Математика и Информатика

2015/2, стр. 180 - 194

APPLYING CLOUD COMPUTING FOR A MORE EFFICIENT EVALUATION OF PRACTICAL PROJECTS

Emil Delinov
E-mail: delinov@gmail.com
Sofia, Bulgaria

Резюме: Significant competitive advantage both for businesses and for the other entities are the well prepared, adaptive, and constantly improving staff. One approach of the education system for the creation and development of adequate to the needs staff, is the development of projects with topics from real economy. Important preconditions for successful realization of the project are the close collaboration between the trainer (teacher, lecturer, mentor, supervisor/consultant, etc.) and the learner and the motivation of the latter to create a product of high quality. The accurate and objective evaluation, set and announced on time, could play a significant role for the positive motivation and respectively for the successful outcome of the project and the acquisition and consolidation of knowledge. This paper considers some features of Cloud Computing used to increase the efficiency in the evaluation of projects with topics from real economy.

Ключови думи: Cloud Computing; Cloud Computing in education; usage of Cloud technologies in education; project work; evaluation of project work; road map of practical projects; Cloud Computing for evaluation

Significant competitive advantage both for the businesses and for the central and local administration is well-prepared, adaptable and continuously improving staff. In today’s dynamic stage of human existence, seeking and finding appropriate experts is a difficult and vital process that does not always end successfully. This often leads to direct losses or missed opportunities. Ernst & Young conclude in one of their surveys that “German SMEs have difficulties finding qualified staff, which causes them missed opportunities of € 33 billion a year”1. According to an IBM report (IBM’s 2012 Tech Trends), only one of 10 organizations has professionals with the skills needed for effective implementation of technologies such as “business intelligence”, “mobile computing”, “Cloud Computing” and “social business”2.

The minimization of time from the occurrence of the need till knowledge acquisition and application in practice becomes more and more significant for all industries, services, management, etc. One approach of the education system for the creation and development of adequate staff needs is developing projects with themes from the real economy. So the learners (students, graduates, employees in companies, etc.) acquire practical knowledge and skills.

It is well known that the occurrence of the project method is closely related to the acquisition of practical knowledge and skills. Project work was used even back in 1763 in the architectural school “San Luca” in Rome - according to a study by M. Knoll (Knoll, 1997). Significant development and justification of this method is made by the U.S. educator and psychologist John Dewey and his student William Kilpatrick (Nikolaeva, 2004). Institutionalization of the term “project” is done in 1911, when the Bureau of Education of the United States legalized it.

Fig. 1. Road Map for developing practical projects

Nowadays the project method is being reassessed and developed. Over the past 20 years a number of authors, including Bulgarian ones, actively explored the main issues of the project-based learning. Plovdiv teams (A. Rahnev, E. Angelova, K. Gurov, S. Aneva, etc.) have worked hard on issues related to the project activity and its improvement. A number of scholars and teachers in different subjects (B. Toshev, A. Gendzhova, B. Yordanova, I. Marasheva) has studied and implemented project-based learning (Marasheva-Delinova, 2012). In the past few years, in terms of evaluation in our country, there has also been solid theoretical and practical experience (Bankov, 2012), (Stoimenova, 2000), (Lazarov, 2009), etc.

The development of practical (on topics from the real economy) projects in mathematics, computer science, information technology, etc. is an iterative process, consisting of seven phases (Delinov & Marasheva, 2013), whose block diagram is shown on Fig. 1. Important preconditions for the successful end of the process are the close cooperation between the trainer (teacher, lecturer, mentor, scientific supervisor / consultant, etc.) and the learner, on one hand, and the motivation of the latter to create a “top-quality” product out of his efforts and work, on the other (Marasheva, 2011). In this respect, the ability of the trainer, to form positive motivation attitude in students mind (learners), which is one of its most important tasks (Andreev, 1996).

Evaluating the projects: Evaluation, as part of learning, plays an important role for motivation. According to one of the definitions, evaluation is “the process of comparing the measured actual performance with pre-set and required quantitative and qualitative standards, norms, criteria” (Radev, 2005). According to another one, “it is a process of differentiation by comparison aiming regulation and analysis” (Stamm, 1998), and so on. It is clear that there is no uniform and standardized definition of evaluation, but in all cases it is understood that this is a process of comparison, cross-check, analysis, etc. of the achievements against pre-set criteria. But it’s not just stating the results of a comparison. The evaluation of one activity and single knowledge cannot be considered outside the development of the learner’s overall personality. Therefore the tutor (teacher, trainer, scholar, etc.) should be very well aware of his/her students (Grozdev, 2007). Through the evaluation of acquired knowledge and skills the students form significant parts of selfawareness and self-assessment criteria, compares the social and psychological significance of their achievements with those of others (Andreev, 1996). In (Andreev, 1996) and (Andreev, 1987) Marin Andreev sets the functions of check and evaluation. Three of these are:

– Diagnostic and prognostic - establishing the status of the work done and acquired knowledge to a given date gives feedback and helps to predict future conditions and progress management.

– Stimulating - objective evaluation plays an important stimulating function because it encourages students to work systematically, ensuring fair remuneration for the work.

– Developing skills for self-control - students form their own criteria for evaluation of the nature of their mistakes and find ways to overcome them.

The accurate and objective evaluation, set and announced on time, could play a significant role in the positive motivation and respectively in the successful outcome of the project and the acquisition and consolidation of knowledge. It is therefore a good practice to evaluate the work throughout the whole cycle of development, preparation and presentation of the project. The measurement during the entire project development is also necessary in order to provide operational feedback. In this aspect, in the different phases of the map, the verification by teacher and/or mentor is a sort of evaluation of the activities to date. The process of verification, respectively evaluation, could be significantly improved and optimized by using Information technologies (IT), and more specifically “Cloud Computing” (Grozdev et al., 2013a).. Essential for the learners (especially students) is the final score that they receive for the public defense of the project in front of an audience. The latter usually consists to a greater extent of their peers, often even classmates from their class or school. According to a survey conducted among the students from the “upper classes”, developing projects, one of the most important evaluation of their work is the one given by their peers during classroom and school conferences (Marasheva-Delinova, 2012). It turns out that the assessment is not the only important thing for the young people. A survey, conducted among students from 21st Secondary School “Hr. Botev”, Sofia, shows that a very important incentive for the development of projects is the dissemination of results among their peers. When asked how they wish to popularize their results, 50% of the students answer: “On the school website”, and 41% say: “On the school’s board”. The massive selection of the first two answers by the students is natural because at this age the defining factors are their environment and the approval of their peers. According to the American psychologist Judith Harris (Stamatov & Minchev, 2010), the socialization of children is done not by their parents, but by their peer groups. Moreover, 20% of students recommend when organizing school conferences to invite younger students. This also serves to build credibility and popularity. The competition for prestige and popularity is powerful incentive for the development of young people, for their expression and accumulation of knowledge (MarashevaDelinova, 2013). The researches conducted among students from economic specialties, confirm the conclusion that for the majority of the students developing projects it is of practical importance that their work is presented to an audience of their peers. When asked “How would you like to popularize the results of your projects?” more than 66% indicate a response “Using a poster in front of the group/course/Institute”. Over 50% chose the answer “On the web site of the Institute”. This choice was probably made as it is supposed that the web site of the Institute is most often visited by students and/or future students (i.e. peers).

To achieve a greater objectivity of the project evaluation for the development of practical knowledge it is necessary to set up evaluation criteria and that the students (learners) get acquainted with them. Such criteria are for example, designed to evaluate projects in mathematics using IT (Marasheva-Delinova, 2009). Part of the criteria for evaluation of mathematical projects is the basis of the developed evaluation criteria for projects, forming practical knowledge (Delinov & Marasheva-Delinova, 2014). These are unified, coherent and to a greater extend fixed (unchangeable) through the years of students education. They are developed by taking into consideration the comments, opinions and recommendations of the learners. Project evaluation is conducted with the help of evaluation cards, based on the criteria. They are used by the jury of the conference and by the participants and/or guests entitled to the right of voting. This mechanism for evaluation and self-evaluation of projects is described in (MarashevaDelinova, 2012). Its effectiveness has been demonstrated by analyzing more than 650 completed evaluation cards and given over 1,500 assessments on developed projects (Marasheva-Delinova, 2012).

From the above it is clear that the timely, accurate and targeted evaluation is one of the main levers for successful project development, in particular with topics from real economy, forming practical knowledge. Among the destinations in which one may be looking for effectiveness of evaluation are:

– Recruitment and creation of a suitable audience for the evaluation of the projects.

– Development and implementation of appropriate instruments enabling objective evaluation of the projects.

– Search and implementation of appropriate tools for timely evaluation of the projects both during the development process, and of the final version.

Cloud technologies and the possibilities for their application in the process of project evaluation: We think that one good tool to make the process of project evaluation more effective, both throughout the whole development cycle, and in the final phase (the presentation of the finished project) is “Cloud Computing” due to the possibilities it provides for sharing of large amount of data, for mutual work, for creation and processing of forms. These features are platform and geographically independent.

It is believed that the initial idea of “Cloud Computing” dates back to the 60s of the 20th century, when John McCarthy3,4 states the theory that “If computers of the kind I have advocated become the computers of the future, then computing may someday be organized as a public utility just as the telephone system is a public utility...”5, “… The computer utility could become the basis of a new and important industry.” (McCarthy, 1961). Several decades later, in 1997 Ramnath Chellappa uses the term “Cloud Computing”6. Serious contribution to the rapid development and application of technologies that are identified with this term is given by the competition between tech giants and industry leaders: Google, Amazon, Microsoft, Oracle, IBM, HP, Dell, Fujitsu and others. According to Gartner “Cloud Computing” is scalable and elastic IT - related resources that are provided as a service, using Internet technologies7. Cloud service is a specialized technology that provides customers tools (processing power, memory, disk space, network resources, specialized controllers, software, etc.) by a group of interconnected servers that for the user look like one8,9 . The term “Cloud” is taken from telecommunication companies10. In 2009 Maria Spinola attempted to systematize and clarify the terms and content of “Cloud Computing”11,12 and the related services, referring to the five defining characteristics of “Cloud Computing” given by the USA National Institute of Standards and Technology (NIST)13.

The five characteristics that define “Cloud Computing” are:

– On-demand self-service.

– Ubiquitous network access.

– Location independent resource pooling.

– Rapid elasticity.

– Pay per use.

Cloud technologies offer basically three types of services:

– SaaS – Software as a Service – users rent certain software application installed and provided in the “Cloud”.

– IaaS – Infrastructure as a Service – users rent “virtual hardware”: computing power, memory, network bandwidth, storage space for information flows, etc.

– PaaS – Platform as a Service - users rent both infrastructure and software provided in the “Cloud”.

Types of Clouds:

– Private Cloud: The entire infrastructure of a Cloud is owned or rented by one company and is managed by it.

– Community Cloud: The infrastructure is shared by several companies and serves to maintain a specific user community.

– Public Cloud: The infrastructure is owned by the company selling Cloud services. This company provides them to wide range of customers.

– Hybrid Cloud: The infrastructure is a combination of two or more Clouds (private, community, public).

There are a lot of criticisms and unresolved issues, regarding “Cloud Computing”. These mainly affect the security of the information, its possession and dependence, as well as its location in some types of “Clouds”. When it comes to corporate, confidential, and “sensitive” data such comments and questions are of great importance. For the solution of this problem are focused the efforts of the largest technology companies, as well as a number of governmental, international, regional, etc. organizations. When considering the usage of “Cloud Computing” in the learning process (including project development) (Grozdev et al., 2013b) we must have in mind that some of the criticisms and remarks are not significant. The learning process does not cover “sensitive” data and with the correct selection of a provider of public “Cloud services” can be overcome some of the other threats. Students, however, should be aware of all the advantages, disadvantages and risks.

The advantages of “Cloud Computing”, which make them particularly attractive and are dynamic driving force for their development and application, are several. Some of the features and opportunities that “Cloud Computing” provides are quite useful for the learning process and could significantly improve the quality and effectiveness, including that part of the evaluation of projects and the formation of an individual learning path:

– Easy, fast, platform independent access (via WEB and/or via “local client”) to the information in any Internet-compatible device (PC, Tablet or Smartphone) with direct access to the “Cloud resources” (Grozdev et al., 2012a).

– Publishing, sharing and processing (including WEB based on “office” documents) of information. Possibilities for organizing co-working on the materials with almost instant notification updates. The participants in the virtual groups work in the same way, as if they are in a local area network and even as they are in a the same room, although located in different geographical locations (including cities and countries).

Popular “Cloud resources” are: iCloud, OneDrive (old name - SkyDrive), Google Drive, Dropbox, Amazon Cloud Drive, Open Drive, Mega, Box, etc.

As for the evaluation in the development process, we have already noted that the application of “Cloud Structures” for verification of material by the teacher (and/or mentor) significantly optimizes the performance and thus represents a kind and timely assessment of the activities at the precise moment at which the project is located. For the evaluation of the final drafts by a wider audience (at conferences and/or conference connections enabled by digital technologies) we chose the less popular functionality of Google Drive for form processing.

This choice was made despite the large range of specialized capabilities (Survey Monkey, Poll Everywhere, etc.). One of the main advantages of the “Google forms” is the fact that this technology, although poor in features, is integrated with other widely used and well-known and popular Google resources. “Cloud structures” are used more frequently by trainees and trainers in the process of project development and other educational and extra-curricular activities. This makes Google Drive (along with Dropbox, OneDrive etc.) somewhat familiar or easier to explore and use. Another advantage is platform independence. It is especially important in the process of completion and submission of the evaluation maps. It allows the usage of any technical device with any operating system and any connection to the Internet. These are personal and mobile computers (running under Windows, Mac OS, Linux, etc.), Tablets (running under iOS, Android, Windows, etc.), and Smartphones (running under iOS, Android, Windows, etc.). The Internet connection may go via local area network, wireless access point or mobile network. Useful feature is the option to arrange each project evaluation in a separate table. This opens the way for the formation and organization of a data set with grades for all projects evaluated with “Google Drive forms”. Last but not least is the fact that the resources that are provided free by “Google Drive” are sufficient for the purposes of the paper work, including the evaluation of projects.

Stages of the evaluation process, using “Cloud” and others online technologies:

1. Preparation of the form

It is prepared based on an evaluation card. Each of the criteria is formed as a question and the possible answers are his performance indexes. For the sake of simplicity it is possible to form several separate pages with criteria sets. А copy (model) of the form is prepared for each project by changing only the names (of the project and form) - Fig. 2.

2. Referral of the Form

The model with the evaluation card of the project is directed at the right moment (classroom, school, etc. conferences, seminars, workshops, e-conference connection, etc.) to the people with voting rights. An individual group (audience) of evaluators (jury, classmates, colleagues, teachers, etc.) can be set up for each of the projects. A period of time can be defined for the project evaluation.

3. Evaluation

The evaluators give their assessments in the time given. For each of the criteria (in the given form) they point their choice – which index suits best which project. At the moment they have terminated answering all criteria (this is an option for each of the „questions“ on the form), the evaluator may submit his/her card (evaluation of the given project) if the time for filing has not expired - Fig. 3.

4. Processing

The set by the evaluation cards estimates are processed in a timely manner and the results are presented to the developer of the project and the audience (if there is any, and if the results should be declared before it). Using the selected technology makes possible the formation of the final results of the evaluation with cards within the nearly complete presentation of the project and completion of the appointed time for evaluation. Possible are variants of summarizing and displaying the final score, criteria, and indicators – Fig. 4. Technology provides good conditions for quantitative measures of the evaluation and options for export to a spreadsheets (MS Excel, OpenDocument) and compatible ones (csv, text file), pdf and HTML. The latter makes it possible for further processing, by means of which can be obtained high quality, averaging, weighted formal evaluations, rapid processing, publishing, etc. There are preconditions for the application of nonlinear methods and evaluation, as well as contributing to the management of the processes by changing some of the conditions.

Fig. 2. Preparation of the form

Fig. 3. Evaluation of a practical projects

An individual „officer“ („questor“) can be „assigned“ for the greater efficiency of each project. He directs the evaluation cards to the group; monitors the time window in which one can vote (evaluate); processes and provides the results to the authorized person for their announcement. „Cloud“ technology provides each participant the opportunity to review the evaluation results online after submitting the evaluation. This would be particularly useful in cases of different geographical locations involved.

The described in the stages activities are valid and enforceable for similar online technologies (almost with no differences or with very small adjustments).

The described technology for project evaluation using the “Google Form” has been piloted with students from 21st Secondary School “Hristo Botev”, Sofia. It was explained preliminary, and “tried” with test cards, then 4 real projects were evaluated by 9 students (who are not prominent in the fields of mathematics and IT). The experiment showed that students very quickly managed with their tasks. They accepted and got used with the activities they had to perform:

Fig. 4. One of possible variants of summarizing and displaying the final score

– Acceptance of the evaluation cards using mobile devices (tablets and phones).

– Filling in the cards by marking these indicators for each of the criteria that most closely match their judgment for each of the projects.

– Timely submission of the evaluation card in the “open” timeframe.

– Waiting patiently their classmates to give and their evaluation.

The Form for each project is prepared in advance and sent to the evaluators at the time of the conclusion of the presentation and its discussion. The evaluation procedure and processing of the results for each project takes about 5 minutes. This is the time required for changing of the presenters. Meanwhile, the “questor” processes the results. The final results for all projects are announced within 10 minutes after the last performance. It is planned that the projects for the next conferences at school will be evaluated based on the described technology.

Conclusion: The possibility to form a set of data for project evaluation would be very useful if organized as part of the database for the electronic library of projects (Grozdev et al., 2012b). In this way, the students (developers) would have access not only to the projects developed by their „predecessors“, but also to their evaluation. This is very helpful in order to “see how the land lies”, avoid errors, omit mistakes, apply positive experience, minimize the negative aspects, and pre-form conditions to maximize the individual performance evaluation. In the process of evaluating the young people (students, learners, etc.) are usually on the side of being evaluated. The evaluation of others is crucial for them because it places them on the other side – this of the people who evaluate. Gaining experience in evaluation leads to the commensurability between the grades of others and one’s own. The evaluated can control the results of their developments in advance and to reach their own true assessment. The more evaluations given, the more experience gained. This experience, in return is a prerequisite for the greater approximation of the final result against its preliminary set criteria. The use of „Cloud Computing“ shortens the time from the evaluation till the presentation of the overall results, and the resulting evaluation is timely.

This method of evaluation leads to the adoption of new technologies. The competences formed during this process may become a serious competitive advantage to those who gained them, as business has, and will have growing need for professionals with knowledge and skills in IT.

NOTES

1. http://banks.dir.bg/2013/08/08/news14671900.html
2. http://public.dhe.ibm.com/common/ssi/ecm/en/xie12346usen/XIE12346USEN.PDF
3. http://en.wikipedia.org/wiki/John_McCarthy_%28computer_scientist%29
4. http://www-formal.stanford.edu/jmc/
5. http://www.hp.com/hpinfo/newsroom/press_kits/2011/HPDiscover2011/DISCOV
ER_5_Myths_of_Cloud_Computing.pdf
6. http://www.bus.emory.edu/ram
7. http://www.gartner.com/it/initiatives/pdf/KeyInitiativeOverview_CloudComputing.

pdf
8. http://www.gartner.com/technology/research/cloud-computing/
9. http://tuj.asenevtsi.com/CNS/CNS21.htm
10. http://www.cloudtweaks.com/2011/02/a-history-of-cloud-computing/
11. http://blog.mariaspinola.com/2009/08/what-exactly-is-cloud-computing.html
12. http://cloudcomputing.sys-con.com/node/1087426
13. http://csrc.nist.gov/publications/nistpubs/800-145/SP800-145.pdf

REFERENCES

Knoll, M. (1997) The project method: its vocational education origin and international development, Journal of Industrial Teacher Education, 34(3), 59 – 80.

Nikolaeva, S. (2004) About the history of the project method in education, Pedagogics, 4.

Marasheva-Delinova, I. (2012) Developing Interest in Mathematics by Creating Projects Applying Information Technology, Abstract of dissertation, Plovdiv.

Bankov, K. (2012) Large-scale evaluative and diagnostic pedagogical research, Habilitation for academic position professor, Sofia.

Stoimenova, E. (2000) Measuring quality of tests, NBU, Sofia.

Lazarov, B. (2009) Innovative Assessment Of Students’ Achievements In Mathematics in TEMIT-Proceedings, Part II, Sofia, IMI.

Delinov, E., Marasheva, I. (2013) Roadmap for developing projects leading to the acquisition of working knowledge, Reports of Jubilee National Scientific Conference with international participation „Tradition, directions, challenges“, Smolyan: University publishers “University of Plovdiv”, Volume 2, Part 2, 157 – 162.

Marasheva, I. (2011) Motivating Students to Develop Projects in Mathematics, Reports of 40. Spring Conference of UMB: Mathematics and Mathematics Education, UMB, Sofia, 433 – 437.

Andreev, M. (1996) The learning process. Didactics., Publishing House “St. Kl. Ohridski”, Sofia, 245 – 246.

Radev, Pl. (2005) General school didactics, University Publishing House “Paisij Hilendarski”.

Stamm, M. (1998) Qualitätsevaluation und Bildungsmanagement im sekundären und tertiären Bildungsbereich, Aarau, 21.

Grozdev, S. (2007) For High Achievements in Mathematics. The Bulgarian Experience (Theory and Practice), Sofia: Association for the Development of Education.

Andreev, M. (1987) Didactics, Narodna Prosveta, Sofia, 243 – 244 .

Grozdev, S., Marasheva-Delinova, I., Delinov, E. (2013a) Use of cloud technologies in the verification of projects for formation of practical knowledge, Reports of 42. Spring Conference of UMB: Mathematics and Mathematics Education, UMB, Sofia, 366 – 372 .

Stamatov, R., Minchev, B. (2010) Human psychology, Sofia.

Marasheva-Delinova, I. (2013) Math projects using information technology, InfoDar, Sofia.

Marasheva-Delinova, I. (2009) A workshop at the Sigma mathematical club at Hristo Botev Secondary School, Reports of 38. Spring Conference of UMB: Mathematics and Mathematics Education, UMB, Sofia, 212 – 217.

Delinov, E., Marasheva-Delinova, I. (2014) Assessment criteria for project with practical application, Reports of 43. Spring Conference of UMB: Mathematics and Mathematics Education, UMB, Sofia, 248 – 254.

McCarthy, J. (1961) Speaking at the MIT Centennial in 1961. Architects of the Information Society, Thirty-Five Years of the Laboratory for Computer Science at MIT, Edited by Hal Abelson.

Grozdev, S., Marasheva-Delinova, I., Delinov, E. (2013b) Cloud technologies and capabilities for use in education, Mathematics and Informatics, issue. 3, 239 – 257.

Grozdev, S., Marasheva-Delinova, I., Delinov, E. (2012a) Math Club “Sigma” in light of the “Success” project, Mathematics and Informatics, issue. 5, 453 – 460.

Grozdev, S., Marasheva-Delinova, I., Delinov, E. (2012b) Electronic library of student projects in mathematics and information technology, Reports of 41. Spring Conference of UMB: Mathematics and Mathematics Education, UMB, Sofia, 325 – 329.

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