INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS»
Formulation of the problem. Analysis of the issue of including the topic "The simplest functional equations" in the model curricula for studying the subject "Algebra and the beginnings of analysis" for specialized classes with in-depth study of mathematics. A model curriculum stu...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Makarenko Sumy State Pedagogical University
2023-05-01
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| Series: | Фізико-математична освіта |
| Subjects: | |
| Online Access: | https://fmo-journal.org/index.php/fmo/article/view/219 |
| _version_ | 1797835943592329216 |
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| author | Тетяна Бохонова Юрій Бохонов Ірина Матвєєва Олексій Томащук Вікторія Тихонова Олег Лещинський Валентина Гроза |
| author_facet | Тетяна Бохонова Юрій Бохонов Ірина Матвєєва Олексій Томащук Вікторія Тихонова Олег Лещинський Валентина Гроза |
| author_sort | Тетяна Бохонова |
| collection | DOAJ |
| description | Formulation of the problem. Analysis of the issue of including the topic "The simplest functional equations" in the model curricula for studying the subject "Algebra and the beginnings of analysis" for specialized classes with in-depth study of mathematics. A model curriculum studies the approximate sequence of achieving the expected learning outcomes, the content of the subject or integrated course, and the types of students’ educational activities. The inclusion of this topic aims to start a creative understanding of functional relationships existing in real systems and processes, in particular, ecological, economic, and social ones.
Materials and methods. Theoretical method of analysis of methodical and educational literature on the researched issue; comparative analysis to understand different views on the problem; systematization and generalization to create recommendations for the content of the proposed topic, as well as formulating conclusions and integrating the pedagogical experience of authors who teach relevant disciplines in educational institutions of various levels.
Results. The possible content of the topic "The simplest functional equations" in the model programs for studying the subject "Algebra and the beginnings of analysis", examples for an explanation by the teacher, and confirmation by students are proposed. For some examples, different approaches to their solution are proposed; convenient tables are provided for students to find partial solutions to some types of functional equations.
Conclusions. The authors believe that the topic "The simplest functional equations" will be useful and acceptable for studying within the scope of the subject "Algebra and the beginnings of analysis" by students of specialized classes with an in-depth study of mathematics. Within the eleven-year school education, of course, it was impossible to find time to study this topic due to the saturation and density of the material necessary for study. But in the twelve-year New Ukrainian School, marked by a deeper differentiation of specialized education, the topic "The simplest functional equations" can strengthen the fundamentality of mathematical education in classes with in-depth study of mathematics, computer science, etc. Further research in this direction may concern the method of solving the simplest recurrent equations. |
| first_indexed | 2024-04-09T15:00:42Z |
| format | Article |
| id | doaj.art-576d01ee1091473ba84231f3bb064390 |
| institution | Directory Open Access Journal |
| issn | 2413-1571 2413-158X |
| language | English |
| last_indexed | 2024-04-09T15:00:42Z |
| publishDate | 2023-05-01 |
| publisher | Makarenko Sumy State Pedagogical University |
| record_format | Article |
| series | Фізико-математична освіта |
| spelling | doaj.art-576d01ee1091473ba84231f3bb0643902023-05-01T18:14:03ZengMakarenko Sumy State Pedagogical UniversityФізико-математична освіта2413-15712413-158X2023-05-01382152110.31110/2413-1571-2023-038-2-003221INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS»Тетяна Бохонова0https://orcid.org/0000-0002-8186-5238Юрій Бохонов1https://orcid.org/0000-0002-3355-008XІрина Матвєєва2https://orcid.org/0000-0002-8636-0538Олексій Томащук3https://orcid.org/0000-0001-5631-3418Вікторія Тихонова4Олег Лещинський5https://orcid.org/0000-0001-6005-7779Валентина Гроза6https://orcid.org/0000-0003-1668-1878Kyiv Natural Science Lyceum № 145, UkraineНаціональний технічний університет України «Київський політехнічний інститут» імені Ігоря Сікорського, УкраїнаНаціональний авіаційний університет, УкраїнаNational Aviation University, UkraineФаховий коледж інженерії, управління та землевпорядкування НАУ, УкраїнаProfessional College of Engineering, Management and Land Management of the National Aviation University, UkraineNational Aviation University, UkraineFormulation of the problem. Analysis of the issue of including the topic "The simplest functional equations" in the model curricula for studying the subject "Algebra and the beginnings of analysis" for specialized classes with in-depth study of mathematics. A model curriculum studies the approximate sequence of achieving the expected learning outcomes, the content of the subject or integrated course, and the types of students’ educational activities. The inclusion of this topic aims to start a creative understanding of functional relationships existing in real systems and processes, in particular, ecological, economic, and social ones. Materials and methods. Theoretical method of analysis of methodical and educational literature on the researched issue; comparative analysis to understand different views on the problem; systematization and generalization to create recommendations for the content of the proposed topic, as well as formulating conclusions and integrating the pedagogical experience of authors who teach relevant disciplines in educational institutions of various levels. Results. The possible content of the topic "The simplest functional equations" in the model programs for studying the subject "Algebra and the beginnings of analysis", examples for an explanation by the teacher, and confirmation by students are proposed. For some examples, different approaches to their solution are proposed; convenient tables are provided for students to find partial solutions to some types of functional equations. Conclusions. The authors believe that the topic "The simplest functional equations" will be useful and acceptable for studying within the scope of the subject "Algebra and the beginnings of analysis" by students of specialized classes with an in-depth study of mathematics. Within the eleven-year school education, of course, it was impossible to find time to study this topic due to the saturation and density of the material necessary for study. But in the twelve-year New Ukrainian School, marked by a deeper differentiation of specialized education, the topic "The simplest functional equations" can strengthen the fundamentality of mathematical education in classes with in-depth study of mathematics, computer science, etc. Further research in this direction may concern the method of solving the simplest recurrent equations.https://fmo-journal.org/index.php/fmo/article/view/219function of one variablefunctional equationsgeneral solution of a functional equationpartial solution of a functional equationinjectivity of a function |
| spellingShingle | Тетяна Бохонова Юрій Бохонов Ірина Матвєєва Олексій Томащук Вікторія Тихонова Олег Лещинський Валентина Гроза INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS» Фізико-математична освіта function of one variable functional equations general solution of a functional equation partial solution of a functional equation injectivity of a function |
| title | INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS» |
| title_full | INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS» |
| title_fullStr | INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS» |
| title_full_unstemmed | INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS» |
| title_short | INCLUSION OF THE TOPIC «THE SIMPLEST FUNCTIONAL EQUATIONS» IN THE MODEL PROGRAMS FOR STUDYING THE SUBJECT «ALGEBRA AND THE BEGINNINGS OF ANALYSIS» |
| title_sort | inclusion of the topic the simplest functional equations in the model programs for studying the subject algebra and the beginnings of analysis |
| topic | function of one variable functional equations general solution of a functional equation partial solution of a functional equation injectivity of a function |
| url | https://fmo-journal.org/index.php/fmo/article/view/219 |
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