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Author Redakce
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Synthetic Solution in Geometry and Possibilities of Current Software [CZ]

Author J. Blažek
Abstract The article concerns synthetic solution in geometry and possibilities offered in this connection by current Dynamic Geometry Software (DGS). In the beginning of the article, the author tries to describe some characteristic steps during the process of searching synthetic solution, illustrated on a particular problem chosen from Mathematical Olympiad. Then author identifies some obstacles often preventing successful achievement of the solution. On this background, the possible aid offered by current software is discussed.
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Elementary Prospective Teachers Preparedness for Using Digital Technologies in Mathematics Teaching [CZ]

Author R. Dofková
Abstract The aim of the paper is analyzing elementary teachers preparedness for using digital technologies in mathematics teaching. There was a research among 95 prospective teachers in lessons of didactics of mathematics. We used the modified questionaries from international surveys Teacher Education and Development Study in Mathematics (TEDS-M).
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Sum of Squares Decomposition of Polynomial by Computer in The Context of History [CZ]

Author J. Frank
Abstract One of the basics problems in mathematics is to prove that a certain polynomial f is a positive semidefinite polynomial it means that for all variable x from real numbers is polynomial f nonnegative. One method of proof is sum of squares decomposition. This is related to Hilbert’s seventeenth problem from year 1900. In elementary cases (polynomial of one variable) is possible to solve some examples at high school. In more complicated cases (polynomial in two or more variable), it is necessary to use computer technology and special mathematical software.
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Two Views of One Number Theory Application [CZ]

Author J. Hora, M. Kašparová, Š. Pěchoučková
Abstract Number theory was once considered to be a useless discipline, but today has important applications in message encryption. The article contains a wealth of information on this development, processed in a form useful to mathematics teachers or for people interested in number theory.
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Pollard’s Rho Algorithm for Prime Factorization of Natural Numbers [CZ]

Author J. Hora
Abstract With the development of modern cryptographic methods, there is an increased interest in modern algorithms for finding decomposition of a composite number in the product of prime numbers. The method of factorization, designed by J. M. Pollard in 1975, was around 1980 the best known algorithm for factorization of composite natural numbers. This is a probability method and can be explained to secondary school students.
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Real-world Applications of Number Theory

Author J. Klaška
Abstract The present paper is concerned with practical applications of the number theory and is intended for all readers interested in applied mathematics. Using examples we show how human creativity can change the results of the pure mathematics into a practical usable form. Some historical notes are also included.
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Automated Reasoning Tools in GeoGebra: A New Approach for Experiments in Planar Geometry

Author Z. Kovács
Abstract Computing numerical checks of certain relations between geometric objects in a planar construction is a well known feature of dynamic geometry systems. GeoGebra's newest improvements offer symbolic checks of equality, parallelism, perpendicularity, collinearity, concurrency or concyclicity. Also dragging of locus curves, defined explicitly or implicitly (or as an envelope curve) is a new feature in GeoGebra to visually check conjectures in planar geometry. By combining plotting and proving we can focus on some new possibilities to teach Euclidean geometry in the classrooms.
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ICT Support of Inquiry-based Approach in Teaching Mathematics at Elementary Schools [CZ]

Author D. Nocar, P. Polejová, J. Laitochová
Abstract Currently, one of the constructivist approaches in teaching is known as inquiry-based teaching. In the article, we point out the results of the research among teachers of mathematics at elementary schools which aim was to find out what awareness of inquiry-based teaching teachers have, whether they know this approach, whether they use it, whether they implement it in their teaching, what particular experience have they, in which parts of mathematics have they use it, what ICT tools they use to do so and what barriers impede them more frequent application of these methods in their teaching.
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Teaching Mathematics in Digital Technology Environment [CZ]

Author J. Robová
Abstract This article deals with present problems of technology integration in teaching mathematics, especially at the secondary level. The first part is focused on the role of the teacher in teaching supported by digital technology and on his knowledge needed for developing pupils’ understanding and skills. The second part is concerned with technology integration from the pupils’ learning point of view, with the emphasis on pupils’ knowledge needed for effective using technology in mathematics. The examples illustrating discovering and testing hypotheses in dynamic geometry Geogebra are included.
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