software, and communication standards that
allow users to access information, communicate, and perform various tasks using mobile devices [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
Moreover, the authors discuss the implementation of national AI strategies and perspectives on applying
AI systems [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
      </p>
      <p>
        The article by Marienko et al. [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] examines the issue of using adaptive technologies for personal
development of teachers in a digital environment. The authors investigate this issue in the context of
the continuous development of teaching and the challenges associated with digital transformation. The
work mainly focuses on using learning management systems (LMS), which include artificial intelligence
algorithms, to create personalised learning. The article by M. Popel [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] presents a conceptual model of
a training system aimed at developing professional competencies of mathematics teachers using the
CoCalc cloud service. The author investigated the development and empirically tested the efectiveness
of this system, which is built on the principles of a matrix approach to learning, considering such
elements as goals, content, tools, methods, results, and levels of competence. The work of S. Lytvynova
and O.Melnyk [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ] examines the issue of integrating cloud services into the informal education system
of teachers to improve their digital competence. O. Chubrei et al. [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] examine the process of creating
an adaptive digital environment for the professional growth of teachers in higher education institutions.
The authors emphasise the importance of developing a flexible, technologically rich educational system
that provides personalised learning through the modular organisation of educational content. The need
for professional development in the use of ICT is also confirmed by surveys of teachers conducted in
Ukraine in 2023-2024 [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. Approximately 26,000 teachers were surveyed about their readiness to use
digital tools and the challenges they face. The survey also outlined their needs and perspectives on how
to help improve their digital competencies.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Learning matrix for teachers’ professional development</title>
      <p>The learning matrix is a strategic tool that helps manage the educational process and is designed to
track, plan, and manage learning and teachers’ skills development. Its main purpose is not only to
identify learning needs but also to monitor progress in acquiring teachers’ skills and competencies in
accordance with educational goals. We propose using such a matrix to structure the learning process
using artificial intelligence.</p>
      <p>
        Matrix learning consists of several steps. First, a matrix is developed with two or more dimensions,
with the target skill components isolated on each axis (for example, actions on one axis and results
on another axis). The proposed matrix contains learning components on one axis (vertical) and levels
on another (horizontal). This makes it possible to track the educational progress of professional
development and, if necessary, supplement the matrix with new components or add new descriptors to
the level. In this case, the combinations of components can be flexibly changed [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ].
      </p>
      <p>
        Our special interest mulated into thin-called TPACK model or approach to professional development.
This model consists of four components: technological, pedagogical, content, and knowledge. The
proposed framework by P. Mishra and J. Koehler for teachers’ professional development is focused on
using ICTs [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ].
      </p>
      <p>
        For the development of soft skills of teachers in the use of artificial intelligence tools, the draft
recommendations ’Instructional and methodological recommendations on the use of artificial intelligence
capabilities in secondary education institutions’, a joint work of the Ministry of Education and Science
of Ukraine and the Ministry of Digital Transformation of Ukraine, are useful [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ].
      </p>
      <p>Table 1 presents a generalised example of a Matrix training “Integration of AI tools into teaching”.
The main task is to promote the professional development of teachers by building an individualised
trajectory of the formation of digital and interdisciplinary competencies through a matrix training
focused on integrating artificial intelligence tools into the educational process.</p>
      <p>
        At the first level in the matrix, the “Knowledge” component includes introducing teachers to the
theoretical foundations of artificial intelligence, its key functions, and potential for use in education,
which is the stage of teachers’ initial understanding of AI. At this stage, the “Skills” component covers
the understanding and use of navigation in AI services, while any AI platform can be taken as an
example. Xiao Tan and Gary Cheng and Man Ho Ling, who conducted an analysis of SCOPUS and WEB
of Science articles from 2015 to 2024 on the problem of using AI in the professional activities of teachers
[
        <xref ref-type="bibr" rid="ref15">15</xref>
        ], particularly pay attention to the relevance of Conversational AI (e.g., Dialogflow, IBM Watson,
ChatGPT, SnatchBot) for the use of such platforms in the learning process and professional development
of teaching staf. When considering navigation and further study of AI, a teacher can use ChatGPT
and SnatchBot. Thus, at the first stage, the teacher learns to navigate the interfaces of AI services, find
the necessary tools, and understand the logic of their functioning in the educational process. The first
level’s “Soft skills” component involves forming digital flexibility in the student, that is, the ability to
freely adapt to new digital conditions and technologies. The “Activity” component at the familiarisation
stage includes the teacher reading instructions, attending webinars or consultations on implementing
AI in the educational process. The result of this stage is a completed introductory course, which can be
represented by a test for self-assessment of the knowledge that the teacher has mastered at the first level
of training. At the second level of “Use” when considering the “Knowledge” component, it should be
noted that the teacher begins to understand the principles of operation of specific AI tools, such as text
generators, adaptive learning systems or automatic assessment services. At the same time, the teacher’s
knowledge of how specific AI tools work (for example, ChatGPT, adaptive LMS, AI material designers,
etc.) deepens. The “Skills” component expands to the ability of the teacher to use AI to create practical
tasks, taking into account the individual learning paths of students. The “Soft skills” component at
this stage involves the development of critical thinking, responsibility and ethical use of AI in the
teacher. The “Activity” component covers the teacher’s participation in workshops, creation of lessons,
educational projects and other activities using AI. The result of this stage can be the development of
a lesson, educational project, etc., using AI. At the third level, “Transformation”, the teacher is able
not only to use, but also to create or customise AI solutions for the needs of educational content,
for example, to generate didactic materials or create chatbots to support learning. The “Knowledge”
component covers the teacher’s understanding and acquired knowledge of how to create AI to form
and expand educational content. The “Skills” component expands to the teacher’s ability to develop
original integrated solutions, analyse AI proposals, and adapt them to the educational process. When
considering the “Soft skills” component, the teacher can be ofered a test that involves analysis and
self-analysis of the teacher’s creativity and ethical awareness regarding AI use in the educational
process.
      </p>
      <p>The need to develop Soft skills for teachers is stated in Ukrainian regulatory documents. Thus, the
professional standard of a teacher adopted in 2020 defines professional competencies that relate to Soft
skills, including: linguistic and communicative, informational and digital, psychological, emotional
and ethical, pedagogical partnership competence, inclusive, health-preserving, design, prognostic,
organisational, evaluative and analytical, innovative, lifelong learning ability, reflective. This
professional standard is taken into account for the development of the New Ukrainian School. Since the
development of these skills is considered a necessary component of preparing children for a successful
future, attention is focused on the need to integrate these skills into curricula, which will contribute to
both academic achievements and social development of the personality, self-regulation, self-awareness
and empathy. Accordingly, teachers need to develop soft skills. The order on approval of the Conceptual
Principles of Reforming Specialised Secondary Education (Academic Lyceums), adopted in 2024 by the
Ministry of Education and Science of Ukraine, states the need for measures to develop the soft skills of
teachers and students, including training and workshops on teamwork, leadership, communication,
time management, etc. In this context of soft skills development, it is important to focus on developing
qualities such as digital flexibility, critical thinking, responsibility, creativity and ethical awareness.
These skills are particularly efective and necessary for using artificial intelligence tools in a teacher’s
educational activity. For example, the ability to adapt to new technologies is most important at the
familiarisation stage, analysing information and ethically applying AI are necessary at the use stage,
and the ability to develop innovative approaches to learning at the transformation level. All these soft
skills allow teachers to efectively integrate AI into the educational process, thereby contributing to
forming a responsible attitude towards modern technologies in students.</p>
      <p>Within the framework of the matrix table we have proposed, we propose three levels of Soft skills for
teachers to use artificial intelligence efectively in the educational process. At level 1 (familiarisation),
the teacher becomes familiar with various artificial intelligence tools (chatbots, content generators, and
analytical platforms) while developing Digital flexibility to adapt to new digital technologies. At this
level, the teacher needs to understand artificial intelligence’s opportunities for educational activities
and be ready to experiment with these technologies. At level 2 (use), the teacher begins to use artificial
intelligence to solve his needs actively (for example, text analysis or creating interactive exercises and
chatbots) while developing his critical thinking and assessing the reliability and quality of AI results
and is also responsible for the ethical use of these results when creating practical tasks. At level 3
(transformation), the teacher integrates AI into the educational process by developing their products
(personalised learning trajectories or interdisciplinary projects, etc.). At the same time, the development
of unique approaches by the teacher is ensured by his creativity, and the use of AI must comply with
ethical principles (avoidance of plagiarism, respect for copyright, and awareness of the moral and social
consequences of the use of AI).</p>
      <p>
        The “Activity” component covers the organisation of interaction between participants in the
educational process using AI. As a result, the teacher must present his own AI project for implementing a
lesson, educational project, and other events in the educational process. It should be noted that it is
worth determining the level of digital competence of the teacher to build a matrix of individual learning.
It can be determined using special tests such as, for example, the test “Digital Grammar for Teachers”
ofered by the web portal “Diya”, developed by the Ministry of Transformation of Ukraine (designed for
30-40 minutes); the test “SELFIE for TEACHERS” developed by the European Commission together with
a group of education experts from all over Europe (designed for 30 minutes) [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] and questionnaires
that are focused on identifying problems, obstacles and other risks when using ICT by teachers in the
educational process according to certain teaching goals in general secondary education institutions.
      </p>
      <p>Let us take a closer look at the proposed Level 1 (Introduction) of the matrix for applying artificial
intelligence tools for teachers (figure 1).</p>
      <p>The “Knowledge” component allows the formation of a theoretical basis for studying and using AI as
a teacher’s tool. It includes understanding AI capabilities, ethical aspects of its application, and benefits
for personal and professional development. The main topic of this component is “What AI is and its
potential in education. A teacher should know the definition of AI (machine learning algorithms), its
types (generative: ChatGPT, Canva AI; conversational: Google Gemini), capabilities (content generation,
task personalisation), as well as ethical aspects (avoiding plagiarism, ensuring responsibility for quality),
and ways of adapting them to students’ needs.</p>
      <p>We suggest the teacher develop a mathematics exercise for 7th-grade students on the topic “Fractions:
Addition and Subtraction, using AI. For example, entering a prompt into ChatGPT: “Create five exercises
on adding fractions for 7th grade with answers, at diferent dificulty levels (basic, intermediate,
advanced)”, checking accuracy, adding personal explanations, and avoiding direct copying. To prepare for
this task, the teacher can review videos and online resources such as the YouTube course “Big Course
on AI in Education” (Ministry of Digital Transformation of Ukraine, Ministry of Education and Science
of Ukraine), and use tools such as ChatGPT (for exercise generation), Canva AI (for visualisation), Grok
(for creative ideas), etc.</p>
      <p>To assess progress, we propose designing a test “What do I know about AI?” with 5–10 questions
(multiple choice and open-ended), lasting 15–20 minutes, using Google Forms (at least 70 percent correct
answers should be achieved; if less, it is recommended to repeat the topic). For self-assessment, teachers
may take the “Digital Grammar for Teachers” test on the Diia portal and answer reflection questions
such as: “What did I learn from this material? How can I deepen my knowledge of AI?”</p>
      <p>In the next component, “Skills”, the teacher develops practical abilities related to navigating and
basic use of AI services, following the principles of step-by-step learning. The main theme here is
“Navigation in AI Services”, as hands-on experience with AI interfaces helps transition from theoretical
understanding to active application. This includes registration, finding tools, entering prompts, and
analysing results. For example, a teacher may be asked to prepare an explanation of fractions for 7th
grade, completing all stages – from registration, entering a query, analysing the answer, to refining the
prompt (e.g., “Add an example with diferent denominators”) to test flexibility.</p>
      <p>For this task, the teacher may use ChatGPT for prompt input and analysis, SnatchBot to explore
conversational bots, and Grok to generate creative responses. To evaluate progress, it is recommended
to record a short screen capture (1–2 minutes) of the navigation process: logging into the platform (e.g.,
ChatGPT), entering the query “Explain adding fractions for 7th grade”, receiving the response, and
briefly commenting on its relevance (1–2 sentences). For self-assessment, the teacher can review the
recording, evaluate their own actions (e.g., “Did I easily find the input field? Was the answer clear?”),
and note achievements and dificulties.</p>
      <p>The “Soft Skills” component is about developing digital flexibility through adapting to new
technologies in education. At this stage, teachers overcome psychological barriers such as the fear of the
“unknown” by completing one task using multiple platforms, comparing results, and preparing for
confident AI use. At Level 1, the teacher becomes familiar with diferent AI platforms, evaluates their
potential, and develops a positive attitude toward innovative technologies. A suggested task: compare
AI tools for explaining fractions for 7th grade. For example, enter the query “Explain adding fractions
1/2+1/4=? for 7th grade” into ChatGPT and Grok, compare results, and create a visual diagram in Canva
AI. To prepare, teachers are encouraged to consult the “Instructional and Methodological Guidelines for
Using AI in Schools” issued by the Ministry of Education and Science of Ukraine and the Ministry of
Digital Transformation, and to take the “Digital Grammar for Teachers” test on the Diia portal to assess
digital competence and identify growth areas. Teachers may keep a journal for personal reflection to
record their insights and ideas, answering questions such as: “What new things have I learned? How
will this impact my work?” with a focus on shifting from “fear” to “interest”.</p>
      <p>The “Activity” component involves teachers working with methodological materials, manuals, and
instructions on using AI tools, participating in webinars and discussions, consolidating theoretical
knowledge and preparing them for practical application. This also allows teachers to share and discuss
experiences with colleagues. For example, teachers may review AI-generated instructions for creating
fraction exercises, consult the “Instructional and Methodological Guidelines for Using AI in Schools”,
which provide basic prompts, and in a Telegram group for math teachers, share their own AI-generated
fraction tasks (e.g., creating five exercises on fractions for 7th grade using ChatGPT), then discuss ideas
with colleagues and receive feedback.</p>
      <p>For self-assessment, teachers may keep notes documenting how they applied ideas from the guidelines
(e.g., in Google Docs or Word) and create a short report about their AI exploration, such as a presentation
in Google Slides or Canva AI entitled “My First Experience with AI for a Math Lesson”.</p>
      <p>The “Result” component reflects the completion of the introductory stage of professional development,
showcasing achievements and readiness to progress further. At this level, the teacher synthesises
acquired knowledge (basic AI concepts), skills (AI navigation), and activities (using instructions) into a
practical product, demonstrating readiness to integrate AI into the teaching process. This may include
preparing a report or presentation about initial AI experiences. The teacher is also prepared to share
knowledge with colleagues and receive feedback, building confidence for independent AI use in the
classroom. Teachers are encouraged to take the online course “Teacher’s Digital Competence” on the
Diia for further development and self-assessment – education platform, which includes a self-check
module.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusions</title>
      <p>The article examines approaches to teacher professional development in a digital environment using
artificial intelligence. The authors proposed and developed a Matrix of Teacher Professional
Development using artificial intelligence, which allows teachers to be flexible in their choice of professional
development. The outlined matrix contains components such as knowledge, skills, soft skills, activity,
and result, as well as three levels of teacher acquisition of these qualities. Skills and soft skills are
correlated with levels to measure outcomes. The blocks of the proposed matrix aim to develop in teachers a
critical attitude towards the use of AI in their work, an application of a creative approach to teaching,
and the ability to find solutions and be independent in the choice of methods. An example of a practical
implementation of the AI tools matrix for teachers at Level 1 (Introduction) was developed (figure
1). This example demonstrates the completion of the introductory stage of professional development
related to teachers’ use of AI tools. Possible limitations in using matrix learning to enhance skills in
using AI may be related to teachers’ reliance on self-assessment, their access to online resources, and a
lack of necessary technical support, among other factors. The matrix outlined in the article is currently
in the preliminary stages of development. It will undergo careful refinement and enhancements based
on comprehensive discussions with the identified target groups. This collaborative approach ensures
that the matrix efectively addresses the needs and perspectives of all interested groups. The authors
consider further developing the problem of using the matrix as a planner for teachers’ professional
development using AI tools, studying practical examples and experience, and conducting surveys to
determine teachers’ opinions on the efectiveness of using this tool in the professional development
system.</p>
    </sec>
    <sec id="sec-5">
      <title>Author contributions</title>
      <p>Conceptualization, Oksana Ovcharuk, and Nataliia Soroko; methodology, Oksana Ovcharuk; formal
analysis, Nataliia Soroko; investigation, Oksana Kravchyna, Oksana Ovcharuk and Nataliia Soroko;
resources, Nataliia Soroko and Oksana Kravchyna; data curation, Oksana Ovcharuk; writing – original
draft preparation,Oksana Ovcharuk; writing – review and editing, Oksana Ovcharuk; visualization,
Nataliia Soroko. All authors have read and agreed to the published version of the manuscript.</p>
    </sec>
    <sec id="sec-6">
      <title>Data availability statement</title>
      <sec id="sec-6-1">
        <title>No new data were created or analyzed in this study. Data sharing is not applicable.</title>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>Conflicts of interest</title>
      <sec id="sec-7-1">
        <title>The authors declare no conflict of interest.</title>
      </sec>
    </sec>
    <sec id="sec-8">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author(s) used Grammarly to check grammar and spelling.</p>
    </sec>
  </body>
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