Articles

• Dynamic methods in teaching geometry at different levels

  1-13

  Tamás Árki

  István Krisztin Német

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  9

  In this paper we summarize and illustrate our experiences on DGS-aided teaching geometry of the courses "Computer in mathematics" and "Mathematical software" held for students at Juhász Gyula Teacher Training College of University of Szeged. Furthermore, we show examples from our grammar school experiences too. The figures in this paper were made by using Cinderella ([19]) and Euklides ([21]).

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• Using the computer to visualise graph-oriented problems

  15-32

  Erika Gyöngyösi

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  7

  The computer, if used more effectively, could bring advances that would improve mathematical education dramatically, not least with its ability to calculate quickly and display moving graphics. There is a gap between research results of the enthusiastic innovators in the field of information technology and the current weak integration of the use of computers into mathematics teaching.
  This paper examines what exactly the real potentials of using some mathematics computer software are to support mathematics teaching and learning in graph-oriented problems, more specifically we try to estimate the value added impact of computer use in the mathematics learning process.
  While electronic computation has been used by mathematicians for five decades, it has been in the hands of teachers and learners for at most three decades but the real breakthrough of decentralised and personalised micro-computer-based computing has been widely available for less than two decades. And it is the latter facility that has brought the greatest promise for computers in mathematics education. That computational aids overall do a better job of holding students' mathematical interest and challenging them to use their intellectual power to mathematical achievement than do traditional static media is unquestionable. The real question needing investigation concerns the circumstances where each is appropriate.
  A case study enabled a specification of advantages and obstacles of using computers in graph-oriented questions. Individual students' interviews revealed two less able students' reactions, difficulties and misinterpretations while using computers in mathematics learning.
  Among research outcomes is that the mathematical achievement of the two students observed improved and this makes teaching with computers an overriding priority for each defined teaching method.
  This paper may not have been realised without the valuable help of the Hungarian Eötvös State Grant.

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• Rotation mentale et ordinateur

  33-48

  Mária Bakó

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  4

  P. H. Maier, en se basant sur des recherches psychologiques, distingue cinq éléments d'intelligence spatiale. Dans cet article nous étudions comment l'ordinateur peut intervenir dans le développement de l'élément rotation mentale. Nous avons écrit des logiciels qui utilisent les rétroactions perspectives et nous avons effectué des expériences avec cinq groupes d'éleves. Pour pouvoir poursuivre le travail et le développement de travail de chaque éleve et pour faciliter l'examen des résultats, les tests sont au format HTML et les réponses des éleves ont été traitées par un serveur central. La statistique montre que les résultats des éleves s'améliorent au fur et a mesure.

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• Ein ungewöhnlicher Weg zu Jakob Steiners Umellipse eines Dreiecks und zur Steiner–Hypozykloide

  49-65

  Oswald Giering

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  13

  In real projective geometry of triangles two problems of collinear points are discussed. The problems differ only from the running through the vertices of a given triangle ABC. Resolving the problems we find two cubic curves kS and kT . Affine specialization leads to the circumscribed Steiner ellipse about the triangle ABC and shows us this ellipse in more general surroundings. Euclidean specialization leads to Steiners three-cusped hypocycloid.

  PDF (German)

  9

• Dynamic geometry systems in teaching geometry

  67-80

  Rita Nagy-Kondor

  Views:

  12

  Computer drawing programs opened up new opportunities in the teaching of geometry: they make it possible to create a multitude of drawings quickly, accurately and with flexibly changing the input data, and thus make the discovery of geometry an easier process. The objective of this paper is to demonstrate the application possibilities of dynamic geometric systems in primary and secondary schools, as well as in distance education. A general characteristic feature of these systems is that they store the steps of the construction, and can also execute those steps after a change is made to the input data. For the demonstration of the applications, we chose the Cinderella program. We had an opportunity to test some parts of the present paper in an eighth grade primary school.

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• Comparative geometry on plane and sphere: didactical impressions

  81-101

  Ágnes Makara

  István Lénárt

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  1

  Description of experiences in teaching comparative geometry for prospective teachers of primary schools. We focus on examples that refer to changes in our students' thinking, in their mathematical knowledge and their learning and teaching attitudes. At the beginning, we expected from our students familiarity with the basics of the geographic coordinate system, such as North and South Poles, Equator, latitudes and longitudes. Spherical trigonometry was not dealt with in the whole project.

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• Applications of methods of descriptive geometry in solving ordinary geometric problems

  103-115

  József Szabó

  Ildikó Molnár

  Views:

  8

  The importance of descriptive geometry is well-known in two fields. Spatial objects can be mapped bijectively onto a plane and then we can make constructions concerning the spatial objects. The other significance of descriptive geometry is that mathematical visual perception of objects in three-dimensional space can be improved by the aid of it. The topic of this paper is an unusual application of descriptive geometry. We may come across many geometric problems in mathematical competitions, in entrance examinations and in exercise books whose solution is expected in a classical way, however, the solution can be found more easily and many times more general than it is by the standard manner. We demonstrate some of these problems to encourage to use this geometric method. Understanding the solution requires very little knowledge of descriptive geometry, however, finding a solution needs to have some idea of descriptive geometry.

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• Process or object? Ways of solving mathematical problems using CAS

  117-132

  Gunnar Gjone

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  6

  Graphing and symbol manipulating calculators are now a part of mathematics education in many countries. In Norway symbol manipulating calculators have been used at various exams in upper secondary education. An important finding in mathematics education is the duality of mathematical entities – processes and objects. Building on the theoretical development by Anna Sfard and others, the students' solutions on exam problems in upper secondary education are discussed with reference to procedural and structural knowledge.

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• Die Stichprobe als ein Beispiel dafür, wie im Unterricht die klassische und die bayesianische Auffassung gleichzeitig dargestellt werden kann

  133-150

  Ödön Vancsó

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  4

  Teaching statistics and probability in the school is a new challenge of the Hungarian didactics. It means new tasks also for the teacher- and in service-teacher training. This paper contains an example to show how can be introduced the basic notion of the inference statistics, the point- and interval-estimation by an elementary problem of the public pole. There are two concurrent theories of the inference statistics the so called classical and the Bayesian Statistics. I would like to argue the importance of the simultaneously introduction of both methods making a comparison of the methods. The mathematical tool of our elementary model is combinatorial we use some important equations to reach our goal. The most important equation is proved by two different methods in the appendix of this paper.

  PDF (German)

  3

• Delusions in informatics education

  151-161

  Péter Szlávi

  László Zsakó

  Views:

  8

  In the following article our intention is to try to introduce the negative ideas that exist today in Hungary regarding informatics education within the secondary education system. [Zs] As far as we know, these delusions are characteristic of not only Hungary, but we believe that we should look for our own mistakes, that is why we refer to Hungarian examples.
  We have examined the informatic knowledge taught in the first 10 years of secondary education, the possible curriculum of the general informatics subject.
  To reach our aim, first we have to deviate a bit from our original topic, because without this, it would be more difficult to understand the core subject of the article. In the deviation we will explain what is called informatics, what is called informatics subject. Then we will deal with the main topic and in the summary we will explain what we believe is the aim of general informatics education.

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• Decomposition of triangles into isosceles triangles I: let the students ask bravely

  163-184

  József Kosztolányi

  Zoltán Kovács

  Erzsébet Nagy

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  8

  We report about working up an open geometric problem as a mathematical research with pupils of a mathematics camp. This paper shows the didactic aims and the methods we worked with, the didactic results. The second part of this paper gives a general solution of the problem, using pure mathematics and a computer programme.

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• Writing a textbook – as we do it

  185-201

  István Czeglédy

  András Kovács

  Views:

  5

  Recent surveys studying mathematics teaching show that there is a great variety in the level of mathematics teaching in Hungary. To increase efficiency (and decrease differences between schools) it is essential to create textbooks with new attitudes. The experiment we started after the PISA survey of 2000, produced a textbook that is new, in some sense even unusual in its attitude and methods. This paper presents the experiences we gained in the course of this work.

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• On the models of the hyperbolic plane

  203-206

  László Németh

  Views:

  8

  We can see the most familiar models of the hyperbolic plane in one figure, which shows the connections between them by the help of projections.

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• Proof without words

  207

  Ángel Plaza

  Views:

  4

  | cos α + sin α | ≤ √2 with equality…

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  0