Pub Date : 2023-04-28DOI: 10.53656/math2023-2-3-dua
R. Vernydub, O. Trebenko, O. Shkolnyi
In the article, we analyze the survey results on employers’ (administrators of schools and vocational colleges) interest, readiness and opportunity for cooperation in training math teachers in a dual form of education. The opinion of employers regarding the advantages, disadvantages and obstacles in the implementation of such a study mode was studied. Several specific issues that need to be resolved in order to effectively implement a dual mode of study in math teacher training have been identified. The obtained results could be used by universities that provide training in pedagogical specialties, experts in the field of education, state authorities and local government organizations that take care of education issues, as well as other specialists interested in the spread of the dual form of obtaining education in Ukraine and abroad.
{"title":"DUAL FORM OF OBTAINING EDUCATION IN THE MATHEMATICS TEACHERS TRAINING SYSTEM: EMPLOYERS’ POSITION","authors":"R. Vernydub, O. Trebenko, O. Shkolnyi","doi":"10.53656/math2023-2-3-dua","DOIUrl":"https://doi.org/10.53656/math2023-2-3-dua","url":null,"abstract":"In the article, we analyze the survey results on employers’ (administrators of schools and vocational colleges) interest, readiness and opportunity for cooperation in training math teachers in a dual form of education. The opinion of employers regarding the advantages, disadvantages and obstacles in the implementation of such a study mode was studied. Several specific issues that need to be resolved in order to effectively implement a dual mode of study in math teacher training have been identified. The obtained results could be used by universities that provide training in pedagogical specialties, experts in the field of education, state authorities and local government organizations that take care of education issues, as well as other specialists interested in the spread of the dual form of obtaining education in Ukraine and abroad.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"12 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75438732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two algorithms for constructing all closed knight’s paths of lengths up to 16 are presented. An approach for classification (up to equivalence) of all such paths is considered. Two closed knight’s paths are called equivalent if one can be obtained from the other by applying one or more of the equivalences: translation, rotation, symmetry, or when the corresponding polygons (whose vertices are the cells visited by the knight), are geometrically congruent. By applying the construction algorithms and classification approach, we enumerate both nonequivalent and non-self-intersecting knight’s paths and show the obtained results. Some pedagogical aspects related to the problems under consideration and the teaching of subjects such as “Programming”, “Algorithms and Data Structures”, “Graph Algorithms” and “Competitive Programming” are also discussed.
{"title":"ALGORITHMS FOR CONSTRUCTION, CLASSIFICATION AND ENUMERATION OF CLOSED KNIGHT’S PATHS","authors":"Stoyan Kapralov, Valentin Bakoev, Kaloyan Kapralov","doi":"10.53656/math2023-2-1-alg","DOIUrl":"https://doi.org/10.53656/math2023-2-1-alg","url":null,"abstract":"Two algorithms for constructing all closed knight’s paths of lengths up to 16 are presented. An approach for classification (up to equivalence) of all such paths is considered. Two closed knight’s paths are called equivalent if one can be obtained from the other by applying one or more of the equivalences: translation, rotation, symmetry, or when the corresponding polygons (whose vertices are the cells visited by the knight), are geometrically congruent. By applying the construction algorithms and classification approach, we enumerate both nonequivalent and non-self-intersecting knight’s paths and show the obtained results. Some pedagogical aspects related to the problems under consideration and the teaching of subjects such as “Programming”, “Algorithms and Data Structures”, “Graph Algorithms” and “Competitive Programming” are also discussed.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136046034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-28DOI: 10.53656/math2023-2-5-res
Yavor Dechev
The COVID-19 pandemic has forced a complete lifestyle change. All educational institutions switched to distance training as swiftly as possible. This study engages in analyzing the change of degree of students‘ assimilation of the learning material in distance learning environment. A comparative analysis of the evaluation points obtained from electronic-based tests used for the semester exam is performed. The results achieved by the students for the individual types of questions and answers were examined. In conclusion, suggestions are made on how to modify electronic tests to cover different types of students, according to their individual learning abilities.
{"title":"RESEARCH ON THE IMPACT OF ONLINE LEARNING ON INDIVIDUAL LEARNING STYLES","authors":"Yavor Dechev","doi":"10.53656/math2023-2-5-res","DOIUrl":"https://doi.org/10.53656/math2023-2-5-res","url":null,"abstract":"The COVID-19 pandemic has forced a complete lifestyle change. All educational institutions switched to distance training as swiftly as possible. This study engages in analyzing the change of degree of students‘ assimilation of the learning material in distance learning environment. A comparative analysis of the evaluation points obtained from electronic-based tests used for the semester exam is performed. The results achieved by the students for the individual types of questions and answers were examined. In conclusion, suggestions are made on how to modify electronic tests to cover different types of students, according to their individual learning abilities.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"58 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90314000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-28DOI: 10.53656/math2023-2-7-web
Ivelina Velchevа, H. Hristov
The paper examines a learning method in teaching website building technologies to students in a learning environment where a role-playing game from the practice of a software company is simulated. The data collection and evaluation of the results was carried out through the qualitative methods of participant observation, interviewing, content analysis and survey card. The article analyzes the state of the researched problem by reviewing the normative base of web design training at school, the scientific and educational literature on the methods of learning through role play and teamwork. A staging of the implementation of an experiment for web design training is presented, describing the general framework for organizing the learning process, the stages of conducting the research, as well as the plot and scenario of conducting. The final results of the research were analyzed on the basis of a discussion with students and data from survey cards. The training, according to the experiment, is in the form of a simulation game and takes place in six academic hours of 40 minutes in three consecutive weeks, passing through four stages. The work of two teams of students with representative roles was studied: manager, web designer, graphic designer, stylist and web programmer. The final product of the role-playing game is the development of a website, and its final result for the learning process is knowledge and skills acquired during the formal training by the teacher and the informal training between the students during their team work.
{"title":"WEB DESIGN TRAINING APPROACH IN HIGH SCHOOL STAGE OF SECONDARY PROFILED EDUCATION","authors":"Ivelina Velchevа, H. Hristov","doi":"10.53656/math2023-2-7-web","DOIUrl":"https://doi.org/10.53656/math2023-2-7-web","url":null,"abstract":"The paper examines a learning method in teaching website building technologies to students in a learning environment where a role-playing game from the practice of a software company is simulated. The data collection and evaluation of the results was carried out through the qualitative methods of participant observation, interviewing, content analysis and survey card. The article analyzes the state of the researched problem by reviewing the normative base of web design training at school, the scientific and educational literature on the methods of learning through role play and teamwork. A staging of the implementation of an experiment for web design training is presented, describing the general framework for organizing the learning process, the stages of conducting the research, as well as the plot and scenario of conducting. The final results of the research were analyzed on the basis of a discussion with students and data from survey cards. The training, according to the experiment, is in the form of a simulation game and takes place in six academic hours of 40 minutes in three consecutive weeks, passing through four stages. The work of two teams of students with representative roles was studied: manager, web designer, graphic designer, stylist and web programmer. The final product of the role-playing game is the development of a website, and its final result for the learning process is knowledge and skills acquired during the formal training by the teacher and the informal training between the students during their team work.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"29 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89760963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.53656/math2023-1-5-the
D. Atanasov, Krassimir Manev, Vesela Stoimenova, Ralica Voynova
In the academic year 2021/2022, the first class of Informatics Specialization in Secondary school Informatics graduated and the first State Matriculation Examinations were held for the graduates of the specialization. This article makes some quantitative and qualitative evaluations of the results of this part of the exam, containing multiple-choice and open-ended questions. The obtained results would be useful for improving the test part of the exam in preparing the topics for subsequent exams.
{"title":"THE TEST TASKS FROM THE STATE MATRICULATION EXAMINATION FOR THE INFORMATICS PROFILE DURING THE ACADEMIC YEAR 2021-2022","authors":"D. Atanasov, Krassimir Manev, Vesela Stoimenova, Ralica Voynova","doi":"10.53656/math2023-1-5-the","DOIUrl":"https://doi.org/10.53656/math2023-1-5-the","url":null,"abstract":"In the academic year 2021/2022, the first class of Informatics Specialization in Secondary school Informatics graduated and the first State Matriculation Examinations were held for the graduates of the specialization. This article makes some quantitative and qualitative evaluations of the results of this part of the exam, containing multiple-choice and open-ended questions. The obtained results would be useful for improving the test part of the exam in preparing the topics for subsequent exams.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"43 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78793868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.53656/math2023-1-4-obl
M. Nikolova, Neli Kiskinova
The article analyzes the structure of a school institution and the place of the position of Information and Communication Technologies Department Chair in educational environments. An analysis was made of the necessary qualifications for occupying the position and the main duties according to the job description. The specific knowledge, skills and competences that are necessary for the creation of highly qualified personnel for the position are described. An analysis has been made of the specialized educational preparation by the higher educational institutions, so that the incumbents can be professionally qualified in the activities they have to perform. A survey related to the problems and prospects for the position was analyzed and summarized.
{"title":"OBLIGATIONS AND REQUIREMENTS FOR THE QUALIFICATION AND UNIVERSITY EDUCATION OF THE INFORMATION AND COMMUNICATION TECHNOLOGIES DEPARTMENT CHAIR IN BULGARIAN SCHOOLS","authors":"M. Nikolova, Neli Kiskinova","doi":"10.53656/math2023-1-4-obl","DOIUrl":"https://doi.org/10.53656/math2023-1-4-obl","url":null,"abstract":"The article analyzes the structure of a school institution and the place of the position of Information and Communication Technologies Department Chair in educational environments. An analysis was made of the necessary qualifications for occupying the position and the main duties according to the job description. The specific knowledge, skills and competences that are necessary for the creation of highly qualified personnel for the position are described. An analysis has been made of the specialized educational preparation by the higher educational institutions, so that the incumbents can be professionally qualified in the activities they have to perform. A survey related to the problems and prospects for the position was analyzed and summarized.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"124 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87808947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.53656/math2023-1-1-ane
Jordan Tabov, Asen Velchev, S. Stefanov, Haim Haimov
Here we derive formula for the area of a quadrilateral with angle 45º between the diagonals, which is a special case of a more general formula for the area of a quadrilateral (Haimov 2022). Along the way we obtain formulas for the area of triangles with angle of 45º/135º. We also give formulas for the area of specific kinds of pentagons and hexagons, in the form of problems.
{"title":"Нова формула за лице на четириъгълник (четиво за VII клас)","authors":"Jordan Tabov, Asen Velchev, S. Stefanov, Haim Haimov","doi":"10.53656/math2023-1-1-ane","DOIUrl":"https://doi.org/10.53656/math2023-1-1-ane","url":null,"abstract":"Here we derive formula for the area of a quadrilateral with angle 45º between the diagonals, which is a special case of a more general formula for the area of a quadrilateral (Haimov 2022). Along the way we obtain formulas for the area of triangles with angle of 45º/135º. We also give formulas for the area of specific kinds of pentagons and hexagons, in the form of problems.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"66 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83844579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.53656/math2023-1-2-the
Boyko B. Bantchev
Vector algebra is a very effective calculation language for doing geometry. It is expressive and succinct, and tends to foster generality and simplicity. In this article we consider from a vector perspective a series of problems concerning circles. After presenting a simple but so far seemingly unnoticed property of the notion of power of a point, we show its application to constructing solutions to the problems.
{"title":"THE POWER OF A POINT — A VECTOR PERSPECTIVE","authors":"Boyko B. Bantchev","doi":"10.53656/math2023-1-2-the","DOIUrl":"https://doi.org/10.53656/math2023-1-2-the","url":null,"abstract":"Vector algebra is a very effective calculation language for doing geometry. It is expressive and succinct, and tends to foster generality and simplicity. In this article we consider from a vector perspective a series of problems concerning circles. After presenting a simple but so far seemingly unnoticed property of the notion of power of a point, we show its application to constructing solutions to the problems.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"78 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88389322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.53656/math2023-1-3-for
J. Tabov, Asen Velchev, Stanislav Stefanov, Haim Haimov
А new formula for the area of an arbitrary quadrilateral is applied to derive formulae for the areas of some kinds of polygons with any number of sides; these formulae are further applied to find specific relationships for concrete number of sides.
{"title":"FORMULAE FOR THE AREAS OF SOME KINDS OF POLYGONS AND ITS APPLICATION IN PROVING RELATIONS IN THEM","authors":"J. Tabov, Asen Velchev, Stanislav Stefanov, Haim Haimov","doi":"10.53656/math2023-1-3-for","DOIUrl":"https://doi.org/10.53656/math2023-1-3-for","url":null,"abstract":"А new formula for the area of an arbitrary quadrilateral is applied to derive formulae for the areas of some kinds of polygons with any number of sides; these formulae are further applied to find specific relationships for concrete number of sides.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82185749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.53656/math2023-1-6-sev
Krasimir Harizanov
The article discusses some programming environments that can be applied in the 7th grade “Computer Modeling” classes. Attention is paid to the new active programs in the discipline “Computer Modeling and Information Technologies”. A study was conducted to track the attitudes of teachers related to teaching a scripted text programming language in 7th grade.
{"title":"SEVERAL OPPORTUNITIES FOR IMPLEMENTING THE TRAINING IN “COMPUTER MODELING AND INFORMATION TECHNOLOGIES” IN THE 7TH GRADE","authors":"Krasimir Harizanov","doi":"10.53656/math2023-1-6-sev","DOIUrl":"https://doi.org/10.53656/math2023-1-6-sev","url":null,"abstract":"The article discusses some programming environments that can be applied in the 7th grade “Computer Modeling” classes. Attention is paid to the new active programs in the discipline “Computer Modeling and Information Technologies”. A study was conducted to track the attitudes of teachers related to teaching a scripted text programming language in 7th grade.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":"5 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74602734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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