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Pre-service teachers’ (Mis)-understanding of the constructions of dynamic geometry objects

Sinitsky M.

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

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2017

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Vol. 30

41--45

EN

Future secondary school math teachers learned the basics of GeoGebra and were then tasked with the construction of a specific quadrilateral according to a given description. Qualitative analysis of their solutions discloses typical student misconceptions and errors.

PL

Przyszli nauczyciele matematyki w szkole średniej uczyli się podstaw programu GeoGebra, a następnie mieli za zadanie skonstruowanie określonego czworoboku zgodnie z danym opisem. Jakościowa analiza ich rozwiązań ujawnia typowe błędne wyobrażenia studentów i popełnione przez nich błędy.

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Presentation of a new bilingual mathematical dictionary

Novák M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

81-86

EN

In the contribution I am presenting a new English-Czech-English mathematical dictionary, which was prepared for university students in the Czech Republic, in the form of an on-line application with unrestricted access.

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About some difficulties in doing proofs encountered by the students from the first year of mathematics

Hawro J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

221-226

EN

This paper contains some results of diagnostic research on the difficulties that students who begin studies at the tertiary level encounter when doing proofs from a section devoted to applying definitions in proofs. The considerations concern the issues connected with understanding of the role of definition and understanding of the texts of definitions by students. In these considerations the examples of solutions given by students to two diagnostic tasks applied in the research are used.

4

Pietro Mengoli szeregi liczbowe prehistoria funkcji ζ Riemanna

Maślanka K.

Kwartalnik Historii Nauki i Techniki

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2004

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R. 49, nr 1

47--64

EN

The article deals with the work of the 17th-century Italian mathematician. Rev. Pietro Mengoli (1625-1686), who was the forerunner of research on numerical series.The legacy of Mengoli, a scientist well-known and well respected in Italy, but almost altogether forgotten in the West, has never been thoroughly analyzed in Polish historical writing. Yet it was Mengoli who first posed a number of problems related to finding the sums of an infinite number of fractions. He solved most of those problems, but he failed in one case - in the case of the sum of the inverse of squares of successive natural numbers. For fundamental reasons, which had not been understood until several dozen years later, Mengoli was unable to find a compact expression for the sum of this series. He himself, with a humility rarely found in the history of science, admitted that this problem required a "richer intellect". This series turned out to be the first example of a fundamental function investigated later by Euler and Riemann, and called, in honour of the latter mathematician, the Riemann ζ (dzeta) function. This function constitutes the key to solving one of the greatest mathematical puzzles of all times - the distribution of prime numbers. Connected with this riddle is also the most important and most difficult of the hitherto unsolved problems of the famous list presented in 1900 by Hilbert at the 2nd International Mathematical Congress in Paris, the Riemann hypothesis. The generalizations of the series considered by Mengoli continue to be researched by mathematicians today. The aim of the article is to show, on the example of Mengoli’s achievements and failures, a general regularity: the solution of a given mathematical problem is the result of the subtle interplay between, on the one hand, the scientists’s knowledge, talent and effort, and, on the other, the level of general knowledge at a given time, which stems from the collective achievements of many previous generations of mathematicians.