Математика и Информатика

2013/5, стр. 476 - 488

BOOSTING EFFICIENCY OF PROJECT-ORIENTED TEACHING AND LEARNING THROUGH CLASSROOM MANAGEMENT AND ONLINE TESTING

Ivan Shotlekov
E-mail: ivan@shotlekov.net
PhD in Methodology
FMI Plovdiv University “Paissiy Hilendarski”
Vanya Ivanova
E-mail: vantod@abv.bg
FMI Plovdiv University “Paissiy Hilendarski”
Kirina Boykova
E-mail: kirina.boykova@gmail.com
FMI Plovdiv University “Paissiy Hilendarski”

Резюме: A set of classroom management and testing policies was elaborated and, after two years of piloting, it was further developed and administered to 247 students at the Faculty of Mathematics and Informatics, Plovdiv University “Paisiy Hilendarski”. The main purpose of this effort was to enhance the efficiency of project-oriented teaching and learning. The findings confirmed the positive outcome of this approach and the potential to be successfully applied to traditional classroom settings.

Ключови думи: classroom management, project-oriented learning, The Common European framework of reference for languages: learning, teaching, assessment, testing

Theoretical background

Contemporary cognitive theory studies no longer regard learning as a passive process of knowledge accumulation, but rather as a process of dynamic construction of internal knowledge representation, individual interpretation and processing of current experience. (Tsvetanska, 2006, p. 167) For this reason, over the last decade there has been a dramatic change which has affected not only the teaching methods and techniques of in higher education, but also the work of teachers/tutors, as well as students’ expectations and requirements. The English language curriculum at the Faculty of Mathematics and Informatics (FMI) of Plovdiv University Paisiy Hilendarski has also undergone such smooth change. Instead of the traditional teaching of knowledge which requires memorizing and repeating, a modern educational institution should provide knowledge about the method - mastering learning strategies based on performance and individual expression. (Tsvetanska, 2006, p. 159)

According to experiential education proponent John Dewey (Dewey, 1941, p. 26), considered a reformer in teaching, education is perceived by the student’s experience and what s/he learns from their environment rather than by previously formally structured subjects. The overall experience of the learner forms the curriculum, and that is what has the greatest value in the process of learning. Therefore, a developing education essential prerequisite is learning by doing or the process of gaining knowledge through experience. It is Dewey who first spoke about active methods of learning that are associated with the so-called active learning. It stimulates learners do more than just receive information from a teacher or textbook and memorize and repeat it. (Gyurova et al., 2006, p. 176)

Stemming from these new theories is the need for a new approach towards education and classroom management, and reconsideration of traditional models. Thus, the methods of active and interactive learning appeared. Active learning is learning based on questions. It is a process of change - through different states, experiences, stages of searching, and self-discovery, rather than learning (memorizing) facts and important conclusions made by somebody else in another time and under different conditions. In the active learning paradigm, the basic idea is adopting theories and concepts through student’s involvement in problematic situations, case studies, simulation games, and work in small groups. Therefore, many techniques that stimulate the activity of the learner are engaged within its framework. (Tsvetanska, 2006, p. 162)

On the other hand, education in an interactive learning environment also has a number of indisputable advantages. Interactive classroom management requires that knowledge learning, formation of skills, attitudes building, provocation of independent thinking, and personal development happen simultaneously. Furthermore, the interaction realized in the learning process is not merely between teachers/tutors and trainees but between trainees themself, where they learn from each other’s previous knowledge and experience. From passive consumers of already existing ideas and truths, students become active partners of the teacher and create their own knowledge. What is more, teachers/tutors themself are participants in the process of group learning and development - they are open, flexible, sensitive to others, able to cope equally well with academic challenges and the pedagogical and life aspects of the educational environment and interaction. A peaceful, positive and stimulating learning environment is maintained, as well as effective feedback.

It is necessary to distinguish active and interactive teaching methods when we consider effective classroom management. Active methods place the learner in active learning position where s/he can acquire knowledge themselves. Interactive methods, in turn, require association with a particular group; they suggest an interaction with other learners and dialogical communication with these learners, which is extremely useful when learning a foreign language, e.g. English.

English teaching at FMI certainly has an established history. But the rapidly changing socio-economic conditions imposed a serious and thorough reconsideration of this activity. The English teacher’s most important task is to place students in a situation where they can reflect on their experience so that it becomes an effective, usable knowledge. The teacher/tutor should try to create a positive and supportive learning environment, motivate students to take an active role in the learning process, and provoke their interest not to memorize the textbook material but to study the subject themself and discover the knowledge and skills that will be useful to them.

Among methods offering highest levels of interactivity (case studies, project work, role plays, discussions, and working in small groups) teachers of English at FMI have chosen as most effective project-oriented teaching enhanced by trainer-developed tests. In comparison with traditional teaching tools such as teacher-centered lectures, etc., the use of interactive methods in much greater extent provokes students to communicate with each other as each of them is free to seek information and interaction with a chosen partner in order to succeed in the implementation of the learning tasks.

V. Gyurova and co-authors (2006, p. 43) outline two types of interactive classroom management systems - systems based on technology and people-oriented systems. Contemporary educational practice aims at integrating the capabilities of both types of interactive techniques to increase the participation of learners. Technology-based systems rely on the use of various technical means such as computer products and technology, electronic books, videos, etc. Their goal is to create an environment that supports learning. People-oriented learning systems are based on the feedback and direct communication between the participants in the learning process. The goal here is to establish active contacts between students who share information based on their past experiences. English language teaching at FMI has established an effective symbiosis between the two systems. Students’ excellent command of Information Technology allows the use of technology, while the teacher builds a creative environment for direct communication and discussion of the course content.

Placing students in small groups is another successful classroom management technique in English language teaching at FMI. This is the most adequate learning environment as it offers more opportunities for decentralized cooperation, more local autonomy and diversity. Since 2001, when the Common European Framework of Reference for Languages (CEFR) came out, there have been some regulations which help teachers adequately determine each student’s level of proficiency in English. Thus, a curriculum is developed according to the group’s needs and the use of the appropriate interactive method complies with the students’ skills. The group work, combined with the right amount and type of individual work and the assessment in English classes at FMI are all aligned with the Common European Framework of Reference for Languages (CEFR).

FMI language classroom policy

The process of teaching English at the Faculty of Mathematics and Informatics is founded on the redistribution of students from administrative groups into language groups. In the administrative groups all the students from a given speciality, or programme, are assigned, depending on their faculty numbers, to groups 1, 2, 3, etc. In contrast, language groups are formed on the basis of the students’ knowledge and skills in English and thus the groups respectively become A, B, C, etc. as shown in Figure 1.

Figure 1. Language placement procedure at FMI

This redistribution is made by means of placement tests administered online. The multiple choice QPT (Quick Placement Test, 2001) is most handy – it takes only 30 minutes and the scores are mapped against the Common European Framework of Reference for Languages (CEFR). There are a host of other placement tests, some available for free. In accordance with the CEFR, learners can be divided into three main categories: A – Basic User, B – Independent User, and C – Proficient User. These three divisions can be further subdivided into six levels as follows:

– A1 Breakthrough or beginner

– A2 Waystage or elementary

– B1 Threshold or intermediate

– B2 Vantage or upper intermediate

– C1 Effective Operational Proficiency or advanced – C2 Mastery or proficiency.

After the students at FMI are redistributed into language groups of the same level, they are given a language needs analysis questionnaire and then are informed about the teaching materials they will be using during the two trimesters of studies and the basic rules for forming the final grades in English. The educational policy at FMI is for continuous assessment in English in which students are examined continuously during their language education instead of sitting for a test during their exam session.

The final grades of this discipline are formed on the six-point scale at the end of the course based on the average of the two grades for the two trimesters of English studies, each of which is formed as follows:

– continuous assessment (tests or other assignments during the course which account for 30% of the final grade)

– individual work (project assignments during the course - 40% of the final grade), and

– exams (during the last week of each of the two trimesters a test is given covering all the material studied until then and it represents 30% of the final grade).

Then the students are informed of their so formed final grades, cf. Figure 2, which are entered in the examination records and in the students’ books.

Final GradeFinal Grade

Figure 2. Grading Policy at FMI

This diagram is illustrative – grading policies may vary between teachers from other departments or universities who wish to adopt it for their own use. The full text is available on http://english.shotlekov.net/ to ensure transparency and integrity in teacher-student relations. Trainees can refer to it as necessary and it reassures them the subjective components in assessment and evaluation have been reduced to a minimum because of quantified criteria for the grading components.

All the students who have not received a passing grade at the end of the course are given a second chance to retake the final exam which tests all of the covered material during their English studies. The grades obtained from the students’ continuous assessment and individual work remain as they were at the end of the course and cannot be changed. The updated final grade is then recalculated in accordance with the basic grading scheme: continuous assessment 30%, individual work 40%, and exam results 30%.

Students who studied at another higher education school before being admitted to Plovdiv University can have their grades in English recognized. This grade recognition is based on the academic transcript of the university where the student was taught before, with a minimal workload as follows:

– For full time students majoring in Mathematics, Applied Mathematics, Business Mathematics and Mathematics and Informatics, 100 academic hours are required.

– For full time students majoring in Informatics the required number of academic hours is 100, and respectively 50 hours for part time students of the same speciality.

– For full time students majoring in Business Information Technologies are required 80 academic hours and respectively 50 for part time students.

In case the workload was smaller or in the absence of a grade in English, students are awarded the following final grades:

Satisfactory 3, or they sit for an examination and obtain a grade on the basis of the language level demonstrated:

– A1 A2 - Satisfactory (3)

– B1 - Good (4)

– B2 – Very Good (5)

– C1 C2 - Excellent (6).

Additionally, students who have been transferred from other universities, specialities, etc. are allowed to attend classes and join the standard assessment and evaluation procedure.

Those students who are holders of internationally recognized certificates for language skills will be assessed after developing a project in English for specific purposes assigned by their teacher, which accounts for 40% of their final grade. The student’s certified language level is recognized as a continuous assessment grade (30%) and an exam grade (30%) as follows:

– A1, A2 and B1 corresponds to Satisfactory (3)

– B2 - Good (4)

– C1 - Very Good (5)

– C2 - Excellent (6).

The students need to show the original of their certificate and leave a photo copy for the teachers’ archive.

During the course of studies those groups of students that are at a language level from A1 to B 1 study English for General Purposes with elements of English for Specific Purposes. Suitable textbooks that are currently used are New Headway Elementary and Pre-Intermediate levels, which comprise a student book and a workbook and can be supplemented by adapted photocopiable or teacher-designed materials. The individual work of students includes doing the exercises in the workbook as well as developing project assignments such as preparing and delivering PowerPoint or oral presentations, writing essays, collecting information about assigned topics and then applying it to complete individual tasks, etc. The continuous assessment covers two tests per trimester, the dates of which are announced on the dedicated website. They are usually carried out online in class every third and sixth week of the ten-week long trimester. If a student fails to turn up for a test or presentation of their individual work, they obtain a poor grade for that particular task.

The tests given to the students during and at the end of the trimesters are developed by their teachers to measure how much of the material taught within a certain period of time has been learnt and they use the obtained feedback to make adjustments, if necessary, to their lesson plans. The tests used at the FMI can be classified as achievement, limited time, group, computer tests which are current (or final), objective, norm-referenced and non-standardized. The types of tasks used most often are multiple choice questions, True or False, matching and ordering of text, the grades of which are calculated automatically, as well as short answer questions and translations that need to be assessed additionally by the teacher. The different test methods have their own advantages and disadvantages. Multiple choice questions with three or more distractors, for example, take longer time to create but a large number of questions can be answered within a comparatively short time and they are easy to score. However, teachers try to use more than one method for testing any language ability. By varying the test methods the predictability of the test format is reduced and possibly the learning of test-taking strategies for particular test formats (Alderson, 1995, p. 46).

When constructing a test, the teacher goes through several stages to verify it comprises all the studied material and to assure its good quality.

First of all, the test author draws an overall plan of the test. At this stage they have to consider in detail what exactly they need to measure, what its manifestations are, and which circumstantial factors could influence the results of the measurement. At the second stage the teacher has to determine what content is to be tested. During the third stage the test author makes a test specification which represents a detailed plan of the test including its purpose, the sort of learners who will be taking the test, the number of sections and types of questions in the test, which language skills will be tested, etc., as well as the test methods and assessment criteria to be used. The next stage involves item development i.e. this is the time when an initial set of test items is constructed. After that the test author deals with the test design and assembly making sure that the content actually tested corresponds to the content of the specification. The sixth stage concerns the production and printing or publication of the test. The remaining stages of the test creation process control the test administration, scoring the test responses, establishing the passing scores, reporting the test results to the students, item banking – the process of securely storing test items for potential future use, and preparing a test technical report (Ivanova, 2011, pp. 278-284).

As already stated, tests constitute an important part of the grading at FMI but they are not considered in isolation from the overall student performance during the process of education in English. If a student has failed a test for a certain reason, they have the opportunity to prove their knowledge and skills in other tests as well as in developing and presenting their individual work.

The experiment - classroom implications

This approach has been in place at FMI for quite a long time in an effort to enhance students’ performance in the settings of using English as a medium in web-based interdisciplinary project-oriented teaching of Information Technology to students of Computer Science. One of the issues in such an approach, as highlighted by Shotlekov (2012, pp. 100-101), is capable of compromising the teaching and learning process: absenteeism. In settings where attendance is not mandatory and trainers have no administrative leverages to encourage it, this issue is even more topical because it leads to demotivation of all stakeholders: absent students, attending students, and teachers alike. Students’ failure to attend classes, either physically or virtually, renders impossible or inefficient brainstorming, discussions, multimedia project presentations, and other class-level or team-level activities. Hence, rates of failed deliveries are high. This in turn leads to plummeting motivation in the rest, i.e. performing students. They face two possibilities: either bear the missing peers’ burden, or put up with a lower team grade if each team is assigned a team grade which then becomes each member’s grade. Therefore, a more detailed assessment policy is needed both on a project evaluation level and on a course assessment level in order to take into account each student’s contribution and to encourage trainees to be involved in the learning process. “When some students have missed progress tests, feedback questionnaires, etc. they wish to catch up in class, but during this time they cannot take part in the work of their teams which leads to understaffing in these teams and plummets motivation because it hinders advancement… On the other hand, late students take the test later than their peers and are thus vulnerable to the washback effect, thus scoring less than they would have under normal conditions.” (Shotlekov, 2012, p. 102). There are yet other students who show up only during tests, if the in-house rules and regulations allow this, which strongly undermines teachers’ efforts to develop team work skills. The same author has found that the approach described in this article more often than not helps raise students’ awareness of the need to be active participants in the learning process as well as assure more fair assessment. Different weights have been used through the years but the ones applied the last two years have been found most consensual among students and teachers alike. More details on various weight distribution patterns are presented in Appendix 1.

Table 1. Grade distribution (%) at weights: Continuous assessment – 0.3, Self-Study – 0.4, Final test – 0.3

Teacher:Fail 2Satisfactory 3Good 4Very good 5Excellent 6Teacher 1, N=6529.227.715.421.56.2Teacher 2, N=444.520.5252525Teacher 3, N=1389.425.414.520.330.4Theoretical distribution3.222.44427.23.2

Continuous assessment in the FMI language learning policy covers student performance in terms of attendance of contact classes, involvement in the learning process, and formative assessment (e.g. quizzes). By Self-Study we designate project work and homework, while Test stands for a Final test administered at the end of the trimester or during the re-sits. The theoretical grades for all components are obtained after a conversion of the total scores for the three components based on quantitative criteria thereof. Since the actual grades are rarely natural numbers, but rather decimals rounded to the second decimal place, this may lead to some deviations between our simplified calculations in Appendix 1 and the actual real-life scenarios. Nevertheless, using adjusted values, i.e. rounded to whole numbers, leads to insignificant differences that can be ignored for our purposes. Certificate holders have been excluded from the data. Figure 3 provides a visual representation of the numbers in Table 1.

Figure 3. Percentage distribution of the grades (Continuous assessment – 0.3, Self-Study – 0.4, Test – 0.3)

For the Fails, the graph reveals that Teachers 2 and 3 were very close to the theoretical distribution, while Teacher 1 deviated, probably due to the fact that first-year university students are not accustomed to a new university environment where rules are applied without major concessions. Besides, these were more proficient students who expected that their knowledge of English was enough for a good grade and did not participate in the learning process ignoring the weight on attendance and projects on the Final grade – 70% altogether. For the Satisfactory grades, as well as for the Very goods, all three teachers scored close to the theoretical share. For the Goods, none of the teachers went close to the theoretical distribution, as Teacher 2 was less far away. As for the excellent grades, only Teacher 1 complied while the other two trainers differed largely. This can be accounted by the lower language levels of the students which presupposed higher awareness of the need for more contact time with the teacher and more intensive classroom participation. We believe the discrepancy between some students’ expectations and the final grades will beneficial to them in their real life careers where performance and compliance matters enormously. No one can expect a lucrative paycheck at the end of the month just because of the assumption that s/he is a great software engineer unless this has been demonstrated in the quality of work as required by the employer.

Conclusion

As Staribratov & Angelova (2011, р 331) have put it, “New technologies pose new challenges to learners’ training: more flexible and time-efficient learning process (transition from a discrete to continuous model of study); access to information and diversity of knowledge; wider range of knowledge sources”. In such settings, some of them have experienced difficulties with their motivation, discipline and direction on the learning path. The approach described in this article has been field-tested with courses in English, but it can be directly deployed for any kind of training regardless of the content matter: be it Mathematics, Computer Science, Business, or another domain. It can also be applied to some of the course modules, e.g. set theory, algebra, mathematical logic or graph theory. Each of these according to Garov & Radev (2012, p. 345) is indispensable for the correct formulation of the concepts and ideas of different application tasks, their formalization and computerization, as well as the mastering and development of modern Information Technology.” We have found that our classroom management and testing policies, while beneficial to the traditional classroom practices, boost the efficiency of project-oriented teaching and learning.

Acknowledgements

This work was partially supported by the project „Enhancing the quality of education in Informatics and ICT at FMI, Plovdiv University “Paissiy Hilendarski” through elaborating and deploying a sustainable model for updating the curricula and syllabi in compliance with the EU’s growth strategy - Europe 2020 and the demands of the labor market”, Contract No D01-3609/19.02.2013.

Appendix 1 Theoretical percentage distribution of grades according to the weight of the components making up the final grade

Components, weightFinal Grades, %AttendanceSelf-StudyTestFail 2Satisfactory 3Good 4Very good 5Excellent 60.40.50.14.82439.225.66.40.50.40.14.82439.225.66.40.30.60.15.625.633.628.86.40.60.30.15.625.633.628.86.40.70.20.17.226.429.6288.80.20.70.17.226.429.6288.80.10.80.11225.623.22415.20.80.10.11225.623.22415.20.30.50.23.225.639.227.24.80.50.30.23.225.639.227.24.80.40.40.2424442440.20.60.24.828.832.828.84.80.60.20.24.828.832.828.84.80.10.70.27.226.429.6288.80.70.10.27.226.429.6288.80.40.30.33.222.44427.23.20.30.40.33.222.44427.23.20.50.20.33.225.639.227.24.80.20.50.33.225.639.227.24.80.60.10.35.625.633.628.86.40.10.60.35.625.633.628.86.40.30.30.43.222.44427.23.2
0.40.20.4424442440.20.40.4424442440.50.10.44.82439.225.66.40.10.50.44.82439.225.66.40.30.20.53.225.639.227.24.80.20.30.53.225.639.227.24.80.40.10.54.82439.225.66.40.10.40.54.82439.225.66.40.20.20.64.828.832.828.84.80.10.30.65.625.633.628.86.40.30.10.65.625.633.628.86.40.10.20.77.226.429.6288.80.20.10.77.226.429.6288.80.10.10.81225.623.22415.2

REFERENCES

Alderson, J. C., C. Clapham, D. Wall. (1995) Language test construction and evaluation. Cambridge University Press.

Council of Europe (2001) The Common European framework of reference for languages: Learning, teaching, assessment, Cambridge: Cambridge University Press.

Dewey, J. (1941) Experience and Education, (Bulgarian translation) , “Stoyan Georgiev” - Sofia

Garov K.A., Radev V.I. (2012) Methodological tools for solving problems in Discrete Mathematics in Primary School. Mathematics And Education In Mathematics, 2012. Proceedings of the Forty-First Spring Conference of the Union of Bulgarian Mathematicians. Borovets, April 9–12

Gyurova, V., Demerdhzieva, G., Bozhilova V., Varbanova S. (2006) The adventure called learning process (in Bulgarian) , „Agencia Evropres“ Sofia

Staribratov I., E. Angelova. (2011) Methodological approaches to training using eLearning resources, Proceedings of The IVth Nat. Conference Education in the Information Age 26-27 May 2011, Plovdiv, pp. 329-336. (in Bulgarian)

Ivanova, V. (2011) Construction and evaluation of achievement tests in English. National Conference “Education in Information Society”, pp. 276-285.

Quick Placement Test (2001) Oxford University Press, Oxford, England 250 user CDROM Pack 978-0-19-453584-7 Paper and Pen Version Pack 978-0-19-453579-3

Shotlekov I. (2012) Web-based interdisciplinary project-oriented teaching of Information Technology to students of Informatics. PhD thesis paper. Plovdiv (in Bulgarian)

Tsvetanska, S. (2006) Challenges in pedagogical communication. Prosveta - Sofia

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 Canatalay, Ashima, Kukkar, Sadiq Hussain, Arun Baruah, Jiten Hazarika, Silvia Gaftandzhieva, Esraa Mahareek, Abeer 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 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 MODIFIED DICE

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
EDITORIAL / КЪМ ЧИТАТЕЛЯ

Сава Гроздев

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
SEVERAL PROOFS OF AN ALGEBRAIC INEQUALITY

Šefket Arslanagić, Шефкет Арсланагич

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