Articles

• Forming the concept of congruence I.

  181-192

  Éva Szeredi

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  Teaching isometries of the plane plays a major role in the formation of the congruence-concept in the Hungarian curricula.
  In the present paper I investigate the way the isometries of the plane are traditionally introduced in most of the textbooks, especially the influence of the representations on the congruence concept, created in the teaching process.
  I am going to publish a second part on this topic about a non-traditional approach (Forming the concept of congruence II). The main idea is to introduce the isometries of the two dimensional plane with the help of concrete, enactive experiences in the three dimensional space, using transparent paper as a legitimate enactive tool for building the concept of geometric motion. I will show that this is both in strict analogy with the axioms of 3-dimensional motion and at the same time close to the children's intuitive concept of congruence.

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• Über die sogenannte Regel von de l’Hospital im Mathematikunterricht

  193-208

  Sándor Kovács

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  3

  The aim of this paper is to provide an insight into the problems of the socalled indeterminate expressions, in order to make the students understand them better. The paper deals with the conditions and the proof of the theorem about the limit of a quotient of certain functions of one variable, usually named after l'Hospital. The question is of some interest, since the formulation of the result in several textbooks often appears redundant and the proof is more complex than necessary. First, the historical background is briefly sketched. Second, the theorem is formulated and justified, where three different, simple proof techniques are presented. Finally, possible applications are suggested for teaching, which are usually not treated in this problem area.

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• Can a language be before “the first programming language”?

  209-224

  László Menyhárt

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  8

  I would like to present a potential new language which can be before "the first programming language". We can use this to write down the algorithms and source code can be generated from this. The keyword is XML. This can be used for describing algorithms, easy to check the syntax and the semantic. Source code can be transformed with XSLT. So the usage of this new language can help us to answer the question, which is the best first programming language?

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• Arithmetic progressions of higher order

  225-239

  Vlastimil Dlab

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  9

  The aim of this article is to clarify the role of arithmetic progressions of higher order in the set of all progressions. It is important to perceive them as the pairs of progressions closely connected by simple relations of differential or cumulative progressions, i.e. by operations denoted in the text by r and s. This duality affords in a natural way the concept of an alternating arithmetic progression that deserves further studies. All these progressions can be identified with polynomials and very special, explicitly described, recursive progressions. The results mentioned here point to a very close relationship among a series of mathematical objects and to the importance of combinatorial numbers; they are presented in a form accessible to the graduates of secondary schools.

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• Teaching integral transforms in secondary schools

  241-260

  Sándor Király

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  9

  Today, Hungarian students in the secondary schools do not know the idea of complex numbers, and they can not integrate except those ones who learn mathematics in advance level. Without this knowledge we can teach Fourier transform for students. Why should we teach Fourier transform (FT) or Wavelet transform (WT) for them? To teach image file formats like JPEG, (JPEG2000) we need to talk about integral transforms. For students who are good in computer programming, writing the program of 1D FT or 2D FT is a nice task. In this article we demonstrate how we can teach Fourier and Wavelet transform for students in secondary school.

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• Longest runs in coin tossing. Teaching recursive formulae, asymptotic theorems and computer simulations

  261-274

  Zsolt Karácsony

  Józsefné Libor

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  11

  The coin tossing experiment is studied, focusing on higher education. The length of the longest head run can be studied by asymptotic theorems ([3]), by recursive formulae ([10]) or by computer simulations . In this work we make a comparative analysis of recursive formulas, asymptotic results and Monte Carlo simulation for education. We compare the distribution of the longest head run and that of the longest run (i.e. the longest pure heads or pure tails) studying fair coin events. We present a method that helps to understand the concepts and techniques mentioned in the title, which can be a useful didactic tool for colleagues teaching in higher education.

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• Implementation opportunities of the Moodle learning management system in virtual environment the Sloodle project

  275-293

  Zsolt Kristóf

  Károly Bodnár

  Péter Takács

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  7

  Using e-learning was firstly appeared in companies' sphere. It should be very useful if learning management systems were applied. Nowadays e-learning is used in different fields and gives useful informations in case of basics and its knowledge. It is essential to know the arranging technics and applicated handling methods of some supporting learning management systems of e-learning. The Moodle is the best-known learning management system.
  The Second Life is one of the virtual environments which is useful in learning-teaching methods that is used in most educational institute all over the world. Sloodle is an open source project which connects the Second Life with Moodle learning management system. Sloodle is a kind of "bridge" in which different kind of activities and registering and provided in both Moodle and Second Life.
  In our department, University of Debrecen Health Faculty of Nyíregyháza ILIAS learning management system has operated since February, 2008. In the interest of higher level education we decided to use and made available some courses through Moodle learning management system.
  Some tools of Sloodle will be presented in our article. It will be the first study for our research in which we would use the Moodle learning management system, the virtual environment of Second Life and the project of Sloodle itself. Our article will contain the starting details and its statistical confirmation of our Sloodle project. We like to demonstrate that the results of the Sloodle-aided group are significantly better than the results of the control group in the most cases.

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