The Development of a Mathematical Model of an Algorithm for Constructing an Individual Educational Trajectory for the Development of Methodological Competence among IT Discipline Teachers
Abstract
:1. Introduction
- Limited effectiveness of educational practices: insufficient training of teachers from a methodological point of view may lead to suboptimal use of modern methodological tools, thereby reducing the effectiveness of educational practices and limiting the students’ learning of material;
- Resistance to outdated pedagogical approaches: a lack of methodological readiness leads to the use of outdated pedagogical strategies that do not align with the dynamics and requirements of the contemporary field of information technology;
- Inadequate adaptation to IT realities: instructors’ inability to adapt teaching methods to the specificities of IT specialties can hinder the transmission of relevant knowledge and the development of appropriate skills;
- Lack of psychological support: a low methodological level in the areas of psychology and pedagogy can impede the provision of necessary psychological support to students, especially given the high levels of stress and uncertainty inherent in the IT field;
- Insufficient objectivity in assessment: teachers may encounter difficulties in designing objective assessment methods, which, in turn, increases the likelihood of subjectivity and unfairness in evaluation procedures;
- Challenges in implementing innovations: a low methodological level may restrict the adoption and use of innovative educational technologies—an essential aspect in IT education for preparing students to meet dynamic market demands;
- Lack of selection and use of inclusive technologies: insufficient training of teachers may lead to insufficient selection and use of inclusive technologies, making it difficult to create a favorable educational environment for different categories of students;
- Impact of methods and means on students’ motivation: students may face a problem related to the impact of methods, means, and organizational forms of learning on their motivation in the process of learning IT technologies.
2. Literature Review
- The cognitive component encompasses the foundational knowledge and understanding of essential concepts, methods, and principles related to the teaching and learning process.
- The didactic component is one of the key elements of professional competence. It covers knowledge, skills, and abilities associated with designing, organizing, and conducting educational processes.
- The design component plays a crucial role in the preparation and organization of the educational process. This component includes the knowledge, skills, and abilities necessary to develop courses, training materials and methodological strategies.
- The information component is vital in the educational context. This component involves knowledge of current educational theories, scientific research, teaching methods and educational materials.
- The communicative component plays a significant role in an effective educational process. This component covers skills and abilities in the field of communication, interaction, and creation of an enabling educational environment.
- The reflective component represents the ability for self-analysis and self-reflection, as well as the capacity to make informed decisions based on this analysis. This component enables teachers to continually refine their teaching methods and adapt them to changing conditions and student needs.
- The monitoring component is essential for ensuring quality education. It involves an instructor’s ability to systematically track and evaluate the teaching process, student learning outcomes, and the effectiveness of their teaching methods.
- The personal–motivational component plays an important role in the formation of high-quality education and the impact on the success of students’ education. It is linked to a teacher’s personality traits, motivation, and psychological characteristics, which enable them to effectively fulfill their educational responsibilities.
- Further, the soft skills were combined into one component (communicative, reflective, personally motivational). Research on professional education, pedagogical competence, instructional activities of teachers, teaching and upbringing methodologies (Hoffman, J. V., Svrcek, N., Lammert, C., Daly-Lesch, A. [11]) has demonstrated that experts highly value these components as the most important and useful in the context of actual pedagogical practice.
3. Research Methodology
- (a)
- Methods of installation, input diagnostics, which are used at the beginning of teacher training in advanced training courses to differentiate course participants by the level of formation of methodological competence;
- (b)
- Methods of current, in-depth diagnostics to track intermediate results and the effectiveness of the course preparation process, and to identify problems and difficulties faced by students;
- (c)
- The methods used in the final diagnosis after completion of advanced training courses to assess the success of students in completing course training programs and to determine the levels of formation of methodological competence of IT discipline teachers. The evaluation of diagnostic tools was carried out taking into account the quality criteria (according to K. Ingenkamp) as follows: validity, reliability, and objectivity.
4. Main Part
- The availability of different levels of education (on the basis of college, bachelor’s, master’s or doctoral studies);
- Different categories of students, with different levels of need for the development of methodological competence;
- Availability of residual knowledge on certain topics of study;
- Short-term nature and possible interruption during the training period.
- The time of the start of training (start of movement) is t0.
- The starting point of the movement of students in the EE. When accepted, we obtain the following:
- 3.
- The number of motion modeling options in EE—.
- The transition to the next version of the simulation.
- 2.
- Moving on to the next step of the movement, we obtain the following:
- 3.
- Calculation of forces when moving in directions at a time
- 4.
- Selection of shifting subjects. If K* = 0, then:
- 5.
- Calculation of the displacement. If:
- 6.
- Estimation of the obtained target coordinates of movement in PVP.
- The total weight of the competence component is equal to the sum of the weights of all its elements.
- The weight of an element of the competence component is equal to the product of its indices in the matrix of target results of the competence component.
- The current progress is equal to the sum of the weights of the fixed elements of the competence component.
- «Instructional delivery» component;
- «Curriculum design» component;
- «Assessment skill» component;
- «Soft skills» component.
K1,1 | … | Ki,j | |
K1,1 | 1 | v1,m | v1,j |
… | vn,1 | 1 | vn,j |
Ki,j | vi,1 | vi,m | 1 |
- Personal data—full name, date of birth, education, work experience and other personal data of the teacher;
- Pedagogical experience—periods and place of teaching in educational institutions;
- Specialization and subject areas—indication of the names of the disciplines taught by the user, indicating the periods;
- Scientific activity—data on scientific publications, research, participation in scientific conferences and projects;
- Results of the questionnaire on the input testing of the system;
- Additional data—information about internships, advanced training (taking place in the system or other educational institutions), etc.
- Likert-based questionnaires are one of the most common methods. Respondents answer the questions by choosing one of the proposed answer options (for example, from “strongly disagree” to “strongly agree”). These questionnaires can cover different aspects of competence, such as knowledge, skills, and abilities.
- Case study methodology—respondents are asked to consider specific scenarios or cases related to pedagogical practice and give their assessment for each case.
- Definition of competencies and identification of the necessary competencies for teachers of IT disciplines.
- Creating scenarios and the development of scenarios reflecting typical situations that a teacher may encounter in the process of learning and interacting with students. Using the example of a communicative component, these may be situations when students ask a lot of questions or when there is a conflict in the audience.
- Formulation of questions, specifically, drawing up questions that would allow you to assess the teacher’s reaction to various situations. The questions are structured in such a way that they reflect several aspects of the communicative component, such as the ability to listen, adapt to the audience, emotional intelligence, etc.
- Definition of evaluation criteria for evaluating the answers that were defined for each question. These criteria include the level of activity and flexibility in communication, emotional responsiveness, the ability to resolve conflicts and other important aspects.
- -
- Modularity—each training program of a topic or an independent section within a topic should contain interrelated modules (parts) for different levels of retraining;
- -
- Individuality and variability—for different categories of students there may be different aspects of studying topics (options for training programs);
- -
- Uniqueness—the content of the programs of training modules should not overlap both by levels within the same topic (section of the topic) and between topics (sections of topics);
- -
- Minimization of costs for retraining of students—the training course should be minimal in duration, provided that a given set of knowledge and skills is achieved, and based on the standards for advanced training of teaching staff in Kazakhstan.
- The allocation of retraining cycles;
- The allocation of independent topics and sections of training within each cycle;
- The separation of aspects of the study of the topic (section) depending on the target audience;
- The distribution of target competence states depending on the levels of immersion—zero, situational, basic, advanced, or expert.
- -
- Binary, if there is such a training module (arc pi = (xi, xj)) in the course, which complements the set of knowledge and skills from the state of initial competence (vertex of graph xj) to the target state of competence of this module (vertex of graph xj);
- -
- N-ary, if there is such a training module (oriented hyperrebro pi = {xi, xk, …, xm, xj}) in a course that complements the set of knowledge and skills from the necessary set of states of initial competence (vertices of graph xi ∈ X) to the target state of competence of this module (vertex of graph xj).
- There is such a vertex x0 ∈ X, which has a half-step of entry p + (x0) = 0; this vertex corresponds to zero methodological competence (within this course).
- There are such vertices xi ∈ X, in which the half-degree of the outcome is p − (x0) = 0; these vertices correspond to the final states of the target methodological competence (within this course).
- The set of vertices of the hypergraph X represents ordered subsets X1, X2, …, Xn with a given order ratio at the vertices of the subset (ordered components of methodological competence in terms of aspects and levels of training).
- The binary arc establishes the relationship as follows: initial competence (not lower)—training module—target competence.
- A directed hyperedge has one important property; there is always one, and only one vertex of drain (the vertex of target competence) and several vertices of the source (a set of vertices of minimum initial competence).
- The transition to the top of xj ∈ X (the state of target competence) along the hyperline pi = {xi, xk, …, xm, xj} is possible only if all vertices xi ∈ {pi\xj} are reached (the necessary set of states of minimum initial competencies for the implementation of this training module).
- Each arc of the hypergraph has a weight (the number of academic hours of the module).
- Augments the initial set of knowledge and skills to match the desired competency level;
- Minimizes the training costs associated with achieving this competency.
- (1)
- Correction of the process of developing a teacher’s methodological competence during professional development, taking into account previously obtained results;
- (2)
- Final assessment of the level of development of the teacher’s methodological competence.
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Components | Functions | ||
---|---|---|---|
After | Before | ||
Knowledge | Instructional delivery | The “Instructional delivery” component combines aspects of didactic competence and focuses on the effective transfer of learning material and the development of students’ academic skills, namely:
| |
Design | Curriculum design | The “Curriculum design” component integrates the elements of the educational program design component related to the development of courses, lectures and teaching methodologies and includes:
| |
Monitoring | Assessment Skill | The “Assessment skill” component covers aspects of monitoring methodological competence, including systematic control, assessment of the educational process and students’ success:
| |
Personal–motivational | Soft skills | The “Soft skills” component is a combination of communicative, reflexive, and personal–motivational aspects. This component of methodological competence includes the professional and pedagogical orientation of the individual (values, needs, motives, goals), awareness of the value of continuous development of methodological competence; communicative skills of the teacher; independence, intuition, which allows you to effectively solve pedagogical problems on the basis of insufficient information; manifestation of individuality in methodological activities; empathy, as well as:
| |
Reflexive | |||
Communication |
Level | Characteristics |
---|---|
Level zero (extremely low) | Low values of indicators reflecting various aspects and components of methodical activity. The teacher uses ready-made methodological support to organize the learning process without thinking about the expediency and effectiveness of its application, about the need and possibility of even its slight modification. The teacher is characterized by complete formalism in maintaining methodological support (they care only about the formal purity of educational and methodological documentation). There is a complete lack of connection between methodological activity and research; the latest or relatively new achievements of science are not reflected in the content of training. Didactic modeling of the training course does not correspond to the logic of teaching an isomorphic academic discipline; innovative didactic methods and technologies (corresponding to the competence approach) are practically not applied. Advanced methodological and pedagogical experience is not analyzed at all; there is no aspiration to improve methodological skills. |
Situational level (low) | There is an improvement of information and methodological support of the educational process, replenishment of its content, but neither the latest achievements of science (in the content of training) nor innovative teaching methods and technologies are taken into account; there is practically no development of pedagogical tasks corresponding to the competence paradigm of training; the development of tasks of the traditional type dominates. |
Developing level (average) | Active improvement of methodological support of the educational process (constant modernization of its content), primarily by increasing the number and quality of pedagogical tasks. There is an application of traditional and innovative didactic methods and technologies. The constantly replenished fund of assessment means contains a sufficient number of tasks of traditional type and control-competence assessment tasks. The tasks vary in difficulty level, fully corresponding to the academic discipline and assessed competencies of students. The design of the learning process is characterized by rationality; the teacher is aware of the logic of teaching the academic discipline, and fully takes it into account when designing the course. Information technologies are used mainly in the formation of the educational process support. The quality of electronic educational resources is at an average level. The teacher indicates (in the methodological support) references to the information resources available to students (the arsenal of references is wide), the use of which will help students to better master the course. |
Advanced level (high, systematic) | The teacher’s research activity becomes the leading factor of permanent (rather than episodic) modification of teaching content. The quality of electronic educational resources is at a high or very high level. The teacher actively uses the potential of the scientific and educational environment to improve their methodological activity through all possible ways of analyzing and adapting the advanced experience of pedagogical and methodological activity accumulated by the society, but does not contribute to the replenishment of this experience accumulated by the society (i.e., does not broadcast their experience). |
Expert level (highest, optimal) | It is characterized by the teacher’s activity in broadcasting their own positive experience of methodical and pedagogical activity, its transfer to other scientific–pedagogical workers. The teacher actively assists other scientific–pedagogical workers in improving methodological and psychological–pedagogical competence, participates in the monitoring of methodological activities of scientific–pedagogical teams, in the work of juries and expert commissions, scientific and methodological associations, etc. Actively conducts research in the field of pedagogical sciences (with the publication of results), enriching the theory and methodology of teaching, promotes the results in order to implement them in practice in the scientific and pedagogical community, etc. Methodological activity of a teacher acquires a supra-disciplinary character. |
Component N Total Weight: 100 Levels of Formation | Levels of Manifestation | ||||
---|---|---|---|---|---|
Low | Acceptable | Average | High | Optimal | |
Zero | Element 1 1 | Element 1 2 | Element 1 3 | Element 1 4 | Element 1 5 |
Weight = 0.5 | Weight = 1 | Weight = 1.5 | Weight = 2 | Weight = 2.5 | |
Situational | Element 2 1 | Element 2 2 | Element 2 3 | Element 2 4 | Element 2 5 |
Weight = 1 | Weight = 3 | Weight = 3.5 | Weight = 4 | Weight = 4.5 | |
Developing | Element 3 1 | Element 3 2 | Element 3 3 | Element 3 4 | Element 3 5 |
Weight = 1.5 | Weight = 3.5 | Weight = 5 | Weight = 5.5 | Weight = 6 | |
Advanced | Element 4 1 | Element 4 2 | Element 4 3 | Element 4 4 | Element 4 5 |
Weight = 2 | Weight = 4 | Weight = 5.5 | Weight = 7 | Weight = 7.5 | |
Expert | Element 5 1 | Element 5 2 | Element 5 3 | Element 5 4 | Element 5 5 |
Weight = 2.5 | Weight = 4.5 | Weight = 6 | Weight = 7.5 | Weight = 8.5 |
The Levels of Formation of the Teacher’s Methodological Competence | Instructional Delivery | Curriculum Design | Assessment Skill | Soft Skills | ||||
---|---|---|---|---|---|---|---|---|
Ind. | % | Ind. | % | Ind. | % | Ind. | % | |
Zero | 26 | 42.6 | 36 | 59 | 41 | 67.2 | 29 | 47.5 |
Situational | 18 | 29.5 | 7 | 11.4 | 12 | 19.6 | 19 | 31.1 |
Developing | 11 | 18 | 10 | 16.3 | 5 | 8.1 | 7 | 11.4 |
Advanced | 4 | 6.5 | 2 | 3.2 | 2 | 3.2 | 4 | 6.5 |
Expert | 2 | 3.2 | 6 | 9.8 | 1 | 1.6 | 2 | 3.2 |
The Levels of Formation of the Teacher’s Methodological Competence | Instructional Delivery | Curriculum Design | Assessment Skill | Soft Skills | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
EG1 | EG2 | EG1 | EG2 | EG1 | EG2 | EG1 | EG2 | |||||||||
Ind. | % | Ind. | % | Ind. | % | Ind. | % | Ind. | % | Ind. | % | Ind. | % | Ind. | % | |
Zero | 26 | 42.6 | 1 | 1.6 | 36 | 59 | 6 | 9.8 | 41 | 67.2 | 25 | 40.9 | 29 | 47.5 | 18 | 29.5 |
Situational | 18 | 29.5 | 9 | 14.7 | 7 | 11.4 | 6 | 9.8 | 12 | 19.6 | 6 | 9.8 | 19 | 31.1 | 18 | 29.5 |
Developing | 11 | 18 | 22 | 36 | 10 | 16.3 | 23 | 37.7 | 5 | 8.1 | 10 | 16.3 | 7 | 11.4 | 13 | 21.3 |
Advanced | 4 | 6.5 | 21 | 34.4 | 2 | 3.2 | 11 | 18 | 2 | 3.2 | 16 | 26.2 | 4 | 6.5 | 5 | 8.1 |
Expert | 2 | 3.2 | 8 | 13.1 | 6 | 9.8 | 15 | 24.5 | 1 | 1.6 | 4 | 6.5 | 2 | 3.2 | 7 | 11.4 |
The average value % | 19.96 | 28.75 | 39.87 | 25.41 | 49.81 | 27.69 | 34.11 | 23.91 |
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Toxanov, S.; Abzhanova, D.; Mukhatayev, A.; Biloshchytskyi, A.; Biloshchytska, S. The Development of a Mathematical Model of an Algorithm for Constructing an Individual Educational Trajectory for the Development of Methodological Competence among IT Discipline Teachers. Educ. Sci. 2024, 14, 748. https://doi.org/10.3390/educsci14070748
Toxanov S, Abzhanova D, Mukhatayev A, Biloshchytskyi A, Biloshchytska S. The Development of a Mathematical Model of an Algorithm for Constructing an Individual Educational Trajectory for the Development of Methodological Competence among IT Discipline Teachers. Education Sciences. 2024; 14(7):748. https://doi.org/10.3390/educsci14070748
Chicago/Turabian StyleToxanov, Sapar, Dilara Abzhanova, Aidos Mukhatayev, Andrii Biloshchytskyi, and Svitlana Biloshchytska. 2024. "The Development of a Mathematical Model of an Algorithm for Constructing an Individual Educational Trajectory for the Development of Methodological Competence among IT Discipline Teachers" Education Sciences 14, no. 7: 748. https://doi.org/10.3390/educsci14070748