CONTENTS of issue 1/2019 / СЪДЪРЖАНИЕ на брой 1/2019
EDITORIAL / КЪМ ЧИТАТЕЛЯ – p. 7
Open the full text
EDUCATIONAL MATTERS / НАУЧНО-МЕТОДИЧЕСКИ СТАТИИ
Архивите говорят: Национални състезанията по информатика
[The Archives Speak: National Competitions in Informatics] /
Павел Азълов / Pavel Azalov – p. 11 Open the full text
Методическая система формирования информационной культуры педагогов – психологов в информационной образовательной среде
[A Methodical System for the Formation of Information Culture of Teachers – Psychologists in Information Educational Environment] /
Геннадий Киселев, Альбина Червова / Gennady Kiselev, Albina Chervova – p. 32 Open the full text
Increasing the Digital Competences of Students /
Lyubka Slavova, Kosta Garov – p. 43 Open the full text
EDUCATIONAL TECHNOLOGIES / ОБРАЗОВАТЕЛНИ ТЕХНОЛОГИИ
Система от задачи в обучението по математика
[System of Tasks in Mathematics Education] /
Петя Асенова, Марин Маринов / Petya Asenova, Marin Marinov – p. 53 Open the full text
Euler- Gergonne’ s Theorem and Its Applications /
Šefket Arslanagić – p. 72 Open the full text
Едно твърдение за конкурентност на педални окръжности на точка в равнината на четириъгълник
[A Statement for Concurrence of Pedal Circles of a Point in the Plane of a Quadrilateral] /
Хаим Хаимов / Haim Haimov – p. 77 Open the full text
Polynomials of Fourth Degree with Colinear Central Symmetric Roots
[Полиноми от четвърта степен с колинеарни централно симетрични корени] /
Sava Grozdev, Veselin Nenkov – p. 91 Open the full text
Problem 6. From IMO’2018
[Задача 6. От IMO’2018] /
Sava Grozdev, Veselin Nenkov – p. 97 Open the full text
CONTEST PROBLEMS / КОНКУРСНИ ЗАДАЧИ
Решения на задачите от брой 2, 2018
[Solutions of the Contest Problems from Issue 2, 2018] – p.108 Open the full text
Contest Problems of this Issue
[Contest Problems of this Issue] – p.113 Open the full text
READ IN THE LATEST ISSUES OF „AZBUKI“ JOURNALS /
В НОВИТЕ БРОЕВЕ НА СПИСАНИЯТА НА ИЗДАТЕЛСТВО „АЗ БУКИ“ ЧЕТЕТЕ – p. 115
АРХИВИТЕ ГОВОРЯТ: НАЦИОНАЛНИ СЪСТЕЗАНИЯТА ПО ИНФОРМАТИКА
Dr. Pavel Azalov
Пенсилвански държавен университет (САЩ)
Abstract.. В статията са представени основните събития, допринесли за инициирането и утвърждаването на първите състезания по информатика за ученици в България. Подробно е описана предисторията на Националната олимпиада по информатика (НОИ). Тя включва първите състезанията по програмиране у нас. Те са проведени в Шумен, Пловдив и Пазарджик съответно през 1982, 1983 и 1984 година и са инициирани от автора на статията. В тях учениците използват компютри от Единната серия и ФОРТРАН като основен език за програмиране. Подробно е описана Първата НОИ, проведена през 1985 г. По-накратко са представени някои от следващите олимпиади. Дадени са сведения за Зимните математически празници и ученическата секция на Пролетните конференции на Съюза на математиците в България. Представена е и кратка история от създаването на Пролетния турнир по информатика. Поради документалния характер на статията в нея са цитирани много статии, има извадки от текстове на публикации, както и снимки, с които точно се документират фактите в представените състезания по информатика.
Keywords: programming contests; оlympiad in informatics; national olympiad in informatics; NOI; national spring tournament in informatics
THE ARCHIVES SPEAK: NATIONAL COMPETITIONS IN INFORMATICS
Abstract. The article discusses the key events leading to the ideation, initiation, and establishment of the first programming contests for high school students in Bulgaria. The competitions preceding the First National Olympiad in Informatics (NOI) are presented in detail. More specifically, they include the programming contests, initiated by the author and held in Shoumen, Plovdiv and Pazardjik in 1982, 1983, and 1984 respectively. At the time, the main programming language used was FORTRAN for IBM/360 compatible computers. Next, the first NOI is discussed at length. Some of the subsequent NOIs are also outlined. The paper also includes facts about the Winter Mathematics Competitions and the high school student competitions held during the Spring Conferences of the Union of Bulgarian Mathematicians. A brief historical data about the Spring Tournament in Informatics is also presented. Due to its factual nature, the article contains an extensive list of references, including text excerpts, citations, pictures, and other relevant materials, supporting the historical facts related to the competitions in informatics.
Dr. Pavel Azalov
Professor Emeritus of Computer Science
Penn State, U.S.A.
МЕТОДИЧЕСКАЯ СИСТЕМА ФОРМИРОВАНИЯ ИНФОРМАЦИОННОЙ КУЛЬТУРЫ ПЕДАГОГОВ – ПСИХОЛОГОВ В ИНФОРМАЦИОННОЙ ОБРАЗОВАТЕЛЬНОЙ СРЕДЕ
Киселев, Геннадий Михайлович,
АНО ВО «Московский региональный социально-экономический институт» (Россия)
Червова, Альбина Александровна,
Шуйский филиал ФГБОУ ВО «Ивановский государственный университет» (Россия)
Аннотация. Применение информационных технологий в современном образовательном пространстве продолжает вызывать повышенный интерес как отечественной, так и зарубежной психолого-педагогической науки. Это в первую очередь связано со стремлением участников психолого-педагогического процесса совершенствовать свои технологии. Фрагментарность существующей информационной подготовки в вузе, направленной преимущественно на инструментально-технологический уровень информационной деятельности, ее репродуктивный характер не способствует формированию мировоззренческих, ценностно-смысловых аспектов информационной деятельности будущих педагогов-психологов. В статье рассматриваются особенности разработки и реализации методической системы формирования информационной культуры педагогов – психологов в информационной образовательной среде вуза. Авторы пытаются сформировать и повысить уровень информационной культуры интегрируя информационные и психолого-педагогические дисциплины при постоянном применении информационных и коммуникационных технологий на всех видах и формах психолого-педагогической деятельности.
Keywords: information culture; information technologies in professional activity; information educational environment; methodical system
A METHODICAL SYSTEM FOR THE FORMATION OF INFORMATION CULTURE OF TEACHERS – PSYCHOLOGISTS IN INFORMATION EDUCATIONAL ENVIRONMENT
Abstract. The use of information technologies in the modern educational environment continues to cause increased interest in both domestic and foreign psychological and pedagogical science. This is primarily due to the desire of participants in the psychological and pedagogical process to improve their technologies. The fragmentary nature of the existing information training in universities, aimed mainly at instrumental and technological level of information activity, its reproductive nature does not contribute to the formation of ideological, value-semantic aspects of information activities of future teachers-psychologists. The article discusses the features of the development and implementation of a methodical system for the formation of information culture of teachers – psychologists in the information educational environment in universities. The authors try to form and improve the level of information culture by integrating information, psychological and pedagogical disciplines with the constant use of information and communication technologies in all types and forms of psychological and pedagogical activity.
Prof. Dr. Gennady Kiselev
Moscow Regional Social-Economic Institute
Vidnoe, Russia
Prof. Dr. Albina Chervova
Shuisky Branch of Ivanovo State University
Shuya, Ivanovo region, Russia
INCREASING THE DIGITAL COMPETENCES OF STUDENTS
Lyubka Slavova, Kosta Garov
Plovdiv University “Paisii Hilendarski” (Bulgaria)
Abstract. The present paper examines the digital competences of secondary school students in Bulgaria in the light of the National External Evaluation of the 10th grade that has been held during the last years by the Ministry of Education and Science. There are ways to raise these competences and to improve the practical experience using the results of a specific experiment in a school in the city of Plovdiv. The main results are discussed in the paper.
Keywords: digital competence; national external evaluation; information literacy; information technology; education
Ms. Lyubka Slavova, PhD student
Prof. Dr. Kosta Garov
Faculty of Mathematics and Informatics
Plovdiv University “Paisii Hilendarski”
Plovdiv, Bulgaria
СИСТЕМА ОТ ЗАДАЧИ В ОБУЧЕНИЕТО ПО МАТЕМАТИКА
Петя Асенова, Марин Маринов
New Bulgarian University
Abstract.. Статията разглежда понятието „система от задачи“ като метод за обучение, което означава обучение чрез задачи. Тя покрива всички етапи на усвояване на новото знание – въвеждане, затвърждаване и приложение. Предложен е модел на система от задачи на различни равнища. Проектирането на системата е йерархично и включва: цел; очаквани резултати; подбор на задачите; организация, методи и средства при преподаването. Реализацията на системата е илюстрирана върху система от задачи първо равнище по темата „Сечение на многостен с равнина“ за свободноизбираема подготовка в XI клас. Методиката предполага използване на компютърни системи за визуализация и анимация.
Keywords: education in Mathematics; intersections; system of tasks; computer visualization and animation
SYSTEM OF TASKS IN MATHEMATICS EDUCATION
Abstract. This paper presents a view to the notion System of tasks as a peda-gogical approach, which means education trough tasks. It covers all steps in the teaching process – introduction of a new knowledge, training and application. The multilevel model of the system of tasks is proposed here. Its design is based on hierarchy: objectives and planned achievements; selection of the tasks; organiza-tion, teaching technics and tools. The implementation of the system of tasks is il-lustrated for the first level on the Solid geometry topic on Intersections for upper secondary school, elective form of education. The teaching technics proposed are strongly based on using computer software as a tool for visualization and animation.
Dr. Petya Asenova, Assoc. Prof.
Prof. Dr. Marin Marinov
Department of Computer Science
New Bulgarian University
Sofia, Bulgaria
EULER- GERGONNE’ S THEOREM AND ITS APPLICATIONS
Šefket Arslanagić
University of Sarajevo (Bosnia and Herzegovina)
Abstract. The present paper considers a proof of the Euler-Gergonne’s theorem and its application to two assertions.
Keywords: triangle; circumcentre; orthocentre; incentre; centroid; radius of the circumcircle; radius of the incircle of a triangle
Prof. Šefket Arslanagić, DSc.
Faculty of Mathematics and Natural Sciences
University of Sarajevo
Sarajevo, Bosnia and Herzegovina
ЕДНО ТВЪРДЕНИЕ ЗА КОНКУРЕНТНОСТ НА ПЕДАЛНИ ОКРЪЖНОСТИ НА ТОЧКА В РАВНИНАТА НА ЧЕТИРИЪГЪЛНИК
Хаим Хаимов
Absract. В тази публикация се доказва, че педалните окръжности на произволна точка в равнината на четириъгълник относно триъгълниците, определени от страните и диагоналите на последния, се пресичат в една точка. С помощта на това твърдение се дефинира едно изображение в равнината на произволен четириъгълник. Намират се образите на някои забележителни точки в четириъгълника. Описват се връзките на изображението с други трансформации в равнината на четириъгълник.
Keywords: quadrilateral; pedalcircles; transformations; remarkablepoints
A STATEMENT FOR CONCURRENCE OF PEDAL CIRCLES OF A POINT IN THE PLANE OF A QUADRILATERAL
Abstract. It is proved in the present paper that the pedal circles of an arbitrary point in the plane of a quadrilateral, determined by its sides and diagonals, are concurrent. With the help of this statement a transformation is defined in the plane of an arbitrary quadrilateral. The images of some notable points in the quadrilateral are found. The connection of this transformation with other transformations in the plane of the quadrilateral are described.
Mr. Haim Haimov, Resercher
Varna, Bulgaria
POLYNOMIALS OF FOURTH DEGREE WITH COLINEAR CENTRAL SYMMETRIC ROOTS
Sava Grozdev,
University of Finance, Business and Entrepreneurship – Sofia (Bulgaria)
Veselin Nenkov,
Nikola Vaptsarov Naval Academy – Varna (Bulgaria)
Abstract. A geometric relation is considered between a polynomial of fourth degree with symmetrically located roots on a line and the roots of its derivative. A special ellipse is used for the purpose, which is generated by the roots of the polynomial.
Keywords: polynomial of fourth degree; derivative; symmetric points; equilateral triangle; square; center; ellipse; circle; vertices
Prof. Sava Grozdev, DSc.
University of Finance, Business and Entrepreneurship
Sofia, Bulgaria
Dr. Veselin Nenkov, Assoc. Prof.
Nikola Vaptsarov Naval Academy
Varna, Bulgaria
Sava Grozdev,
University of Finance, Business and Entrepreneurship – Sofia (Bulgaria)
Veselin Nenkov,
Nikola Vaptsarov Naval Academy – Varna (Bulgaria)
Abstract. The International Mathematical Olympiad is one of the respectable events and one of the most long-lived international educational and scientific competitions. It is the largest, oldest and most prestigious scientific Olympiad for high school students. The 59th edition of the event took place in Cluj-Napoca, Romania, 3 – 14 July 2018. The present paper is dedicated to the sixth problem on the Olympiad paper. A detailed analysis of the problem is proposed in a methodological way, which will be useful for students and teachers in the preparatory process for future participations in mathematical competitions.
Keywords: Olympiad; problem solving
Prof. Sava Grozdev, DSc.
University of Finance, Business and Entrepreneurship
Sofia, Bulgaria
Dr. Veselin Nenkov, Assoc. Prof.
Nikola Vaptsarov Naval Academy
Varna, Bulgaria
