EDUCATIONAL MATTERS / НАУЧНО-МЕТОДИЧЕСКИ СТАТИИ
Интегративни връзки в компетентностния подход в обучението по математика и информационни технологиии
[Information Integrative Relationships in the Competent Approach in Mathematics Technology Training]
/ Коста Гъров, Севдалина Георгиева, Елена Ковачева, Ангел Ангелов / Kosta Garov, Sevdalina Georgieva, Elena Kovacheva, Angel Angelov – стр. 439
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Някои начини за решаване на алгебрични задачи
[Some Ways in Solving Algebraic Problems]
/ Диана Стефанова / Diana Stefanova – стр. 450
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Второй международный сетевой исследовательский проект учащихся в рамках MITE
[Second International Net Research Student Project in the Frames of MITE]
/ Мария Шабанова, Марина Белорукова, Роза Атамуратова, Веселин Ненков / Maria Shabanova, Marina Belorukova, Roza Atamuratova, Veselin Nenkov – стр. 457
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Дидактически сценарий върху една задача от XXI младежка балканска математическа олимпиада
[Didactic Scenario on a Problem from the 21st Junior Balkan Mathematical Olympiad]
/ Борислав Лазаров / Borislav Lazarov – стр. 466
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EDUCATIONAL TECHNOLOGIES / ОБРАЗОВАТЕЛНИ ТЕХНОЛОГИИ
Some Numerical Sequences Concerning Square Roots (Part One)
[Числови редици, свързани с квадратни корени (първа част)]
/ Rosen Nikolaev, Tanka Milkova, Yordan Petkov – стр. 474
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Доказателства и уточнения на експериментално получените твърдения чрез принципа за дуалност
[Proofs and Specifications of Experimentally Derived Assertions by the Duality Principle]
/ Сава Гроздев, Веселин Ненков / Sava Grozdev, Veselin Nenkov – стр. 481
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Erdös’ Distinct Distances Problem
[Проблемът на Ердьош за различните разстояния]
/ Houssam Zenati – стр. 501
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Optimizing the Positioning of Serving Units in Tourism Business
[Оптимизация на позиционирането на обслужващи единици в туристическия бизнес]
/ Radan Miryanov, Velina Yordanova – стр. 515
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CONTEST PROBLEMS / КОНКУРСНИ ЗАДАЧИ
Contest Problems of this Issue
[Contest Problems of This Issue] – стр. 521
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Решения на задачите от брой 6, 2016
[Solutions of the Contest Problems from Issue 6, 2016] – стр. 523
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READ IN THE LATEST ISSUES OF „AZBUKI“ JOURNALS / В НОВИТЕ БРОЕВЕ НА СПИСАНИЯТА НА ИЗДАТЕЛСТВО „АЗБУКИ“ ЧЕТЕТЕ – стр. 530
GUIDE FOR AUTHORS / УКАЗАНИЯ ЗА АВТОРИТЕ – стр. 532
ИНТЕГРАТИВНИ ВРЪЗКИ В КОМПЕТЕНТНОСТНИЯ ПОДХОД ВОБУЧЕНИЕТО ПО МАТЕМАТИКА И ИНФОРМАЦИОННИ ТЕХНОЛОГИИИ
Коста Гъров – ПУ „Паисий Хилендарски“ – Пловдив
Севдалина Георгиева, Елена Ковачева – Шуменски университет, ДИКПО – Варна
Ангел Ангелов – СУ „Сава Доброплодни“ – Шумен
Absract. С приемането на новия закон за предучилищно и училищно образование се поставиха основите на приложението на компетентностния подход в българското образование. Реализирането на този подход може да стане по много начини, един от които е прилагането на интегративни връзки в процеса на обучение на структурно и функционално ниво. Настоящата работа предлага компетентностен модел на обучение по математика и информатика с интегративни връзки.
Keywords: competent approach; integrative approach; model of training
INTEGRATIVERELATIONSHIPS IN THE COMPETENT APPROACH IN MATHEMATICS TECHNOLOGY TRAINING
Abstract. The adoption of the new law on preschool and school education laid the foundations for a competent approach in Bulgarian education. The implementation of this approach can be done in many ways, one of which is the implementation of integrative links in the process of training on a structural and functional level.
The present paper provides a competent model of mathematics and information technology training with integrative links.
Prof. Dr. Kosta Garov
University of Plovdiv “Paisii Hilendarski”
Plovdiv, Bulgaria
Ms. Sevdalina Georgiewa, Assist. Prof.,Dr. Elena Koleva, Assist. Prof.
Department for Information, Qualification and Continuing Education
University of Shumen
Varna, Bulgaria
Mr. Angel Angelov
Sava Dobroplodni Secondary School
Shumen, Bulgaria
НЯКОИ НАЧИНИ ЗА РЕШАВАНЕ НА АЛГЕБРИЧНИ ЗАДАЧИ
Absract. В статията се разглеждат възможностите на някои връзки между темите в училищния курс по математика при решаването на задачи.
Keywords: problem solving; algebra; links between topics
SOME WAYS IN SOLVING ALGEBRAIC PROBLEMS
Abstract. The paper considers the possibilities of some relations among topics of the mathematical school curriculum in problem solving.
Dr. Diana Stefanova
Asenovgrad, Bulgaria
ВТОРОЙ МЕЖДУНАРОДНЫЙ СЕТЕВОЙ ИССЛЕДОВАТЕЛЬСКИЙ ПРОЕКТ УЧАЩИХСЯ В РАМКАХ MITE
Мария Шабанова
Московский институт открытого образования – Москва (Россия)
Марина Белорукова
Муниципальное бюджетное общеобразовательное учреждение „Средняя школа № 8“ – Архангельск (Россия)
Роза Атамуратова
Regional Specialized Boarding School for Gifted
Children with In-Depth Study of Various Subjects - Aktau, Kazakhstan
Веселин Ненков
Technical College - Lovech
Abstract. Одной из задач Международного проекта MITE (Методики и информационные технологии в образовании) является создание условий для выявления и развития молодых талантов. Среди зарекомендовавших себя форм работы является Международный конкурс «Математика и проектирование». Конкурс пользуется большой популярностью среди учащихся Болгарии, Казахстана и России. В 2017 году второй раз в программу конкурса была включена номинация «Сетевые исследовательские проекты». Первое ме сто в этой номинации занял проект «Математическая мозаика», подготовленный объединенной командой учащихся из трех стран: Болгарий, Казахстана и России. Данная статья подводит итоги работы учащихся и представляет методику организации их совместной работы по подготовке проекта.
Keywords: secondary education; student; geometry; research; international network collaboration; dynamical geometry software; cloud service
SECOND INTERNATIONAL NET RESEARCH STUDENT PROJECT IN THE FRAMES OF MITE
Abstract. One of the goals of the International project MITE (Methods and Information Technologies in education) is to create conditions for identification and development of young talents. Among the active forms with proven efficiency is the International contest “Mathematics and Projecting”. The contest is very popular in Bulgaria, Kazakhstan and Russia. In 2017 the nomination “Network Research Projects” was included in the contest program for a second time. The project “Mathematical Mosaic” was awarded first place in this nomination. The project was elaborated by a combined international group of students from three countries: Bulgaria, Kazakhstan and Russia. The present paper summarizes details of the students’ collaboration and presents the organizational methodology in their common work during the project preparation.
Prof. Maria Shabanova, DSc.
Moscow Institute of Open Education
125167 Moscow, Russia
Ms. Marina Belorukova, teacher
Public Secondary School № 8
163002 Arkhangelsk, Russia
Ms. Roza Atamuratova, teacher
Regional Special Boarding School for Gifted Children with In-Deep Studying of Various Subjects
130000 Aktau, Kazakhstan
Dr. Veselin Nenkov, Assoc. Prof.
Technical College
5500 Lovech, Bulgaria
ДИДАКТИЧЕСКИ СЦЕНАРИЙ ВЪРХУ ЕДНА ЗАДАЧА ОТ XXI МЛАДЕЖКА БАЛКАНСКА МАТЕМАТИЧЕСКА ОЛИМПИАДА
Prof. Dr. Borislav Lazarov
Institute of Mathematics and Informatics – BAS
Absract. В статията е представена лекция в Сократов стил, изнесена от автора на математическия майсторски клас „Черноризец Храбър“, 2017 г. Оригиналната задача 1 от XXI младежка балканска математическа олимпиада е декомпозирана в серия спомагателни задачи за конкретната целева група. По време на експерименталното обучение са проследени два индикатора за прогрес. Направените предварителни изводи биха могли да бъдат полезни при подготовката на изявени ученици по математика, ориентирана към внедряване на изследователски подход.
Keywords: inquiry-based approach; problem decomposition; Socratic style teaching
DIDACTIC SCENARIO ON A PROBLEM FROM THE 21ST JUNIOR BALKAN MATHEMATICAL OLYMPIAD
Abstract. The paper presents a lecture in Socratic style given by the author during the Chernorizec Hrabar Math Master Class, 2017. The genuine Problem 1 from the competition paper of the 21stJunior Balkan Math Olympiad has been decomposed in series of auxiliary problems with respect to a particular target group. Two indicators for progress have been observed during the experiment, both related to the inquiry-based teaching. The conclusions drawn could be potentially helpful in training advanced students in mathematics via the inquiry-based method.
Prof. Dr. Borislav Lazarov
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
1113 Sofia, Bulgaria
SOME NUMERICAL SEQUENCES CONCERNING SQUARE ROOTS (PART ONE)
Abstract. The article is dedicated to one type of problems with an infinite number of nested square radicals proposed in mathematical competitions. A generalization is considered and the deduced theoretical relation is proved by the method of the complete mathematical induction.
Keywords: infinite sequence; nested radical; convergence; mathematical induction.
Dr. Rosen Nikolaev, Assoc. Prof., Dr. Tanka Milkova, Assoc. Prof., Dr. Jordan Petkov, Assist. Prof.
University of Economics – Varna
9002 Varna, Bulgaria
ДОКАЗАТЕЛСТВА И УТОЧНЕНИЯ НА ЕКСПЕРИМЕНТАЛНО ПОЛУЧЕНИТЕ ТВЪРДЕНИЯ ЧРЕЗ ПРИНЦИПА ЗА ДУАЛНОСТ
Сава Гроздев, Висше училище по застраховане и финанси – София
Веселин Ненков, Технически колеж – Ловеч
Absract. В статията са доказани свойствата, които характеризират геометричните конструкции, описани в (Grozdev & Nenkov, 2017). Предложените доказателства водят до уточнения на някои от свойствата, формулирани в (Grozdev & Nenkov, 2017).
Keywords: triangle; centroid; circumcurve; Euler curve; Euler line
PROOFS AND SPECIFICATIONS OF EXPERIMENTALLY DERIVED ASSERTIONS BY THE DUALITY PRINCIPLE
Abstract. Properties are proved in the paper, which characterize the geometric constructions described in (Grozdev & Nenkov, 2017). The proposed proofs lead to specifications of some of the properties formulated in (Grozdev & Nenkov, 2017).
Prof. Sava Grozdev, DSc
University of Finance, Business and Entrepreneurship
1618 Sofia, Bulgaria
Dr. Veselin Nenkov, Assoc. Prof.
Technical College
5500 Lovech, Bulgaria
ERDÖS’ DISTINCT DISTANCES PROBLEM
Abstract. In discrete geometry, the Erdös’ distinct distances problem states that between n distinct points in a plane there are at least distinct distances. The problem was posed by Paul Erdös in 1946. In 2010, Larry Guth and Net Hawk Katz claimed to have a solution. The solution was published in 2015 in the Annals of Mathematics. This article aims at popularizing this problem to young students in mathematics, therefore no big background in mathematics is needed to understand it. It is open to every reader and shall be improved with any remarks or questions.
Keywords: geometry; the Erdös’ distinct distances problem; young students
Mr. Houssam Zenati
Centrale Supelec (Ecole Centrale)
France
OPTIMIZING THE POSITIONING OF SERVING UNITS IN THE TOURISM BUSINESS
Abstract. In the present paper an idea for optimizing the positioning of serving units in tourism business is revealed using some applications of mathematics in economics. The elaboration has a methodological character. Methodologically the authors assume that some tourist objects (hotels, restaurants, etc.) are given and they try to determine the best possible position for a serving unit (store, office, etc.) using a set of optimization problems. Finally, an approbation of the results with a real example is considered.
Keywords: optimization; tourism; serving unit; positioning
Dr. Radan Miryanov, Assist. Prof., Dr. Velina Yordanova, Assist. Prof.
University of Economics – Varna
Varna, Bulgaria
