Pub Date : 2022-04-28DOI: 10.53656/math2022-2-3-pro
O. Shkolnyi, Vasyl Shvets, I. Akiri
Mathematical problems that contain a common condition and an ordered list of tasks are traditionally called cascade problems. Problems of this type are extremely popular during teaching of mathematics. At the same time, they can be used both in the formation of knowledge, skills and abilities (competencies) of students, and to assess their academic achievements. In the paper we give a thorough theoretical analysis of possible types of cascade problems, describe methodology and provide examples of their applications on different stages of studying mathematics at school, in particular, during the final attestation of graduates. According to our statistical survey of mathematics teachers in Ukraine and Republic of Moldova, we clarify their attitude to problems of cascade type, as well as the advantages and disadvantages of using such problems. It is shown that the use of cascading problems in the school course of mathematics contributes to the adequate formation of important competencies of students in their learning process.
{"title":"Problems of Cascade Type and Their Use for Assessment of Students’ Academic Achievements in Mathematics","authors":"O. Shkolnyi, Vasyl Shvets, I. Akiri","doi":"10.53656/math2022-2-3-pro","DOIUrl":"https://doi.org/10.53656/math2022-2-3-pro","url":null,"abstract":"Mathematical problems that contain a common condition and an ordered list of tasks are traditionally called cascade problems. Problems of this type are extremely popular during teaching of mathematics. At the same time, they can be used both in the formation of knowledge, skills and abilities (competencies) of students, and to assess their academic achievements. In the paper we give a thorough theoretical analysis of possible types of cascade problems, describe methodology and provide examples of their applications on different stages of studying mathematics at school, in particular, during the final attestation of graduates. According to our statistical survey of mathematics teachers in Ukraine and Republic of Moldova, we clarify their attitude to problems of cascade type, as well as the advantages and disadvantages of using such problems. It is shown that the use of cascading problems in the school course of mathematics contributes to the adequate formation of important competencies of students in their learning process.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81334894","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 : 2022-04-28DOI: 10.53656/math2022-2-5-uch
E. Kelevedjiev
A brief overview of the school student competitions in informatics held in Bulgaria and the participation of Bulgarian students in international competitions in 2021 is considered. Some notes are given about the organization of these competitions and their technological support.
{"title":"The Participation of Bulgarian School Students in Informatics Competitions for 2021","authors":"E. Kelevedjiev","doi":"10.53656/math2022-2-5-uch","DOIUrl":"https://doi.org/10.53656/math2022-2-5-uch","url":null,"abstract":"A brief overview of the school student competitions in informatics held in Bulgaria and the participation of Bulgarian students in international competitions in 2021 is considered. Some notes are given about the organization of these competitions and their technological support.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76332925","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 : 2022-04-28DOI: 10.53656/math2022-2-4-ste
Tsanko Mihov, Gencho Stoitsov, Ivan Dimitrov
Robotics has a significant role in modern life. Complex programmable devices are used in high-tech manufactures as well as in many households. More and more people encounter the need to control and program robotic devices. For this reason, STEM education aims to develop such digital competencies in modern students. This article represents the results from a questionnaire held for students from the primary school stage who participate in a STEM education in robotics and assess the activities positively. We suggest three variants of tasks with solutions suitable for the students and for the working process with the robot Edison and programming environment of EdBlocks.
{"title":"Stem Robotics in Primary School","authors":"Tsanko Mihov, Gencho Stoitsov, Ivan Dimitrov","doi":"10.53656/math2022-2-4-ste","DOIUrl":"https://doi.org/10.53656/math2022-2-4-ste","url":null,"abstract":"Robotics has a significant role in modern life. Complex programmable devices are used in high-tech manufactures as well as in many households. More and more people encounter the need to control and program robotic devices. For this reason, STEM education aims to develop such digital competencies in modern students. This article represents the results from a questionnaire held for students from the primary school stage who participate in a STEM education in robotics and assess the activities positively. We suggest three variants of tasks with solutions suitable for the students and for the working process with the robot Edison and programming environment of EdBlocks.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82666114","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 : 2022-04-28DOI: 10.53656/math2022-2-7-ame
Emiliya Koleva, Evgeni Andreev, M. Nikolova
The aim of this article is to present a developed metagraph model which serves to verify the minimum requirements for cyber security in web-based student information management systems. The model presents the correlation between cyber attacks and cyber defense of the system. The protection is based on a created model for cybersecurity 3-12 and is divided into 3 categories – software, server and information system users. The most common 9 cyber attacks on automated information systems have been selected. Twelve countermeasures to these attacks have been selected. The application of the metagraph model is used to check whether the system meets the requirements of the model 3-12. The developed information system has been tested in foreign language training of students at Nikola Vaptsarov Naval Academy. The developed metagraph model can be applied to other information systems.
{"title":"A Metagraph Model оf Cyber Protection оf аn Information System","authors":"Emiliya Koleva, Evgeni Andreev, M. Nikolova","doi":"10.53656/math2022-2-7-ame","DOIUrl":"https://doi.org/10.53656/math2022-2-7-ame","url":null,"abstract":"The aim of this article is to present a developed metagraph model which serves to verify the minimum requirements for cyber security in web-based student information management systems. The model presents the correlation between cyber attacks and cyber defense of the system. The protection is based on a created model for cybersecurity 3-12 and is divided into 3 categories – software, server and information system users. The most common 9 cyber attacks on automated information systems have been selected. Twelve countermeasures to these attacks have been selected. The application of the metagraph model is used to check whether the system meets the requirements of the model 3-12. The developed information system has been tested in foreign language training of students at Nikola Vaptsarov Naval Academy. The developed metagraph model can be applied to other information systems.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87182041","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 : 2022-04-28DOI: 10.53656/math2022-2-2-voc.
S. Mikhaelis, V. Mikhaelis, D. Mikhaelis
Foreign students coming to study in Russia learn the Russian language at all levels, enriching their vocabulary. Besides possessing the lexical minimum of the Russian language, foreign students studying at the preparatory department of the Russian university need to master specialised terminology used in computer science, physics and mathematics. These subjects are included in the list of disciplines of the supplementary general programme, which aims to provide a preparation course for foreign citizens and stateless persons to master professional educational programmes in the Russian language. This article describes the need and conditions for enriching and activatingthe vocabulary of foreign students, while providing a general description of research methods. It expounds on the structure and content of the computer science course at the pre-university stage of training for foreign citizens. The paper considers the process of teaching foreign studentsthe terminology used in the computer science course. This paper provides a number of examples of new terms as well as exercises related to their acquisition. It is concluded that teaching computer-science vocabulary to foreign students is one of the most important components of teaching information science and expanding the learners’ vocabulary in general.
{"title":"Vocabulary Enrichment in Computer Science for International Students at the Preparatory Department of the University","authors":"S. Mikhaelis, V. Mikhaelis, D. Mikhaelis","doi":"10.53656/math2022-2-2-voc.","DOIUrl":"https://doi.org/10.53656/math2022-2-2-voc.","url":null,"abstract":"Foreign students coming to study in Russia learn the Russian language at all levels, enriching their vocabulary. Besides possessing the lexical minimum of the Russian language, foreign students studying at the preparatory department of the Russian university need to master specialised terminology used in computer science, physics and mathematics. These subjects are included in the list of disciplines of the supplementary general programme, which aims to provide a preparation course for foreign citizens and stateless persons to master professional educational programmes in the Russian language. This article describes the need and conditions for enriching and activatingthe vocabulary of foreign students, while providing a general description of research methods. It expounds on the structure and content of the computer science course at the pre-university stage of training for foreign citizens. The paper considers the process of teaching foreign studentsthe terminology used in the computer science course. This paper provides a number of examples of new terms as well as exercises related to their acquisition. It is concluded that teaching computer-science vocabulary to foreign students is one of the most important components of teaching information science and expanding the learners’ vocabulary in general.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78510731","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 : 2022-04-28DOI: 10.53656/math2022-2-1-com
Toni Chehlarova
Computer models with pool table oriented to the school teaching of mathematics are presented. The pool table in them has a board with six pockets and twelve “diamonds”, due to the expectation when working with these resources to form and apply not only mathematical knowledge, but also to master elements of the game of billiards. These computer models use a frontal impact, i.e. the cue ball hits the object ball in its center. The force of the shot, special shots, friction, etc. are not taken into account. The computer models are developed with dynamic GeoGebra software. They are provided with free access in the Virtual Mathematics Laboratory, developed at the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences.
{"title":"Computer Models for Playing Billiards Using Frontal Shot","authors":"Toni Chehlarova","doi":"10.53656/math2022-2-1-com","DOIUrl":"https://doi.org/10.53656/math2022-2-1-com","url":null,"abstract":"Computer models with pool table oriented to the school teaching of mathematics are presented. The pool table in them has a board with six pockets and twelve “diamonds”, due to the expectation when working with these resources to form and apply not only mathematical knowledge, but also to master elements of the game of billiards. These computer models use a frontal impact, i.e. the cue ball hits the object ball in its center. The force of the shot, special shots, friction, etc. are not taken into account. The computer models are developed with dynamic GeoGebra software. They are provided with free access in the Virtual Mathematics Laboratory, developed at the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81287544","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 : 2022-02-28DOI: 10.53656/math2022-1-5-app
Ivaylo Staribratov, Nikol Manolova
The article shares the practical experience in creating graphic design in the implementation of projects in the field of applied information technology. The creation of digital art is largely based on mathematical models and concepts that give a good perception of graphics, and it is scientifically justified. The STEAM approach is considered with the idea of the transdisciplinary level of integration between mathematics, graphic design and production practice in student education. For the development of projects like logo design, magazine cover and others, we use software specialized in the field of graphic design and computer graphics. For the realization of the considered projects, among which there are also awarded ones, we use CorelDRAW, Adobe InDesign and Desmos.
{"title":"Application of Mathematical Models in Graphic Design","authors":"Ivaylo Staribratov, Nikol Manolova","doi":"10.53656/math2022-1-5-app","DOIUrl":"https://doi.org/10.53656/math2022-1-5-app","url":null,"abstract":"The article shares the practical experience in creating graphic design in the implementation of projects in the field of applied information technology. The creation of digital art is largely based on mathematical models and concepts that give a good perception of graphics, and it is scientifically justified. The STEAM approach is considered with the idea of the transdisciplinary level of integration between mathematics, graphic design and production practice in student education. For the development of projects like logo design, magazine cover and others, we use software specialized in the field of graphic design and computer graphics. For the realization of the considered projects, among which there are also awarded ones, we use CorelDRAW, Adobe InDesign and Desmos.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72516605","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 : 2022-02-28DOI: 10.53656/math2022-1-8-dvu
R. Nikolaev, Tanka Milkova
The methods of linear optimization are well-known, both in the literature and practice, as one of the most effective methods for optimizing economic phenomena and processes. Linear models with determined coefficients have been thoroughly studied so far, but there are still areas in which research related to parametric linear optimization models can be further developed and improved. In the present paper, the graphical method for solving a two-factor linear optimization problem is used to analyze the solution of a problem for optimal distribution of resources with two parameters in the coefficients multiplying the variables in one of the constraints.
{"title":"Two-Parametric Problem for Optimal Distribution of Resources","authors":"R. Nikolaev, Tanka Milkova","doi":"10.53656/math2022-1-8-dvu","DOIUrl":"https://doi.org/10.53656/math2022-1-8-dvu","url":null,"abstract":"The methods of linear optimization are well-known, both in the literature and practice, as one of the most effective methods for optimizing economic phenomena and processes. Linear models with determined coefficients have been thoroughly studied so far, but there are still areas in which research related to parametric linear optimization models can be further developed and improved. In the present paper, the graphical method for solving a two-factor linear optimization problem is used to analyze the solution of a problem for optimal distribution of resources with two parameters in the coefficients multiplying the variables in one of the constraints.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81006259","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 : 2022-02-28DOI: 10.53656/math2022-1-4-kri
Deyan Mihaylov
This paper provides implementations of three well-known ciphers – Caesar Cipher, Vigenere Cipher and Hill Cipher in Microsoft Excel. It is shown how the ciphers can be broken by using Brute-force Attack, Frequency Analysis Attack and Known-plaintext Attack. For the purpose of the cryptanalysis the relative occurrence frequencies of the letters and the index of coincidence (κ ) in Bulgarian language are determined. The classical Frequency Analysis Attack is modified using the cross-correlation between frequencies of letters in the natural language and the cipher text. Modular matrix operations in MS Excel are shown.
{"title":"Cryptography and Cryptanalysis in MS EXCEL","authors":"Deyan Mihaylov","doi":"10.53656/math2022-1-4-kri","DOIUrl":"https://doi.org/10.53656/math2022-1-4-kri","url":null,"abstract":"This paper provides implementations of three well-known ciphers – Caesar Cipher, Vigenere Cipher and Hill Cipher in Microsoft Excel. It is shown how the ciphers can be broken by using Brute-force Attack, Frequency Analysis Attack and Known-plaintext Attack. For the purpose of the cryptanalysis the relative occurrence frequencies of the letters and the index of coincidence (κ ) in Bulgarian language are determined. The classical Frequency Analysis Attack is modified using the cross-correlation between frequencies of letters in the natural language and the cipher text. Modular matrix operations in MS Excel are shown.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76320480","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 : 2022-02-28DOI: 10.53656/math2022-1-3-dev
M. Mollov, P. Petrov
This paper is dedicated to the challenges of the education that high school students are facing while developing specific competencies related to the functional programming style (FPS). The presented educational approach consists of two components: first, learning FPS by comparing it with the imperative, procedural, object-oriented and logic programming paradigms and second, using competencies based approach for solving practical problems with functional programming. The paper presents a problem set and the phases of its application in the learning process. The results and the analysis of the approach are presented in two groups of high school students which develop successfully their specific competencies for using FPS for practical problem solving. The presented results show that the students are understanding easier FPS and its differences from their known paradigms (imperative, procedural, object-oriented and logical) by using a problem set with properly prepared practical problems which they can solve in multiple ways which lead them to the FPS solution.
{"title":"Developing Problem Solving Competency Using Functional Programming Style","authors":"M. Mollov, P. Petrov","doi":"10.53656/math2022-1-3-dev","DOIUrl":"https://doi.org/10.53656/math2022-1-3-dev","url":null,"abstract":"This paper is dedicated to the challenges of the education that high school students are facing while developing specific competencies related to the functional programming style (FPS). The presented educational approach consists of two components: first, learning FPS by comparing it with the imperative, procedural, object-oriented and logic programming paradigms and second, using competencies based approach for solving practical problems with functional programming. The paper presents a problem set and the phases of its application in the learning process. The results and the analysis of the approach are presented in two groups of high school students which develop successfully their specific competencies for using FPS for practical problem solving. The presented results show that the students are understanding easier FPS and its differences from their known paradigms (imperative, procedural, object-oriented and logical) by using a problem set with properly prepared practical problems which they can solve in multiple ways which lead them to the FPS solution.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84088257","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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