Pub Date : 2023-06-30DOI: 10.53656/math2023-3-4-dat
Valentina Dyankova, Milko Yankov
The authors focus on the implementation of blended learning for constructing knowledge of Data Structures. One of the challenges of blended learning is to provide a model for creating an integrated learning environment that ensures an effective learning process. The purpose is to identify key processes, learner’s roles and learning situations, as well as to propose a decomposition of the learning process into manageable learning units using a blended learning approach. An example online data structure system – one developed by the authors that implements experiential learning – is proposed as an illustration of an online blended learning component.
{"title":"DATA STRUCTURE KNOWLEDGE MANAGEMENT THROUGH BLENDED LEARNING","authors":"Valentina Dyankova, Milko Yankov","doi":"10.53656/math2023-3-4-dat","DOIUrl":"https://doi.org/10.53656/math2023-3-4-dat","url":null,"abstract":"The authors focus on the implementation of blended learning for constructing knowledge of Data Structures. One of the challenges of blended learning is to provide a model for creating an integrated learning environment that ensures an effective learning process. The purpose is to identify key processes, learner’s roles and learning situations, as well as to propose a decomposition of the learning process into manageable learning units using a blended learning approach. An example online data structure system – one developed by the authors that implements experiential learning – is proposed as an illustration of an online blended learning component.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80853945","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 : 2023-06-30DOI: 10.53656/math2023-3-2-ana
J. Tabov, Veselin Nenkov, Asen Velchev, Stanislav Stefanov
Lately, the foundations of a complete geometry of the quadrilateral were laid, built in analogy of the classical geometry of the triangle. Several articles were devoted to it, the PhD-dissertation work of one of the authors of this article (Stefanov, St. 2020), and a book encompassing it in its entirety is soon to be published. This publication aims to convince the readers in the benefits of studying this geometry. During the last years the rubrics „Contest problems“ and „Problems М+“ of the journals „Mathematics and Informatics“ and „Mathematics Plus“ included difficult problems, whose solutions are complex for somebody who doesn't know and doesn't use elements of the quadrilateral’s geometry. Knowing the properties of the remarkable points, lines and circles, as well as the mappings in the quadrilateral, which are subjects of its geometry, not only provides ideas for solving this problem, but also serves for their implementation (to carry out the solution). This was shown once in (Nenkov, Stefanov & Haimov 2020). We will confirm it here again, with new interesting examples.
最近，一个完整的四边形几何的基础奠定了，建立在经典几何三角形的类比。有几篇文章专门讨论它，这篇文章的作者之一的博士论文工作(Stefanov, St. 2020)，一本完整包含它的书即将出版。本出版物旨在使读者相信研究这种几何的好处。在过去的几年里，《数学与信息学》和《数学Plus》杂志的标题“竞赛问题”和“问题М+”包括了一些难题，这些难题的解决方案对于不了解和不使用四边形几何元素的人来说是复杂的。了解作为四边形几何主题的重要点、线、圆的性质以及四边形中的映射关系，不仅为解决这一问题提供了思路，而且有助于它们的实施(实现解决方案)。这在(Nenkov, Stefanov & Haimov 2020)中显示过一次。我们将用新的有趣的例子再次证实它。
{"title":"AN APPLICATION OF ELEMENTS OF THE QUADRILATERAL’S GEOMETRY FOR SOLVING NON-STANDARD PROBLEMS","authors":"J. Tabov, Veselin Nenkov, Asen Velchev, Stanislav Stefanov","doi":"10.53656/math2023-3-2-ana","DOIUrl":"https://doi.org/10.53656/math2023-3-2-ana","url":null,"abstract":"Lately, the foundations of a complete geometry of the quadrilateral were laid, built in analogy of the classical geometry of the triangle. Several articles were devoted to it, the PhD-dissertation work of one of the authors of this article (Stefanov, St. 2020), and a book encompassing it in its entirety is soon to be published. This publication aims to convince the readers in the benefits of studying this geometry. During the last years the rubrics „Contest problems“ and „Problems М+“ of the journals „Mathematics and Informatics“ and „Mathematics Plus“ included difficult problems, whose solutions are complex for somebody who doesn't know and doesn't use elements of the quadrilateral’s geometry. Knowing the properties of the remarkable points, lines and circles, as well as the mappings in the quadrilateral, which are subjects of its geometry, not only provides ideas for solving this problem, but also serves for their implementation (to carry out the solution). This was shown once in (Nenkov, Stefanov & Haimov 2020). We will confirm it here again, with new interesting examples.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87182346","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 : 2023-06-30DOI: 10.53656/math2023-3-3-gam
Rosi Georgieva
This article is a natural continuation of its first part, published in the journal “Mathematics and Informatics”, where the terminology related to game-based learning and the role of tasks in learning the learning content, as well as example tasks and methodical implementation for non-profiled training in programming for high school students through the creation of games, are presented using Python's turtle graph. This article follows the structure of its first part and focuses on example tasks implemented with the Python programming language, the Pygame library, and the Mu programming environment. The sample tasks are supported by methodical instructions. Guidelines are also given for their use in training. In the conclusion, the possibilities for game-based programming learning in profiled and non-profiled high schools are discussed using the Pygame Python library.
{"title":"GAME-BASED PROGRAMMING TEACHING FOR BEGINNERS IN PYGAME ZERO MODE – SAMPLE PYTHON TASKS. PART II – PYGAME LIBRARY","authors":"Rosi Georgieva","doi":"10.53656/math2023-3-3-gam","DOIUrl":"https://doi.org/10.53656/math2023-3-3-gam","url":null,"abstract":"This article is a natural continuation of its first part, published in the journal “Mathematics and Informatics”, where the terminology related to game-based learning and the role of tasks in learning the learning content, as well as example tasks and methodical implementation for non-profiled training in programming for high school students through the creation of games, are presented using Python's turtle graph. This article follows the structure of its first part and focuses on example tasks implemented with the Python programming language, the Pygame library, and the Mu programming environment. The sample tasks are supported by methodical instructions. Guidelines are also given for their use in training. In the conclusion, the possibilities for game-based programming learning in profiled and non-profiled high schools are discussed using the Pygame Python library.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88500823","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 : 2023-06-30DOI: 10.53656/math2023-3-7-usi
S. Stavrev, Ivelina Velchevа
In this study, we use two sensors – Kinect v 2.0 and Tobii 5.0 in order to detect and measure the attention levels of primary school students during the road safety educational classes. We use custom-developed road safety serious games for conducting the experiments with students in primary schools. One of the evaluation tools is a web-based e-book – a digital representation of a traditional textbook. The other tool is a 3D virtual platform for safety on the road. Both tools are developed using Unity 3D. Finally, we compare the selected road safety educational tools, discuss their strengths and weaknesses and draw conclusions.
在本研究中，我们使用Kinect v 2.0和Tobii 5.0两种传感器来检测和测量小学生在道路安全教育课上的注意力水平。我们使用特别设计的道路安全严肃游戏，与小学生进行实验。评估工具之一是基于网络的电子书——传统教科书的数字表示。另一个工具是用于道路安全的3D虚拟平台。这两个工具都是使用Unity 3D开发的。最后，我们比较了所选择的道路安全教育工具，讨论了它们的优缺点并得出结论。
{"title":"USING SENSORS TO DETECT AND ANALYZE STUDENTS’ ATTENTION DURING ROAD SAFETY TRAINING IN PRIMARY SCHOOL","authors":"S. Stavrev, Ivelina Velchevа","doi":"10.53656/math2023-3-7-usi","DOIUrl":"https://doi.org/10.53656/math2023-3-7-usi","url":null,"abstract":"In this study, we use two sensors – Kinect v 2.0 and Tobii 5.0 in order to detect and measure the attention levels of primary school students during the road safety educational classes. We use custom-developed road safety serious games for conducting the experiments with students in primary schools. One of the evaluation tools is a web-based e-book – a digital representation of a traditional textbook. The other tool is a 3D virtual platform for safety on the road. Both tools are developed using Unity 3D. Finally, we compare the selected road safety educational tools, discuss their strengths and weaknesses and draw conclusions.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84993062","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 : 2023-06-30DOI: 10.53656/math2023-3-5-fli
Evgeniya Nikolova
Flipped learning is an educational technique in which students engage with instructional materials outside of class (such as films, texts, or interactive tutorials) while using class time for active learning tasks such as problem-solving, group work, and discussions. Flipped learning can be a particularly effective strategy in the context of school-based mathematics education. By allowing for greater differentiation, engagement, and interactivity, it can help to support the learning needs of all students and promote deeper understanding of mathematical concepts. This article looks at some key aspects of the implementation of the flipped classroom in mathematics education and suggests a possibility for its combination with the traditional model of mathematics education in Bulgarian schools to achieve more efficient and effective learning.
{"title":"FLIPPED CLASSROOM AND TRADITIONAL METHOD IN TEACHING MATHEMATICS IN BULGARIAN SCHOOL","authors":"Evgeniya Nikolova","doi":"10.53656/math2023-3-5-fli","DOIUrl":"https://doi.org/10.53656/math2023-3-5-fli","url":null,"abstract":"Flipped learning is an educational technique in which students engage with instructional materials outside of class (such as films, texts, or interactive tutorials) while using class time for active learning tasks such as problem-solving, group work, and discussions. Flipped learning can be a particularly effective strategy in the context of school-based mathematics education. By allowing for greater differentiation, engagement, and interactivity, it can help to support the learning needs of all students and promote deeper understanding of mathematical concepts. This article looks at some key aspects of the implementation of the flipped classroom in mathematics education and suggests a possibility for its combination with the traditional model of mathematics education in Bulgarian schools to achieve more efficient and effective learning.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79245828","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 : 2023-06-30DOI: 10.53656/math2023-3-6-gra
Ivan G. Lenchuk, Alla Prus
Two approaches for drawing of stereometric objects by a constructive method are presented using algorithms designed to help solve problems in the construction of correct, visual and easy-to-draw drawings. The first approach is based on operations borrowed from engineer drawing, where standardized axonometric projections guarantee the quality of drawings. The second one is based on the experience of many generations of teachers and practitioners. A list of methodological advice has been proposed. The analytical method of reasoning in computational problems is promoted, the method of combining with the image plane is established, which visualizes the way to the result, adds empiricism to the discipline. The presented statistical survey among mathematics teachers demonstrates their attitude to the constructive solution of stereometric problems. The advantages and disadvantages of teaching constructivism methods are highlighted. It has been established that the skills of qualitative drawings contribute to the formation of life competencies of pupils.
{"title":"GRAPHIC CULTURE OF CONSTRUCTIVE MODELING OF FIGURES IN METRIC STEREOMETRY","authors":"Ivan G. Lenchuk, Alla Prus","doi":"10.53656/math2023-3-6-gra","DOIUrl":"https://doi.org/10.53656/math2023-3-6-gra","url":null,"abstract":"Two approaches for drawing of stereometric objects by a constructive method are presented using algorithms designed to help solve problems in the construction of correct, visual and easy-to-draw drawings. The first approach is based on operations borrowed from engineer drawing, where standardized axonometric projections guarantee the quality of drawings. The second one is based on the experience of many generations of teachers and practitioners. A list of methodological advice has been proposed. The analytical method of reasoning in computational problems is promoted, the method of combining with the image plane is established, which visualizes the way to the result, adds empiricism to the discipline. The presented statistical survey among mathematics teachers demonstrates their attitude to the constructive solution of stereometric problems. The advantages and disadvantages of teaching constructivism methods are highlighted. It has been established that the skills of qualitative drawings contribute to the formation of life competencies of pupils.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89595269","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 : 2023-06-30DOI: 10.53656/math2023-3-1-ove
N. Pavlova
In this article, we will analyze the needs, interests and realization of the students of Faculty of mathematics and computer science of Konstantin Preslavsky University of Shumen, preparing to become teachers of mathematics, informatics, computer modeling and information technologies. The group we are considering are the students of Bachelor’s and Master’s degree. The data for students who choose to graduate with thesis defense are being studied. The aim is to track the trends and the reflection of current methodological directions in the interests of students. A classification is proposed in the main areas in which students choose to work. A content analysis of the protected developments in the period 2014 – 2022 was made. The realization of the students was tracked. Ideas that are to be realized in diploma thesis in the future are marked.
{"title":"OVERVIEW AND DEVELOPMENT IN THE PROFESSIONAL INTERESTS OF GRADUATE STUDENTS","authors":"N. Pavlova","doi":"10.53656/math2023-3-1-ove","DOIUrl":"https://doi.org/10.53656/math2023-3-1-ove","url":null,"abstract":"In this article, we will analyze the needs, interests and realization of the students of Faculty of mathematics and computer science of Konstantin Preslavsky University of Shumen, preparing to become teachers of mathematics, informatics, computer modeling and information technologies. The group we are considering are the students of Bachelor’s and Master’s degree. The data for students who choose to graduate with thesis defense are being studied. The aim is to track the trends and the reflection of current methodological directions in the interests of students. A classification is proposed in the main areas in which students choose to work. A content analysis of the protected developments in the period 2014 – 2022 was made. The realization of the students was tracked. Ideas that are to be realized in diploma thesis in the future are marked.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81508327","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/math2023-2-2-con
Mitko Kunchev
The article presents a method for constructing the common perpendicular of two skew lines in a given polyhedron. The method is based on constructing the intersecting line of two planes that are respectively perpendicular to the two skew lines. The common perpendicular is constructed parallel to this line so that it intersects the skew lines. Examples of constructing the common perpendicular of skew lines in a cube, a right triangular prism, and a regular tetrahedron are considered.
{"title":"CONSTRUCTING THE COMMON PERPENDICULAR OF TWO SKEW LINES","authors":"Mitko Kunchev","doi":"10.53656/math2023-2-2-con","DOIUrl":"https://doi.org/10.53656/math2023-2-2-con","url":null,"abstract":"The article presents a method for constructing the common perpendicular of two skew lines in a given polyhedron. The method is based on constructing the intersecting line of two planes that are respectively perpendicular to the two skew lines. The common perpendicular is constructed parallel to this line so that it intersects the skew lines. Examples of constructing the common perpendicular of skew lines in a cube, a right triangular prism, and a regular tetrahedron are considered.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74433942","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/math2023-2-6-gam
Rosi Georgieva
In recent years, an increasing digitalization has been observed in all spheres of life on a global scale. The demand for specialists in the field of ICT requires their preparation to start at school with the study of programming and IT. Good practices and increasing interest in game-based learning are observed at all levels of secondary education. Different environments, programming languages and learning approaches is used in the Computer Modeling and Informatics disciplines. The focus of the article are sample tasks and methodical implementation for nonprofiled training in programming for high school students by creating games. The terminology related to game-based learning and the role of tasks in mastering learning content are presented. The main focus is on creating fun games implemented in Python programming language using turtle graphics in Mu programming environment. The sample tasks are supported by methodical instructions. Guidelines are also given for their use in training. In the conclusion, the possibilities for training in programming in profiled and non-profiled high schools are discussed.
{"title":"GAME-BASED PROGRAMMING TRAINING FOR BEGINNERS IN THE PYGAME ZERO ENVIRONMENT - SAMPLE ASSIGNMENTS WITH PYTHON TURTLE GRAPHICS","authors":"Rosi Georgieva","doi":"10.53656/math2023-2-6-gam","DOIUrl":"https://doi.org/10.53656/math2023-2-6-gam","url":null,"abstract":"In recent years, an increasing digitalization has been observed in all spheres of life on a global scale. The demand for specialists in the field of ICT requires their preparation to start at school with the study of programming and IT. Good practices and increasing interest in game-based learning are observed at all levels of secondary education. Different environments, programming languages and learning approaches is used in the Computer Modeling and Informatics disciplines. The focus of the article are sample tasks and methodical implementation for nonprofiled training in programming for high school students by creating games. The terminology related to game-based learning and the role of tasks in mastering learning content are presented. The main focus is on creating fun games implemented in Python programming language using turtle graphics in Mu programming environment. The sample tasks are supported by methodical instructions. Guidelines are also given for their use in training. In the conclusion, the possibilities for training in programming in profiled and non-profiled high schools are discussed.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77250588","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/math2023-2-4-exa
Krassimir Manev
In the academic year 2021/2022, the State Matriculation Exam (the examination taken at the end of Secondary education to qualify for entry into University) was held for the first time for the students studying the profiling subject of Informatics in the Bulgarian secondary school. The article examines the tasks from the two sessions of the exam, which are supposed test the ability of high school students to select/create algorithms. The conditions to which a task of this type must meet and to what extent the tasks of the two exam topics satisfy these conditions are examined in detail.
{"title":"THE ALGORITHMIC TASKS FROM THE STATE GRADUATION EXAMINATION IN THE PROFILING SUBJECT OF INFORMATICS FOR 2022","authors":"Krassimir Manev","doi":"10.53656/math2023-2-4-exa","DOIUrl":"https://doi.org/10.53656/math2023-2-4-exa","url":null,"abstract":"In the academic year 2021/2022, the State Matriculation Exam (the examination taken at the end of Secondary education to qualify for entry into University) was held for the first time for the students studying the profiling subject of Informatics in the Bulgarian secondary school. The article examines the tasks from the two sessions of the exam, which are supposed test the ability of high school students to select/create algorithms. The conditions to which a task of this type must meet and to what extent the tasks of the two exam topics satisfy these conditions are examined in detail.","PeriodicalId":41818,"journal":{"name":"Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89184169","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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