Математика и Информатика

2020/4, стр. 382 - 390

TECHNOLOGIES AND TOOLS FOR CREATING ADAPTIVE E-LEARNING CONTENT

Todorka Terzieva
OrcID: 0000-0003-2925-8534
E-mail: todorka.terzieva@fmi-plovdiv.org
Faculty of Mathematics and Informatics
University of Plovdiv “Paisii Hilendarski”
236 Bulgaria Blvd.
4003 Plovdiv Bulgaria
Valya Arnaudova
E-mail: varnaudova@uni-plovdiv.bg
Faculty of Mathematics and Informatics
University of Plovdiv “Paisii Hilendarski”
236 Bulgaria Blvd.
4003 Plovdiv Bulgaria
Asen Rahnev
E-mail: assen@uni-plovdiv.bg
Faculty of Mathematics and Informatics
University of Plovdiv “Paisii Hilendarski”
236 Bulgaria Blvd.
4003 Plovdiv Bulgaria
Vanya Ivanova
E-mail: vantod@uni-plovdiv.bg
Faculty of Mathematics and Informatics
University of Plovdiv “Paisii Hilendarski”
236 Bulgaria Blvd.
4003 Plovdiv Bulgaria

Резюме: The aim of adapting e-learning systems is to provide effective learning by supplying students with the opportunity to communicate with an environment that meets their needs, behaviour, and knowledge. The design and creation of learning materials is directly dependent on the learning objectives. The more different groups of students a course is adapted to, the higher the degree of personalization of the learning process is. In this article we present the results of a study on the types of adaptive systems depending on the technological tools and methodological approaches for implementing adaptability and personalization in learning. Special attention is paid to the applied technologies in the development and delivery of adaptive learning content as well as to the ways of modeling an individual learning path.

Ключови думи: adaptive e-learning content; adaptive learning systems; electronic learning content

Introduction

Adaptability within e-learning platforms is built in response to the fact that the learning process is different for each student. Adaptive education is an educational approach that provides adaptive e-learning services and learning materials specifically tailored for adaptive learning. The goal is to combine the ability to understand and discover the specific needs of a learner with the appropriate pedagogical strategy to improve the learning process. The modeling of the adjustment of the adaptive e-learning systems (AELS) from the point of view of the methodological aspects of e-learning can be done according to different criteria: user modeling, modeling the educational content, modeling the learning process, modeling the knowledge control, etc.

AELSaims to adapt some of its key functionalities (providing learning content, supporting navigation in a courseof studies, etc.) to the needs and preferences of learners. In this sense, adaptability can be seen as the ability of the system to adapt its behaviour and provide its functionality to users in accordance with their preferences, educational goals, learning styles, levels of knowledge, behaviour in the system, etc.

According to the initial design of adaptive e-learning (AEL), the content of an adaptive course should be suitable for students with different profiles (Modritscher & al., 2004; Brusilovsky, 2012; Tuparov & Tuparova, 2009). These profiles can contain information about the learner’s goals, preferences, level of knowledge, shown performance, learning style, psychological profile, etc. Adaptability can be both individual and group; often the learning content is designed for groups of students who have similar values to one or more parameters of the student’s profile. The more different groups of students a course is adapted to, the higher the degree of personalization of the learning process (Bontchev & Vassileva, 2012).

Types of adaptive e-learning systems

Adaptability in e-learning systems is expressed in the ability to adapt to user needs and preferences depending on the user behaviour and in response to the results shown.

AELS have been the subject of active research for the past three decades. What can be adapted is a topic that is constantly enriched and developed. This also leads to a large number of classifications, often with intertwined terms and ambiguity.

We will present types of adaptive systems depending on the technological tools and methodological approaches for realization of adaptability and personalization in learning.

Macro-adaptive learning systems In them, learners’ test results are dominant. Depending on these systems, the learning process is designed and conducted differently. A number of adaptive systems have been developed that better adapt to the different abilities of students. Since macro-adaptive instruction is regularly used within a class, it often includes elements such as explaining or presenting specific information, asking questions to monitor the learning process, and providing appropriate feedback to learners.

Computer-assisted learning systems – They combine the macro-adaptive and the micro-adaptive approaches (Modritscher et al., 2004). In them, the instructor has tools to monitor and control the learning process.

Another type of system that follows the macro-adaptive approach is the class of computer-managedinstruction (CMI) systems. As described in (Goldberg, 2019), CMI systems have functions for diagnosing students’ learning needs and recommending learning activities suitable for those needs. For example, the PLM (Platon Learning Management) system provides tests at different levels of instruction, such as a learning module, lesson, course, and curriculum. According to the student’s educational outcomes, specific instruction recommendations are provided, such as repeating the assessment or the whole unit, offering additional course instructions, etc. When mastery of all objectives in the module is achieved, the student can proceed to the next module. CMI systems provide very important macro-adaptive learning functions that allow the teacher to monitor and control the student’s learning activities.

Intelligent Learning Systems (ILS) – they automatically personalize the learning process. Their main purpose is to simulate various aspects of teaching; in them, the system itself is the instructor or teacher. ILS are based on artificial intelligence and they can draw conclusions based on knowledge models, which is useful for promoting and evaluating learning. The main function of ILS is to adapt to the learner through understanding or awareness of his/her cognitive, meta-cognitive, and emotional states. Among the characteristics of research in the field of ILS, the emphasis is on the individualization of learning and the requirement that the system has its own expertise for solving problems as well as a specific skill for conducting instruction in order to interact with the learner.

The importance of intelligent learning systems has increased rapidly in recent decades (Bradac & Kostolanyova, 2017). There are various ways in which the approaches of artificial intelligence are used in adaptive educational systems. For example, in some systems the main focus is to study and evaluate learners’ characteristics in order to generate learner profiles. The aim is to assess students’ general level of knowledge and preferences, which should be used as a basis for the pedagogy that is further recommended.

Adaptive Hypermedia Systems(AHS) they try to combine adaptive learning systems and hypermedia-based systems. These systems adapt to user characteristics, usually introducing user models for this purpose. Due to their popularity and accessibility, AHS have been used for educational systems, e-commerce applications, information systems, and support systems.

Adaptive hypermedia methods can be divided mainly into two areas of adaptation – content-level adaptation or adapted presentation, where the content is composed or presented in different ways or in different sequences, and link-level adaptation or adaptive navigation support (Almohammadi, 2017).

In (Brusilovsky, Kobsa & Vassileva, 2013) the adaptability in the adaptive hypermedia is described in detail, as the main accents arethe following:

– possibilities of the system to adapt – user characteristics (knowledge, goals, qualification, previous experience in hypermedia, preferences) and characteristics of the user environment (platform, geographical location);

– what can be adapted – content of the learning pages and the hyperlinks between them, which are called adaptive presentation and adaptive navigation respectively;

– methods and techniques for achieving adaptive presentation and adaptive navigation.

According to Brusilovsky, two main components can be adapted in AHS – the content of the learning pages and the hyperlinks between them. In (Brusilovsky, 2012), adaptability in adaptive hypermedia is comprehensively described from a technical point of view, deriving a taxonomy of adaptive hypermedia technologies, cited by a number of authors also as a taxonomy of Brusilovsky. The two main types of adaptability from a technical point of view are the above-mentioned adaptive presentation and adaptive navigation, which are subsequently divided into eight subclasses of adaptability in terms of pedagogical aspects of adaptive e-learning (Brusilovsky, 2012; Bower, 2016).

Methods and tools for adapting the learning content

Three main components participate in a balanced formula for adaptability: user (learner, student), teacher (instructor, educator), and a set of predefined rules set by the instructor (Arnaudova, Terzieva & Rahnev, 2016). Adaptability is usually focused on the learner. The subject of our research are the methods and tools of adapting the learning content.

When adapting the learning content, resources and activities dynamically change their content similar to adaptive Internet-based learning systems, which use intelligent agents to adapt the presentation or an adaptive presentation (Bradac & Kostolanyova, 2017). In case of content adaptability, it isalso understood to submit learning materialsappropriate to each student’s learning style. The purpose of the adaptive presentation is to adapt the content of each node (page) in accordance with the current state of knowledge, learning objectives, and other characteristics of the user (Brusilovsky, 2014). In adaptive presentation systems, pages are not static; instead, they are adaptively generated and compiled for each user. For example, an advanced learner may receive more detailed and in-depth information, while a beginner may obtain additional explanations.

The modeling of the learning content is directly dependent on the learning objectives. The system of goals reflects the set of knowledge, skills, and competencies that the learner must acquire at the end of the course. The course author is responsible for the creation and management of educational content. The main characteristics that the content must have are the following:

– to be well structured – in a suitable ontology and in an adequate place in the ontological graph;

– to allow for repeated use – i.e.to have the lowest possible structure of the learning objects; thus, it can be used in different places and for different purposes;

– to be described in detail according to the LOM standard or another one.

Standardization allows portability between platforms and storage in learning object repositories. Thus implemented, e-lessons can be used to independently achieve educational goals. This also makes it easier for the instructor or other Internet-based learning systems to find appropriate content.

According to the authors, the creation of static learning material is avoidedin modern web-based learning environments; educational material is presentedto the learner in a linear waydue to the large number of interdependencies and contingent connections between the different pages (Tuparov & Tuparova, 2012; Rahnev, 2014a; Sosnovsky & Brusilovsky, 2015). Often the authors create several versions of the learning resources so that the system can offer the most appropriate oneto the student.

In the general case, after the publication of the learning objects, it is not possible to change their structure, methods, or definitions of basic parameters (such as conditions or properties). However, if the learning objectis designed to allow for real-time changes, the teacher will be able to alter the way the learner perceives the course and the way it is conducted: 1) the teacher will be able to update the content based on predefined learning material or to create new content; 2) the teacher will be able to influence the learning path by uploading files, showing or hiding elements of the content and structure, etc.

The introduction of hypermedia has a major impact on adaptive learning systems. While other types of adaptive systems cannot be implemented without programming skills, adaptive AHS courses can be created using the latest writing tools such as SmexWeb. However, there are some limitations to AHS: De Bra states that the user may be directed to pages that are not relevant or understandable to him/ her if the assumed relationship in the AHS is wrong or omitted by the user (De Bra, 2003). In addition, the assessment of the learner’s knowledge is the most important factor for the successful implementation of AHS.

In hypermedia systems, content is not only textual but it also contains a number of multimedia elements. In this sense, a distinction can be made between an adaptive text presentation and an adaptive multimedia presentation. This also includes adaptations in the learning systems that implement intelligent agents to adapt performance (Almohammadi, 2017), adaptive natural language generation, machine learning, and others. Another aspect of adapting the content is the submission of learning material appropriate to the learning style of each student through the use of various multimedia elements such as text, sound, graphics, video, animation, etc.

Adaptive navigation methods refer to all possibilities for modifying the visual links, which provide navigation – for example, rearranging, hiding, adding annotations, etc. (Brusilovsky, 2014). The main methods for adaptive navigation are the following:

Direct guidance the user can be directed to the material to be studied in accordance with his/her level of knowledge on the subject, learning objectives, pedagogical strategy, or other parameters involved in the user model (Brusilovsky, 2012; Rahnev & al., 2014b).

Adaptive link sorting it aims to arrange all the links in a page in line with certain criteria such as their compliance with previous knowledge or similarity to the current document. The higher a relationship is in the sorting, the more it meets the criteria.

Adaptive link annotation this is a method whose implementation techniques involve providing links along with additional marking, text, coloring, icon, or fading so as to give the learner some additional information about the nodes behind these links (Brusilovsky, 2012; Bower, 2016). The algorithm for generating annotations classifies the students’ level of knowledge into three categories – minimum, average, and maximum. Thresholds for the level of knowledge can be set by the teacher. These three knowledge thresholds allow the adaptation mechanism to finetune how much knowledge each learner needs to demonstrate. The authors also note the motivational effect of the annotation of links – in their opinion, learners answer more questions;they work with the questions more persistently and research a greater variety of materials related to the questions. The adaptive annotation of links helps to significantly increase the commitment of learners to work with optional learning material.

The learners’level of knowledge or their abilities are also often included as parameters of adaptation in the construction of a personalized learning path. Some sources use Bloom’s taxonomy to classify the ability of students (Alshammari & al., 2014; Brusilovsky, 2012), while others use test results to determine the learners’level of knowledge (Rahneva & al., 2008; Rahnev & al., 2014a;Bower, 2016).

Another parameter, as suggested by (Rahnev & al., 2014b; Arnaudova & al., 2016), is the number of visits to the same learning object. To meet the needs of students and to improve the quality of adaptive learning, it is necessary to take into account a number of factors during the formation of a personalized learning path,such as prerequisites for success (results of preliminary tests, number of attempts, etc.), pedagogical consistency, cognitive complexity, successor failure of other learners, and assessment time (Terzieva & al., 2018; Rahnev & al., 2019). The preconditions for achieving the pedagogical goals are fulfilled in order to extract information about the students’preliminary preparation and to choose a suitable pedagogical model for them.

In recent years, cognitive information processing capabilities have also been added to the abilities that influence e-learning. The creation of adaptive e-learning systems, integrating the cognitive load theory (Clark &Mayer, 2016), is beginning. In e-learning, it is easy to succumb to the temptation to provide vast amounts of information through different media simultaneously and leave it in the hands of learners to deal with the associations between sound and text or picture and concept, etc., which strains students’cognitive abilities and leads to low learning efficiency.

The specific features that need to be considered in the process of implementing adaptive e-learning are:

– the learners’level of knowledge and skills, as both the initial level and the current state are essential when conducting interim tests;

– the individual rate of assimilation (working capacity) and level of cognitive and practical autonomy;

– the nature of the thought processes of the different groups of learners, etc.

Conclusions

Each learner has individual needs and characteristics such as basic knowledge, learning style, motivation, etc. These differences affect the effectiveness of the learning process and are a prerequisite for some learners to easily master the learning material of an e-course, whereas others to encounter significant difficulties.

The main goal of the functioning of the system for adaptive learning is to increase the efficiency of learning by reducing the time for access to the necessary learning information, selecting a sufficient amount of learning resources to achieve the set learning goals, providing different learning styles and content accessibility, stimulating self-control and self-learning, motivating students through active forms of education and so on.

Acknowledgment. This paper is supported by the National Scientific Program “Information andCommunication Technologies for a Single Digital Market in Science, Educationand Security (ICTinSES)”, financed by the Ministry of Education and Science.

REFERENCES

Almohammadi, K., Hagras, H, Alghazzawi D. & Aldabbagh G. (2017). A Survey of Artificial Intelligence Techniques Employed for Adaptive Educational Systems Within E-Learning Platforms, Journal of Artificial Intelligence and Soft Computing Research, Vol. 7, Issue 1, 47 – 64.DOI: 10.1515/jaiscr-2017-0004, ISSN (print): 2083-2567, ISSN (on-line): 2449-6499.

Alshammari, M., Anane, R. & Hendley R. (2014). Adaptivity in E-Learning Systems, The Eighth International Conference on Complex, Intelligent, and Software Intensive Systems(CISIS 2014), Birmingham, UK, ISBN print: 978-147994325-8.

Arnaudova, V., Terzieva, T. & Rahnev, A. (2016). A methodological approach for implementation of adaptive e-learning. CBU International Conference Proceedings, Prague, Czech Republic, v. 4, p. 480 – 487, Print ISSN 1805-997X, Online ISSN 1805-9961.

Bower, M. (2016). A Framework for Adaptive Learning Design in a WebConferencing Environment, Journal of Interactive Media in Education, 11, pp. 1–21,http://dx.doi.org/10.5334/jime.406.

Bontchev, B. & Vassileva, D. (2012). Courseware Adaptation to Learning Styles and Knowledge Level, E-Learning – Engineering, On-Job Training and Interactive Teaching, Dr. Sergio Kofuji (Ed.), InTech, ISBN: 978-953-51-0283-0.

Bradac, V. & Kostolányová, K. (2017). Intelligent T utoring Systems, In: Vincenti G., Bucciero A., Helfert M. & Glowatz M. (eds) E-Learning, E-Education, and Online Training, Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, Vol. 180, Springer, 71 – 78, ISSN: 1867-8211, Online ISSN: 1867-822X.

Brusilovsky, P. (2012). Adaptive Hypermedia for Education and Training. In: Adaptive Technologies for Training and Education. Cambridge, UK: Cambridge University Press, pp. 46 – 68. ISBN: 9780521769037. Brusilovsky, P. (2014). Addictive links: engaging students through adaptive navigation support and open social student modeling, WWW ‘14 Companion Proceedings of the 23rd International Conference on World Wide Web, Seoul, Korea, April 07 – 11, 1075 – 1076, ISBN: 978-1-45032745-9.

Clark, R., & Mayer, R. (2016). E-Learning and the science of instruction: proven guidelines for consumers and designers of multimedia learning, 4th. ed, Jossey-Bass/Pfeiffer Edition, pp. 528, ISBN-13: 978-1119158660, ISBN-10: 1119158664.

De Bra, P . (2003). Link-Independent Navigation Support in Web-Based Adaptive Hypermedia, Journal of W eb Engineering (JWE) Vol. 2,1&2 pp. 74 – 89.

Goldberg, B. (2019). Design Recommendations for Intelligent Tutoring Systems: Volume 7 – Self-Improving Systems, U.S. Army Combat Capabilities Development Command – Soldier Center, pp. 194, ISBN: 099772577X, 9780997725773.

Modritscher, F., Manuel Garcia-Barrios, V. & Gutl C. (2004). The Past, the Present and the Future of adaptive E-Learning An Approach within the Scope of the Research Project AdeLE, Proceedings of the International Conference on Interactive Computer Aided Learning (ICL2004), Villach, Austria, ISBN: 3-89958-089-3

Rahnev, А., Pavlov N. & Kyurkchiev, V. (2014a). Distributed Platform for e-Learning – DisPeL , European International Journal of Science and Technology (EIJST), 3 (1), 95 – 109, ISSN: 2304-9693.

Rahnev, A., N. Pavlov, A. Golev, M. Stieger & T. Gardjeva (2014b). New Electronic Education Services Using the Distributed E

Learning Platform (DisPeL), International Electr onic Journal of Pur e and Applied Mathematics (IEJP AM), 7 (2), 63 – 71 (ISSN: 1314-0744).

Rahnev, A., B. Zlatanov , E. Angelova, I. Staribratov , V. Arnaudova & S. Cholakov. (2019). Electronic textbook in overview lectures for state examination in DisPeL, Mathematics and Informatics, Volume 62, Number 2, 156 – 167. ISSN 1314–8532 (Online); ISSN 1310–2230 (Print).

Rahneva, O., A. Golev & N. Pavlov. (2008). Dynamic Generation of Testing Question in SQL in DeTC, Cybernetics and Information Technologies, Vol. 8, No. 1, pp 73 – 81, Print ISSN: 1311-9702, Online ISSN: 13144081.

Sosnovsky, S. & P. Brusilovsky (2015). Evaluation of topic-based adaptation and student modeling in QuizGuide. User Model User-Adap Inter 25, 371–424.https://doi.org/10.1007/s11257-015-9164-4.

Terzieva, T., A. Rahnev & A. Karabov. (2018). Methodological problems for development of adaptive e-learning content, Annual Scientific and Methodological Journal“Education and Technology“,Vol. 9, ISSUE 1, pp. 119 – 124, ISSN 1314 1791.

Tuparov, G. & D. Tuparova (2009). Modelling of Adaptive Learning Scenario in e-Learning Environments, Journal Communication and Cognition, Vol. 42 No1, Gent, Belgium, pp. 19-34, ISSN 0378-0880.

Tuparov, G. & D. Tuparova (2012). Technological Tools for Development, Delivering and Maintenance of e-Learning Content and Courses, Mathematics and Informatics, Volume 3, pp. 2013 – 224, ISSN 1314– 8532 (Online); ISSN 1310–2230 (Print).

2025 година
Книжка 6
ENHANCING STUDENT MOTIVATION AND ACHIEVEMENT THROUGH DIGITAL MIND MAPPING

Mikloš Kovač, Mirjana Brdar, Goran Radojev, Radivoje Stojković

OPTIMIZATION VS BOOSTING: COMPARISON OF STRATEGIES ON EDUCATIONAL DATASETS TO EXPLORE LOW-PERFORMING AT-RISK AND DROPOUT STUDENTS

Ranjit Paul, Asmaa Mohamed, Peren Jerfi Canatalay, Ashima Kukkar, Sadiq Hussain, Arun K. Baruah, Jiten Hazarika, Silvia Gaftandzhieva, Esraa A. Mahareek, Abeer S. Desuky, Rositsa Doneva

ARTIFICIAL INTELLIGENCE AS A TOOL FOR PEDAGOGICAL INNOVATIONS IN MATHEMATICS EDUCATION

Stanka Hadzhikoleva, Maria Borisova, , Borislava Kirilova

Книжка 4
Книжка 3
МОДЕЛИ НА ВЕРОЯТНОСТНИ ПРОСТРАНСТВА В ОЛИМПИАДНИ ЗАДАЧИ

Драгомир Грозев, Станислав Харизанов

Книжка 1
A NOTE ON A GENERALIZED DYNAMICAL SYSTEM OCCURS IN MODELLING “THE BATTLE OF THE SEXES”: CHAOS IN SOCIOBIOLOGY

Nikolay Kyurkchiev, Anton Iliev, Vesselin Kyurkchiev, Angel Golev, Todorka Terzieva, Asen Rahnev

EDUCATIONAL RESOURCES FOR STUDYING MIDSEGMENTS OF TRIANGLE AND TRAPEZOID

Toni Chehlarova1), Neda Chehlarova2), Georgi Gachev

2024 година
Книжка 6
ВЪЗМОЖНОСТИ ЗА ИЗГРАЖДАНЕ НА МЕЖДУПРЕДМЕТНИ ВРЪЗКИ МАТЕМАТИКА – ИНФОРМАТИКА

Елена Каращранова, Ирена Атанасова, Надежда Борисова

Книжка 5
FRAMEWORK FOR DESIGNING VISUALLY ORIENTATED TOOLS TO SUPPORT PROJECT MANAGEMENT

Dalibor Milev, Nadezhda Borisova, Elena Karashtranova

3D ОБРАЗОВАТЕЛЕН ПОДХОД В ОБУЧЕНИЕТО ПО СТЕРЕОМЕТРИЯ

Пеньо Лебамовски, Марияна Николова

Книжка 4
DYNAMICS OF A NEW CLASS OF OSCILLATORS: MELNIKOV’S APPROACH, POSSIBLE APPLICATION TO ANTENNA ARRAY THEORY

Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev, Vesselin Kyurkchiev, Asen Rahnev

Книжка 3
РАЗСТОЯНИЯ МЕЖДУ ЗАБЕЛЕЖИТЕЛНИ ТОЧКИ И НЕРАВЕНСТВА В ИЗПЪКНАЛ ЧЕТИРИЪГЪЛНИК

Йордан Табов, Станислав Стефанов, Красимир Кънчев, Хаим Хаимов

USING AI TO IMPROVE ANSWER EVALUATION IN AUTOMATED EXAMS

Georgi Cholakov, Asya Stoyanova-Doycheva

Книжка 2
ON INTEGRATION OF STEM MODULES IN MATHEMATICS EDUCATION

Elena Karashtranova, Aharon Goldreich, Nadezhda Borisova

Книжка 1
STUDENT SATISFACTION WITH THE QUALITY OF A BLENDED LEARNING COURSE

Silvia Gaftandzhieva, Rositsa Doneva, Sadiq Hussain, Ashis Talukder, Gunadeep Chetia, Nisha Gohain

MODERN ROAD SAFETY TRAINING USING GAME-BASED TOOLS

Stefan Stavrev, Ivelina Velcheva

ARTIFICIAL INTELLIGENCE FOR GOOD AND BAD IN CYBER AND INFORMATION SECURITY

Nikolay Kasakliev, Elena Somova, Margarita Gocheva

2023 година
Книжка 6
QUALITY OF BLENDED LEARNING COURSES: STUDENTS’ PERSPECTIVE

Silvia Gaftandzhieva, Rositsa Doneva, Sadiq Hussain, Ashis Talukder, Gunadeep Chetia, Nisha Gohain

МОДЕЛ НА ЛЕОНТИЕВ С MS EXCEL

Велика Кунева, Мариян Милев

Книжка 5
AREAS ASSOCIATED TO A QUADRILATERAL

Oleg Mushkarov, Nikolai Nikolov

ON THE DYNAMICS OF A ClASS OF THIRD-ORDER POLYNOMIAL DIFFERENCE EQUATIONS WITH INFINITE NUMBER OF PERIOD-THREE SOLUTIONS

Jasmin Bektešević, Vahidin Hadžiabdić, Midhat Mehuljić, Sadjit Metović, Haris Lulić

СИСТЕМА ЗА ИЗВЛИЧАНЕ И ВИЗУАЛИЗАЦИЯ НА ДАННИ ОТ ИНТЕРНЕТ

Георги Чолаков, Емил Дойчев, Светла Коева

Книжка 4
MULTIPLE REPRESENTATIONS OF FUNCTIONS IN THE FRAME OF DISTANCE LEARNING

Radoslav Božić, Hajnalka Peics, Aleksandar Milenković

INTEGRATED LESSONS IN CALCULUS USING SOFTWARE

Pohoriliak Oleksandr, Olga Syniavska, Anna Slyvka-Tylyshchak, Antonina Tegza, Alexander Tylyshchak

Книжка 3
ПРИЛОЖЕНИЕ НА ЕЛЕМЕНТИ ОТ ГЕОМЕТРИЯТА НА ЧЕТИРИЪГЪЛНИКА ЗА РЕШАВАНЕ НА НЕСТАНДАРТНИ ЗАДАЧИ

Йордан Табов, Веселин Ненков, Асен Велчев, Станислав Стефанов

Книжка 2
Книжка 1
НОВА ФОРМУЛА ЗА ЛИЦЕ НА ЧЕТИРИЪГЪЛНИК (ЧЕТИВО ЗА VII КЛАС)

Йордан Табов, Асен Велчев, Станислав Стефанов, Хаим Хаимов

2022 година
Книжка 6
MOBILE GAME-BASED MATH LEARNING FOR PRIMARY SCHOOL

Margarita Gocheva, Nikolay Kasakliev, Elena Somova

Книжка 5
SECURITY ANALYSIS ON CONTENT MANAGEMENT SYSTEMS

Lilyana Petkova, Vasilisa Pavlova

MONITORING OF STUDENT ENROLMENT CAMPAIGN THROUGH DATA ANALYTICS TOOLS

Silvia Gaftandzhieva, Rositsa Doneva, Milen Bliznakov

TYPES OF SOLUTIONS IN THE DIDACTIC GAME “LOGIC MONSTERS”

Nataliya Hristova Pavlova, Michaela Savova Toncheva

Книжка 4
PERSONAL DATA PROCESSING IN A DIGITAL EDUCATIONAL ENVIRONMENT

Evgeniya Nikolova, Mariya Monova-Zheleva, Yanislav Zhelev

Книжка 3
Книжка 2
STEM ROBOTICS IN PRIMARY SCHOOL

Tsanko Mihov, Gencho Stoitsov, Ivan Dimitrov

A METAGRAPH MODEL OF CYBER PROTECTION OF AN INFORMATION SYSTEM

Emiliya Koleva, Evgeni Andreev, Mariya Nikolova

Книжка 1
CONVOLUTIONAL NEURAL NETWORKS IN THE TASK OF IMAGE CLASSIFICATION

Larisa Zelenina, Liudmila Khaimina, Evgenii Khaimin, D. Khripunov, Inga Zashikhina

INNOVATIVE PROPOSALS FOR DATABASE STORAGE AND MANAGEMENT

Yulian Ivanov Petkov, Alexandre Ivanov Chikalanov

APPLICATION OF MATHEMATICAL MODELS IN GRAPHIC DESIGN

Ivaylo Staribratov, Nikol Manolova

РЕШЕНИЯ НА КОНКУРСНИ ЗАДАЧИ БРОЙ 6, 2021 Г.

Задача 1. Дадени са различни естествени числа, всяко от които има прос- ти делители, не по-големи от . Докажете, че произведението на някои три от тези числа е точен куб. Решение: числата са представим във вида . Нека разгледаме квадрат

2021 година
Книжка 6
E-LEARNING DURING COVID-19 PANDEMIC: AN EMPIRICAL RESEARCH

Margarita Gocheva, Nikolay Kasakliev, Elena Somova

Книжка 5
ПОДГОТОВКА ЗА XXV МЛАДЕЖКА БАЛКАНИАДА ПО МАТЕМАТИКА 2021

Ивайло Кортезов, Емил Карлов, Мирослав Маринов

EXCEL’S CALCULATION OF BASIC ASSETS AMORTISATION VALUES

Vehbi Ramaj, Sead Rešić, Anes Z. Hadžiomerović

EDUCATIONAL ENVIRONMENT AS A FORM FOR DEVELOPMENT OF MATH TEACHERS METHODOLOGICAL COMPETENCE

Olha Matiash, Liubov Mykhailenko, Vasyl Shvets, Oleksandr Shkolnyi

Книжка 4
LEARNING ANALYTICS TOOL FOR BULGARIAN SCHOOL EDUCATION

Silvia Gaftandzhieva, Rositsa Doneva, George Pashev, Mariya Docheva

Книжка 3
THE PROBLEM OF IMAGES’ CLASSIFICATION: NEURAL NETWORKS

Larisa Zelenina, Liudmila Khaimina, Evgenii Khaimin, D. Khripunov, Inga Zashikhina

MIDLINES OF QUADRILATERAL

Sead Rešić, Maid Omerović, Anes Z. Hadžiomerović, Ahmed Palić

ВИРТУАЛЕН ЧАС ПО МАТЕМАТИКА

Севдалина Георгиева

Книжка 2
MOBILE MATH GAME PROTOTYPE ON THE BASE OF TEMPLATES FOR PRIMARY SCHOOL

Margarita Gocheva, Elena Somova, Nikolay Kasakliev, Vladimira Angelova

КОНКУРСНИ ЗАДАЧИ БРОЙ 2/2021 Г.

Краен срок за изпращане на решения: 0 юни 0 г.

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 1, 2021

Краен срок за изпращане на решения: 0 юни 0 г.

Книжка 1
СЕДЕМНАДЕСЕТА ЖАУТИКОВСКА ОЛИМПИАДА ПО МАТЕМАТИКА, ИНФОРМАТИКА И ФИЗИКА АЛМАТИ, 7-12 ЯНУАРИ 2021

Диян Димитров, Светлин Лалов, Стефан Хаджистойков, Елена Киселова

ОНЛАЙН СЪСТЕЗАНИЕ „VIVA МАТЕМАТИКА С КОМПЮТЪР“

Петър Кендеров, Тони Чехларова, Георги Гачев

2020 година
Книжка 6
ABSTRACT DATA TYPES

Lasko M. Laskov

Книжка 5
GAMIFICATION IN CLOUD-BASED COLLABORATIVE LEARNING

Denitza Charkova, Elena Somova, Maria Gachkova

NEURAL NETWORKS IN A CHARACTER RECOGNITION MOBILE APPLICATION

L.I. Zelenina, L.E. Khaimina, E.S. Khaimin, D.I. Antufiev, I.M. Zashikhina

APPLICATIONS OF ANAGLIFIC IMAGES IN MATHEMATICAL TRAINING

Krasimir Harizanov, Stanislava Ivanova

МЕТОД НА ДЕЦАТА В БЛОКА

Ивайло Кортезов

Книжка 4
TECHNOLOGIES AND TOOLS FOR CREATING ADAPTIVE E-LEARNING CONTENT

Todorka Terzieva, Valya Arnaudova, Asen Rahnev, Vanya Ivanova

Книжка 3
MATHEMATICAL MODELLING IN LEARNING OUTCOMES ASSESSMENT (BINARY MODEL FOR THE ASSESSMMENT OF STUDENT’S COMPETENCES FORMATION)

L. E. Khaimina, E. A. Demenkova, M. E. Demenkov, E. S. Khaimin, L. I. Zelenina, I. M. Zashikhina

PROBLEMS 2 AND 5 ON THE IMO’2019 PAPER

Sava Grozdev, Veselin Nenkov

Книжка 2
ЗА ВЕКТОРНОТО ПРОСТРАНСТВО НА МАГИЧЕСКИТЕ КВАДРАТИ ОТ ТРЕТИ РЕД (В ЗАНИМАТЕЛНАТА МАТЕМАТИКА)

Здравко Лалчев, Маргарита Върбанова, Мирослав Стоимиров, Ирина Вутова

КОНКУРЕНТНИ ПЕРПЕНДИКУЛЯРИ, ОПРЕДЕЛЕНИ ОТ ПРАВИЛНИ МНОГОЪГЪЛНИЦИ

Йоана Христова, Геновева Маринова, Никола Кушев, Светослав Апостолов, Цветомир Иванов

A NEW PROOF OF THE FEUERBACH THEOREM

Sava Grozdev, Hiroshi Okumura, Deko Dekov

PROBLEM 3 ON THE IMO’2019 PAPER

Sava Grozdev, Veselin Nenkov

Книжка 1
GENDER ISSUES IN VIRTUAL TRAINING FOR MATHEMATICAL KANGAROO CONTEST

Mark Applebaum, Erga Heller, Lior Solomovich, Judith Zamir

KLAMKIN’S INEQUALITY AND ITS APPLICATION

Šefket Arslanagić, Daniela Zubović

НЯКОЛКО ПРИЛОЖЕНИЯ НА ВЪРТЯЩАТА ХОМОТЕТИЯ

Сава Гроздев, Веселин Ненков

2019 година
Книжка 6
DISCRETE MATHEMATICS AND PROGRAMMING – TEACHING AND LEARNING APPROACHES

Mariyana Raykova, Hristina Kostadinova, Stoyan Boev

CONVERTER FROM MOODLE LESSONS TO INTERACTIVE EPUB EBOOKS

Martin Takev, Elena Somova, Miguel Rodríguez-Artacho

ЦИКЛОИДА

Аяпбергенов Азамат, Бокаева Молдир, Чурымбаев Бекнур, Калдыбек Жансуйген

КАРДИОИДА

Евгений Воронцов, Никита Платонов

БОЛГАРСКАЯ ОЛИМПИАДА ПО ФИНАНСОВОЙ И АКТУАРНОЙ МАТЕМАТИКЕ В РОССИИ

Росен Николаев, Сава Гроздев, Богдана Конева, Нина Патронова, Мария Шабанова

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 1. Да се намерят всички полиноми, които за всяка реална стойност на удовлетворяват равенството Татяна Маджарова, Варна Задача 2. Правоъгълният триъгълник има остри ъгли и , а центърът на вписаната му окръжност е . Точката , лежаща в , е такава, че и . Симетралите

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 1, 2019

Задача 1. Да се намерят всички цели числа , за които

Книжка 5
ДЪЛБОКО КОПИЕ В C++ И JAVA

Христина Костадинова, Марияна Райкова

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 1. Да се намери безкрайно множество от двойки положителни ра- ционални числа Милен Найденов, Варна

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 6, 2018

Задача 1. Точката е левият долен връх на безкрайна шахматна дъска. Една муха тръгва от и се движи само по страните на квадратчетата. Нека е общ връх на някои квадратчета. Казва- ме, че мухата изминава пътя между и , ако се движи само надясно и нагоре. Ако точките и са противоположни върхове на правоъгълник , да се намери броят на пътищата, свърз- ващи точките и , по които мухата може да мине, когато: а) и ; б) и ; в) и

Книжка 4
THE REARRANGEMENT INEQUALITY

Šefket Arslanagić

АСТРОИДА

Борислав Борисов, Деян Димитров, Николай Нинов, Теодор Христов

COMPUTER PROGRAMMING IN MATHEMATICS EDUCATION

Marin Marinov, Lasko Laskov

CREATING INTERACTIVE AND TRACEABLE EPUB LEARNING CONTENT FROM MOODLE COURSES

Martin Takev, Miguel Rodríguez-Artacho, Elena Somova

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 1. Да се реши уравнението . Христо Лесов, Казанлък Задача 2. Да се докаже, че в четириъгълник с перпендикулярни диагонали съществува точка , за която са изпълнени равенствата , , , . Хаим Хаимов, Варна Задача 3. В правилен 13-ъгълник по произволен начин са избрани два диа- гонала. Каква е вероятността избраните диагонали да не се пресичат? Сава Гроздев, София, и Веселин Ненков, Бели Осъм

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 5, 2018

Задача 1. Ако и са съвършени числа, за които целите части на числата и са равни и различни от нула, да се намери .

Книжка 3
RESULTS OF THE FIRST WEEK OF CYBERSECURITY IN ARKHANGELSK REGION

Olga Troitskaya, Olga Bezumova, Elena Lytkina, Tatyana Shirikova

DIDACTIC POTENTIAL OF REMOTE CONTESTS IN COMPUTER SCIENCE

Natalia Sofronova, Anatoliy Belchusov

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Краен срок за изпращане на решения 30 ноември 2019 г.

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 4, 2018

Задача 1. Да се намерят всички тройки естествени числа е изпълнено равенството: а)

Книжка 2
ЕЛЕКТРОНЕН УЧЕБНИК ПО ОБЗОРНИ ЛЕКЦИИ ЗА ДЪРЖАВЕН ИЗПИТ В СРЕДАТА DISPEL

Асен Рахнев, Боян Златанов, Евгения Ангелова, Ивайло Старибратов, Валя Арнаудова, Слав Чолаков

ГЕОМЕТРИЧНИ МЕСТА, ПОРОДЕНИ ОТ РАВНОСТРАННИ ТРИЪГЪЛНИЦИ С ВЪРХОВЕ ВЪРХУ ОКРЪЖНОСТ

Борислав Борисов, Деян Димитров, Николай Нинов, Теодор Христов

ЕКСТРЕМАЛНИ СВОЙСТВА НА ТОЧКАТА НА ЛЕМОАН В ЧЕТИРИЪГЪЛНИК

Веселин Ненков, Станислав Стефанов, Хаим Хаимов

A TRIANGLE AND A TRAPEZOID WITH A COMMON CONIC

Sava Grozdev, Veselin Nenkov

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Христо Лесов, Казанлък Задача 2. Окръжност с диаметър и правоъгълник с диагонал имат общ център. Да се докаже, че за произволна точка M от е изпълне- но равенството . Милен Найденов, Варна Задача 3. В изпъкналия четириъгълник са изпълнени равенства- та и . Точката е средата на диагонала , а , , и са ортоганалните проекции на съответно върху правите , , и . Ако и са средите съответно на отсечките и , да се докаже, че точките , и лежат на една права.

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 3, 2018

Задача 1. Да се реши уравнението . Росен Николаев, Дико Суружон, Варна Решение. Въвеждаме означението , където . Съгласно това означение разлежданото уравнение придобива вида не е решение на уравнението. Затова са възможни само случаите 1) и 2) . Разглеж- даме двата случая поотделно. Случай 1): при е изпълнено равенството . Тогава имаме:

Книжка 1
PROBLEM 6. FROM IMO’2018

Sava Grozdev, Veselin Nenkov

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 2, 2018

Задача 1. Да се намери най-малкото естествено число , при което куба с целочислени дължини на ръбовете в сантиметри имат сума на обемите, рав- на на Христо Лесов, Казанлък Решение: тъй като , то не е куб на ес- тествено число и затова . Разглеждаме последователно случаите за . 1) При разглеждаме естествени числа и , за които са изпълнени релациите и . Тогава то , т.е. . Освен това откъдето , т.е. .Така получихме, че . Лесно се проверява, че при и няма естествен

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 1. Да се намерят всички цели числа , за които

2018 година
Книжка 6
„ЭНЦИКЛОПЕДИЯ ЗАМЕЧАТЕЛЬНЫХ ПЛОСКИХ КРИВЫХ“ – МЕЖДУНАРОДНЫЙ СЕТЕВОЙ ИССЛЕДОВАТЕЛЬСКИЙ ПРОЕКТ В РАМКАХ MITE

Роза Атамуратова, Михаил Алфёров, Марина Белорукова, Веселин Ненков, Валерий Майер, Генадий Клековкин, Раиса Овчинникова, Мария Шабанова, Александр Ястребов

A NEW MEANING OF THE NOTION “EXPANSION OF A NUMBER”

Rosen Nikolaev, Tanka Milkova, Radan Miryanov

Книжка 5
ИТОГИ ПРОВЕДЕНИЯ ВТОРОЙ МЕЖДУНАРОДНОЙ ОЛИМПИАДЬI ПО ФИНАНСОВОЙ И АКТУАРНОЙ МАТЕМАТИКЕ СРЕДИ ШКОЛЬНИКОВ И СТУДЕНТОВ

Сава Гроздев, Росен Николаев, Мария Шабанова, Лариса Форкунова, Нина Патронова

LEARNING AND ASSESSMENT BASED ON GAMIFIED E-COURSE IN MOODLE

Mariya Gachkova, Martin Takev, Elena Somova

УЛИТКА ПАСКАЛЯ

Дарья Коптева, Ксения Горская

КОМБИНАТОРНИ ЗАДАЧИ, СВЪРЗАНИ С ТРИЪГЪЛНИК

Росен Николаев, Танка Милкова, Катя Чалъкова

Книжка 4
ЗА ПРОСТИТЕ ЧИСЛА

Сава Гроздев, Веселин Ненков

ИНЦЕНТЪР НА ЧЕТИРИЪГЪЛНИК

Станислав Стефанов

ЭПИЦИКЛОИДА

Инкар Аскар, Камила Сарсембаева

ГИПОЦИКЛОИДА

Борислав Борисов, Деян Димитров, Иван Стефанов, Николай Нинов, Теодор Христов

Книжка 3
ПОЛИНОМИ ОТ ТРЕТА СТЕПЕН С КОЛИНЕАРНИ КОРЕНИ

Сава Гроздев, Веселин Ненков

ЧЕТИРИДЕСЕТ И ПЕТА НАЦИОНАЛНА СТУДЕНТСКА ОЛИМПИАДА ПО МАТЕМАТИКА

Сава Гроздев, Росен Николаев, Станислава Стоилова, Веселин Ненков

Книжка 2
TWO INTERESTING INEQUALITIES FOR ACUTE TRIANGLES

Šefket Arslanagić, Amar Bašić

ПЕРФЕКТНА ИЗОГОНАЛНОСТ В ЧЕТИРИЪГЪЛНИК

Веселин Ненков, Станислав Стефанов, Хаим Хаимов

НЯКОИ ТИПОВЕ ЗАДАЧИ СЪС СИМЕТРИЧНИ ЧИСЛА

Росен Николаев, Танка Милкова, Радан Мирянов

Книжка 1
Драги читатели,

където тези проценти са наполовина, в Източна Европа те са около 25%, в

COMPUTER DISCOVERED MATHEMATICS: CONSTRUCTIONS OF MALFATTI SQUARES

Sava Grozdev, Hiroshi Okumura, Deko Dekov

ВРЪЗКИ МЕЖДУ ЗАБЕЛЕЖИТЕЛНИ ТОЧКИ В ЧЕТИРИЪГЪЛНИКА

Станислав Стефанов, Веселин Ненков

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 2. Да се докаже, че всяка от симедианите в триъгълник с лице разделя триъгълника на два триъгълника, лицата на които са корени на урав- нението където и са дължините на прилежащите на симедианата страни на три- ъгълника. Милен Найденов, Варна Задача 3. Четириъгълникът е описан около окръжност с център , като продълженията на страните му и се пресичат в точка . Ако е втората пресечна точка на описаните окръжности на триъгълниците и , да се докаже, че Хаим Х

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 2, 2017

Задача 1. Да се определи дали съществуват естествени числа и , при които стойността на израза е: а) куб на естествено число; б) сбор от кубовете на две естествени числа; в) сбор от кубовете на три естествени числа. Христо Лесов, Казанлък Решение: при и имаме . Следова- телно случай а) има положителен отговор. Тъй като при число- то се дели на , то при и имаме е естестве- но число. Следователно всяко число от разглеждания вид при деление на дава ос

2017 година
Книжка 6
A SURVEY OF MATHEMATICS DISCOVERED BY COMPUTERS. PART 2

Sava Grozdev, Hiroshi Okumura, Deko Dekov

ТРИ ИНВАРИАНТЫ В ОДНУ ЗАДА

Ксения Горская, Дарья Коптева, Асхат Ермекбаев, Арман Жетиру, Азат Бермухамедов, Салтанат Кошер, Лили Стефанова, Ирина Христова, Александра Йовкова

GAMES WITH

Aldiyar Zhumashov

SOME NUMERICAL SQUARE ROOTS (PART TWO)

Rosen Nikolaev, Tanka Milkova, Yordan Petkov

ЗАНИМАТЕЛНИ ЗАДАЧИ ПО ТЕМАТА „КАРТИННА ГАЛЕРИЯ“

Мирослав Стоимиров, Ирина Вутова

Книжка 5
ВТОРОЙ МЕЖДУНАРОДНЫЙ СЕТЕВОЙ ИССЛЕДОВАТЕЛЬСКИЙ ПРОЕКТ УЧАЩИХСЯ В РАМКАХ MITE

Мария Шабанова, Марина Белорукова, Роза Атамуратова, Веселин Ненков

SOME NUMERICAL SEQUENCES CONCERNING SQUARE ROOTS (PART ONE)

Rosen Nikolaev, Tanka Milkova, Yordan Petkov

Книжка 4
ГЕНЕРАТОР НА ТЕСТОВЕ

Ангел Ангелов, Веселин Дзивев

INTERESTING PROOFS OF SOME ALGEBRAIC INEQUALITIES

Šefket Arslanagić, Faruk Zejnulahi

PROBLEMS ON THE BROCARD CIRCLE

Sava Grozdev, Hiroshi Okumura, Deko Dekov

ПРИЛОЖЕНИЕ НА ЛИНЕЙНАТА АЛГЕБРА В ИКОНОМИКАТА

Велика Кунева, Захаринка Ангелова

СКОРОСТТА НА СВЕТЛИНАТА

Сава Гроздев, Веселин Ненков

Книжка 3
НЯКОЛКО ПРИЛОЖЕНИЯ НА ТЕОРЕМАТА НА МЕНЕЛАЙ ЗА ВПИСАНИ ОКРЪЖНОСТИ

Александра Йовкова, Ирина Христова, Лили Стефанова

НАЦИОНАЛНА СТУДЕНТСКА ОЛИМПИАДА ПО МАТЕМАТИКА

Сава Гроздев, Росен Николаев, Веселин Ненков

СПОМЕН ЗА ПРОФЕСОР АНТОН ШОУРЕК

Александра Трифонова

Книжка 2
ИЗКУСТВЕНА ИМУННА СИСТЕМА

Йоанна Илиева, Селин Шемсиева, Светлана Вълчева, Сюзан Феимова

ВТОРИ КОЛЕДЕН ЛИНГВИСТИЧЕН ТУРНИР

Иван Держански, Веселин Златилов

Книжка 1
ГЕОМЕТРИЯ НА ЧЕТИРИЪГЪЛНИКА, ТОЧКА НА МИКЕЛ, ИНВЕРСНА ИЗОГОНАЛНОСТ

Веселин Ненков, Станислав Стефанов, Хаим Хаимов

2016 година
Книжка 6
ПЕРВЫЙ МЕЖДУНАРОДНЫЙ СЕТЕВОЙ ИССЛЕДОВАТЕЛЬСКИЙ ПРОЕКТ УЧАЩИХСЯ В РАМКАХ MITE

Мария Шабанова, Марина Белорукова, Роза Атамуратова, Веселин Ненков

НЕКОТОРЫЕ ТРАЕКТОРИИ, КОТОРЫЕ ОПРЕДЕЛЕНЫ РАВНОБЕДРЕННЫМИ ТРЕУГОЛЬНИКАМИ

Ксения Горская, Дарья Коптева, Даниил Микуров, Еркен Мудебаев, Казбек Мухамбетов, Адилбек Темирханов, Лили Стефанова, Ирина Христова, Радина Иванова

ПСЕВДОЦЕНТЪР И ОРТОЦЕНТЪР – ЗАБЕЛЕЖИТЕЛНИ ТОЧКИ В ЧЕТИРИЪГЪЛНИКА

Веселин Ненков, Станислав Стефанов, Хаим Хаимов

FUZZY LOGIC

Reinhard Magenreuter

GENETIC ALGORITHM

Reinhard Magenreuter

Книжка 5
NEURAL NETWORKS

Reinhard Magenreuter

Книжка 4
АКТИВНО, УЧАСТВАЩО НАБЛЮДЕНИЕ – ТИП ИНТЕРВЮ

Христо Христов, Христо Крушков

ХИПОТЕЗАТА В ОБУЧЕНИЕТО ПО МАТЕМАТИКА

Румяна Маврова, Пенка Рангелова, Елена Тодорова

Книжка 3
ОБОБЩЕНИЕ НА ТЕОРЕМАТА НА ЧЕЗАР КОШНИЦА

Сава Гроздев, Веселин Ненков

Книжка 2
ОЙЛЕР-ВЕН ДИАГРАМИ ИЛИ MZ-КАРТИ В НАЧАЛНАТА УЧИЛИЩНА МАТЕМАТИКА

Здравко Лалчев, Маргарита Върбанова, Ирина Вутова, Иван Душков

ОБВЪРЗВАНЕ НА ОБУЧЕНИЕТО ПО АЛГЕБРА И ГЕОМЕТРИЯ

Румяна Маврова, Пенка Рангелова

Книжка 1
STATIONARY NUMBERS

Smaiyl Makyshov

МЕЖДУНАРОДНА ЖАУТИКОВСКА ОЛИМПИАДА

Сава Гроздев, Веселин Ненков

2015 година
Книжка 6
Книжка 5
Книжка 4
Книжка 3
МОТИВАЦИОННИТЕ ЗАДАЧИ В ОБУЧЕНИЕТО ПО МАТЕМАТИКА

Румяна Маврова, Пенка Рангелова, Зара Данаилова-Стойнова

Книжка 2
САМОСТОЯТЕЛНО РЕШАВАНЕ НА ЗАДАЧИ С EXCEL

Пламен Пенев, Диана Стефанова

Книжка 1
ГЕОМЕТРИЧНА КОНСТРУКЦИЯ НА КРИВА НА ЧЕВА

Сава Гроздев, Веселин Ненков

2014 година
Книжка 6
КОНКУРЕНТНОСТ, ПОРОДЕНА ОТ ТАНГЕНТИ

Сава Гроздев, Веселин Ненков

Книжка 5
ИНФОРМАТИКА В ШКОЛАХ РОССИИ

С. А. Бешенков, Э. В. Миндзаева

ОЩЕ ЕВРИСТИКИ С EXCEL

Пламен Пенев

ДВА ПОДХОДА ЗА ИЗУЧАВАНЕ НА УРАВНЕНИЯ В НАЧАЛНАТА УЧИЛИЩНА МАТЕМАТИКА

Здравко Лалчев, Маргарита Върбанова, Ирина Вутова

Книжка 4
ОБУЧЕНИЕ В СТИЛ EDUTAINMENT С ИЗПОЛЗВАНЕ НА КОМПЮТЪРНА ГРАФИКА

Христо Крушков, Асен Рахнев, Мариана Крушкова

Книжка 3
ИНВЕРСИЯТА – МЕТОД В НАЧАЛНАТА УЧИЛИЩНА МАТЕМАТИКА

Здравко Лалчев, Маргарита Върбанова

СТИМУЛИРАНЕ НА ТВОРЧЕСКА АКТИВНОСТ ПРИ БИЛИНГВИ ЧРЕЗ ДИНАМИЧЕН СОФТУЕР

Сава Гроздев, Диана Стефанова, Калина Василева, Станислава Колева, Радка Тодорова

ПРОГРАМИРАНЕ НА ЧИСЛОВИ РЕДИЦИ

Ивайло Старибратов, Цветана Димитрова

Книжка 2
ФРАКТАЛЬНЫЕ МЕТО

Валерий Секованов, Елена Селезнева, Светлана Шляхтина

Книжка 1
ЕВРИСТИКА С EXCEL

Пламен Пенев

SOME INEQUALITIES IN THE TRIANGLE

Šefket Arslanagić

2013 година
Книжка 6
Книжка 5
МАТЕМАТИЧЕСКИЕ РЕГАТЬI

Александр Блинков

Книжка 4
Книжка 3
АКАДЕМИК ПЕТЪР КЕНДЕРОВ НА 70 ГОДИНИ

чл. кор. Юлиан Ревалски

ОБЛАЧНИ ТЕХНОЛОГИИ И ВЪЗМОЖНОСТИ ЗА ПРИЛОЖЕНИЕ В ОБРАЗОВАНИЕТО

Сава Гроздев, Иванка Марашева, Емил Делинов

СЪСТЕЗАТЕЛНИ ЗАДАЧИ ПО ИНФОРМАТИКА ЗА ГРУПА Е

Ивайло Старибратов, Цветана Димитрова

Книжка 2
ЕКСПЕРИМЕНТАЛНАТА МАТЕМАТИКА В УЧИЛИЩЕ

Сава Гроздев, Борислав Лазаров

МАТЕМАТИКА С КОМПЮТЪР

Сава Гроздев, Деко Деков

ЕЛИПТИЧЕН АРБЕЛОС

Пролет Лазарова

Книжка 1
ФРАГМЕНТИ ОТ ПАМЕТТА

Генчо Скордев

2012 година
Книжка 6
ДВЕ ДИДАКТИЧЕСКИ СТЪЛБИ

Сава Гроздев, Светлозар Дойчев

ТЕОРЕМА НА ПОНСЕЛЕ ЗА ЧЕТИРИЪГЪЛНИЦИ

Сава Гроздев, Веселин Ненков

ИЗЛИЧАНЕ НА ОБЕКТИВНИ ЗНАНИЯ ОТ ИНТЕРНЕТ

Ивайло Пенев, Пламен Пенев

Книжка 5
ДЕСЕТА МЕЖДУНАРОДНА ОЛИМПИАДА ПО ЛИНГВИСТИКА

д–р Иван А. Держански (ИМИ–БАН)

ТЕОРЕМА НА ВАН ОБЕЛ И ПРИЛОЖЕНИЯ

Тодорка Глушкова, Боян Златанов

МАТЕМАТИЧЕСКИ КЛУБ „СИГМА” В СВЕТЛИНАТА НА ПРОЕКТ УСПЕХ

Сава Гроздев, Иванка Марашева, Емил Делинов

I N M E M O R I A M

На 26 септември 2012 г. след продължително боледуване ни напусна проф. дпн Иван Ганчев Донев. Той е първият професор и първият доктор на науките в България по методика на обучението по математика. Роден е на 6 май 1935 г. в с. Страхилово, В. Търновско. След завършване на СУ “Св. Кл. Охридски” става учител по математика в гр. Свищов. Тук той организира първите кръжоци и със- тезания по математика. През 1960 г. Иван Ганчев печели конкурс за асистент в СУ и още през следващата година започ

Книжка 4
Книжка 3
СЛУЧАЙНО СЪРФИРАНЕ В ИНТЕРНЕТ

Евгения Стоименова

Книжка 2
SEEMOUS OLYMPIAD FOR UNIVERSITY STUDENTS

Sava Grozdev, Veselin Nenkov

EUROMATH SCIENTIFIC CONFERENCE

Sava Grozdev, Veselin Nenkov

FIVE WAYS TO SOLVE A PROBLEM FOR A TRIANGLE

Šefket Arslanagić, Dragoljub Milošević

ПРОПОРЦИИ

Валя Георгиева

ПЪТЕШЕСТВИЕ В СВЕТА НА КОМБИНАТОРИКАТА

Росица Керчева, Румяна Иванова

ПОЛЗОТВОРНА ПРОМЯНА

Ивайло Старибратов

Книжка 1
ЗА ЕЛЕКТРОННОТО ОБУЧЕНИЕ

Даниела Дурева (Тупарова)

МАТЕМАТИКАТА E ЗАБАВНА

Веселина Вълканова

СРАВНЯВАНЕ НА ИЗРАЗИ С КВАДРАТНИ КОРЕНИ

Гинка Бизова, Ваня Лалева