Editorial Board Members
EDUCATIONAL MATTERS
About the Data and the Road Towards the Big Data
Absract. Over the past two decades, data turned into big data. The term big data encompasses the exponential growth of all data but most notably, the semi-structured and unstructured types. The speed with which data is generated and amassed necessitates the introduction of new technologies for their collection, transfer, storage and processing.
In a chronological fashion, this article begins with the foundational work of database development and progresses through the emergence of big data. Concurrently, the scientists, whose theoretical and practical work underpinned the development of data processing systems, are also discussed. The article provides examples to show the pervasiveness of big data in our daily lives. The key technologies utilized to process big data are described, including the Hadoop ecosystem and the NoSQL type of databases. A strong emphasis is given to the role of data analytics, used to transform the raw data into information, decision-making models and knowledge.
Настоящата статия представя хронологията на основните постижения в областта на базите от данни от най-първите им години до възникването на големите данни. Успоредно с това се дава и кратка справка за авторите, чиито научни и практически резултати изградиха теорията и практиката на системите за обработване на данните – малки и големи. Представени са и типични примери на „срещи“ с големите данни от ежедневието. Накратко са описани основните технологии, използвани при големите данни, включително екосистемата Hadооp и NoSQL базите от данни. Специално се отбелязва и ролята на аналитиката на данните като подход за трансформиране на данните във факти, модели и знания.
Keywords: big data; history of databases; NoSQL databases; tructureddata; unstructured data; semistructured data; ecosystem Hadoop
Dr. Pavel Azalov
Professor Emeritus of Computer Science
Penn State, Hazleton, U.S.A.
Contemporary Means and Teaching Methods, Using Cloud Technologies
Absract. The present work is dedicated to contemporary means and teaching methods, using cloud technologies in Bulgarian secondary education. A review is elaborated on the development and essence of cloud technologies. Digital instruments are listed which are applied to new teaching methods. Some new and adaptive methods are indicated and examples are shared for their application in a concrete Bulgarian school. It is shown that the use of contemporary means and teaching methods applying cloud technologies facilitates teacher’s work and raises student’s interest towards the learning process including active attitude to it.
Keywords: cloud technologies; innovative technologies; secondary education; teaching methods; learning process
Ms. Lyubka Slavova, Prof. Dr. Kosta Garov
Faculty of Mathematics and Informatics
„Paisii Hilendarski“ University of Plovdiv
Integrative Classes on the Subject “Mathematical Technology” Under Distant Learning Teaching
Absract. The aim of the present article is to show that - regardless limitations, distant learning enables also opportunities to Bulgarian teachers. Such proof is the “Young Farmer” classes realized successfully under distant learning teaching. The aim of the classes is to revise already known measuring units of area in 5th grade by integrative teaching – m2, dm2, cm2, mm2, introducing new ones – are, decare, hectare, and also to show the application of mathematics to farmer’s work.
Keywords: mathematics; technology and entrepreneurship; measuring units; distant learning
Mr. Kostadin Petleskov
Department of Mathematics
Faculty of Sciense
SWU "Neofit Rilski"
Designing a Professional Training Program for Working with Gifted Children Using Software Office 365 /
Abstract. This article describes the Master Program of professional training of specialists for working with gifted children using software Office 365. We justify the relevance and identify key ideas and content of the program. It includes activity-based learning based on modern educational technologies and digital resources, work with an empirical database with the results of leading educational centers which are focused on working with gifted children, with the identification of relevant problems and effective practices; attracting leading experts in the field of work with gifted children to conduct research etc…. The program is implemented in a face-to-face network format with the use of modern distance learning and Office 365 software, which allows us to organize collaborative work with documents in real-time regime using Word Web App, PowerPoint Web App or Excel Web App.
Keywords: professional training; gifted children; Office 365
Oleg Zverev, Tatiana Sergeeva
Moscow City University (Russia)
EDUCATIONAL TECHNOLOGIES
Mathematical Modelling in Learning Outcomes Assessment (Binary Model for the Assessment of Student’s Competences Formation)
Abstract. In modern educational institutions there is a necessity for effective assessment methods of competence formation. Both achievement and summative assessment of students’ progress needs to be produced with due expertise. One of the effective ways of improving students’ qualification assessment is through the development and use of a competence formation assessment model. The article presents mathematical models of the subject area as well as competence formation assessment models. These models are determined by subsets of operators, i.e. evaluation operations themselves and necessary materials and equipment. In general, the obtained models describe the structure of the competence formation assessment system corresponding to the disciplines of the particular study field curriculum. The models take into account the specifics of the subject area. They are expandable and customizable.
Keywords: mathematical modeling; theory of polychromatic sets; competence formation assessment; indicator
L. E. Khaimina, E. A. Demenkova, M. E. Demenkov,
E. S. Khaimin, L. I. Zelenina, I. M. Zashikhina
Northern (Arctic) Federal University named after M. V. Lomonosov (Russia)
Problems 2 and 5 on the IMO’2019 Paper
Abstract. The aim of the present note is to discuss Problem 2 and Problem 5 on the IMO’2019 paper. The 60th edition of the International Mathematical Olympiad (IMO) took place in the city of Bath, United Kingdom, 11 – 22 July 2019, with the participation of 621 students from 112 countries. The event is the most prestigious scientific Olympiad for high school students. Problem 2 and Problem 5 are of mean difficulty on the paper. Problem 2 was solved fully (7 points) by 98 participants, 92 students were marked with 6 points, 3 with 5 points, 6 with 4 points, 6 with 3 points, 30 with 2 points, 135 with 1 point and 251 with 0 points. The mean result of all the 621 participants in the Olympiad is 2,399. Analogously, Problem 5 was solved fully (7 points) by 250 participants, 3 students were marked with 6 points, 7 with 5 points, 5 with 4 points, 12 with 3 points, 168 with 2 points, 20 with 1 point and 156 with 0 points. The mean result of all the 621 participants is 3,567.
Keywords: Olympiad; problem solving; collinear points; concyclic points; parallel lines; Reim’s theorem
1)Sava Grozdev, 2)Veselin Nenkov
1) University of Finance, Business and Entrepreneurship – Sofia (Bulgaria)
2) “Nikola Vaptsarov” Naval Academy – Varna (Bulgaria)
Configurations оf Pedal Circles
of an Arbitrary Point
in the Plane of a Polygon
Absract. In this paper it is described the mutual location of the pedal circles of an arbitrary point in the plane of an arbitrary quadrilateral and pentagon with respect to the triangles determined by their sides and diagonals. As a result it is defined Simson circle of a point in the plane of an arbitrary pentagon. Simson lines are found for points on determined lines in the plane of the pentagon.
Keywords: quadrilateral; pentagon; pedal circles; Simson line
1) Prof. Dr. Veselin Nenkov, 2) Mr. Stanislav Stefanov
Department of Mathematics and Physics
Faculty of Engineering
“Nikola Vaptsarov” Naval Academy
2) Department of Маthematical modeling and numerical methods
Faculty of Аpplied mathematics and informatics
Technical University Sofia
On the Polynomials with Roots in the Vertices of a Class of Convex Quadrilaterals
Absract. A geometrical relation is derived for the roots of polynomials of complex variable with multiple roots in the vertices of a convex quadrilateral and the roots of the corresponding derivatives. As an application some polynomials of real variable and with real coefficients are considered.
Keywords: polynomial; derivative a polynomial; polynomial roots; convex quadrilateral; ellipse; focus
1)Prof. Sava Grozdev, DSc., 2)Dr. Veselin Nenkov, Assoc. Prof.
1) University of Finance, Business and Entrepreneurship
Department of Mathematics and Physics
Faculty of Engineering
Nikola Vaptsarov Naval Academy
Analysis of an Inquiry Examination of Teachers in Technologies and Еntrepreneurship
Absract. The inquiry examination aims at establishing whether teachers in Technologies and entrepreneurship in 5th grade respect the order of the sections and topics as scheduled in the course syllabus or change it according to the realization of integrative links with Mathematics and other school subjects.
Keywords: inquiry; technology and entrepreneurship; interrelationship; mathematics; integration
Mr. Kostadin Petleskov
Department of Mathematics
Faculty of Sciense
SWU "Neofit Rilski"
REVIEWS AND ANNOTATIONS
Mathematical Competence Increase through Dynamic Geometry
Prof. Sava Grozdev
University of Finance, Business and Entrepreneurship
Reflective Model for Teaching Computer Modeling in Primary Stage of Education
Julia Doncheva
"Angel Kanchev", University of Ruse (Bulgaria)
CONTEST PROBLEMS
Contest Problems of this Issue
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Solutions of the Contest Problems from Issue 4, 2019
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