Year LX, Issue 5, 2017<<Archive>>
In this issue:
Еducаtionаl Маttеrs
INTEGRATIVE RELATIONSHIPS IN THE COMPETENT APPROACH IN MATHEMATICS AND INFORMATION TECHNOLOGY TRAINING
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 pro...
competent approach; integrative approach; model of training
SOME WAYS IN SOLVING ALGEBRAIC PROBLEMS
The paper considers the possibilities of some relations among topics of the mathematical school curriculum in problem solving.
problem solving; algebra; links between topics
SECOND INTERNATIONAL NET RESEARCH STUDENT PROJECT IN THE FRAMES OF MITE
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 “Math...
secondary education; student; geometry; research; international network collaboration; dynamical geometry software; cloud service
DIDACTIC SCENARIO ON A PROBLEM FROM THE 21 ST JUNIOR BALKAN MATHEMATICAL OLYMPIAD
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 probl...
inquiry-based approach; problem decomposition; Socratic style teaching
Еducаtionаl Tеchnologiеs
SOME NUMERICAL SEQUENCES CONCERNING SQUARE ROOTS (PART ONE)
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 i...
infinite sequence; nested radical; convergence; mathematical induction.
PROOFS AND SPECIFICATIONS OF EXPERIMENTALLY DERIVED ASSERTIONS BY THE DUALITY PRINCIPLE
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).
triangle; centroid; circumcurve; Euler curve; Euler line
ERDÖS’ DISTINCT DISTANCES PROBLEM
In discrete geometry, the Erdös’ distinct distances problem states that between \(n\) distinct points in a plane there are at least \(n^{1-o(1)}\) distinct distances. The problem was posed by Paul Erdös in 1946. In 2010, Larry Guth and Net Hawk Katz claimed...
geometry; the Erdös’ distinct distances problem; young students
OPTIMIZING THE POSITIONING OF SERVING UNITS IN THE TOURISM BUSINESS
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 to...
optimization; tourism; serving unit; positioning