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• The application of modelling tasks in the classroom – why and how? with reflections on an EU teacher training course

  231-244

  Gabriella Ambrus

  Ödön Vancsó

  Balázs Koren

  Views:

  34

  The aim of the article is to present the concept of mathematical modelling in the classroom. LEMA (Learning and Education in and through Modelling and Applications) was an EU Comenius funded project in which mathematics educators from six countries worked to produce materials to support teachers' professional development. A group of voluntary Hungarian mathematics teachers were taught modelling for a year and we were and still are given feedback continously. The article leads us from the general concept of mathematical modelling to its practice in the classroom. It presents difficulties that teachers have to face when doing modelling lessons and their students' reactions are also mentioned. We present sample tasks from the material of the teacher training course as well as tasks that were created by the participants.

• Bemerkungen zur Prototypentheorie – Begriffs - und Konzeptbildung

  365-389

  Éva Vásárhelyi

  Views:

  25

  Psychological theories of prototypes are put forward by mathematical modelling. Some didactical consequences are discussed on the background of this analysis. By the help of an example (classification of convex quadrangles) hints are given for didactical interpretations of actual models of cognitive psychology dealing with problems of constructing prototypes.

• Über die Verwendung von Maple für die Simulation von Mechanismen

  21-39

  Engin Can

  Views:

  25

  Maple is used to do numerical computation, plot graphs and do exact symbolic manipulations and word processing. This paper demonstrates how Maple can be used for the simulation of mechanisms. This offers the possibility for students to become familiar with this particular section of mathematical modelling. The mechanism under consideration is a so-called F-mechanisms, i.e., a planar parallel 3-RRR robot with three synchronously driven cranks. It turns out that at this example it is not possible to find the poses of the moving triangle exactly by graphical methods with traditional instruments only. Hence, numerical methods are essential for the analysis of motions which can be performed by an F-mechanism.

• Aspects théoriques de la classification à base de treillis

  125-135

  Katalin Bognár

  Views:

  28

  La classification est une notion cruciale dans les systémes orientés objets et se fait de plus en plus présente en représentation de connaissances. Elle permet principalement de trouver des regularités dans un grand tableau de nombres. Dans ce sens général, il s'agit donc d'une méthode qui joue un role important dans différents domaines scientifiques oú les connaissances sont á organiser selon certaines hiérarchies (biologie, chimie, etc.). En informatique nous parlons aussi de langages de classes sans mentionner es aspects mathématiques de la classification. Dans cet article l'auteur a pour but de proposer une introduction á la classification á travers la notion de treillis. Nous sommes persuadés que l'étude de la classification permet aux étudiants de familiariser leurs connaissances sur la modélisation et la programmation orientée objet.
  The classification is a crucial notion in the object oriented systems and more and more appears in the knowledge representation. It allows us to find the regularities in a huge table of numbers. In this general sense the classification plays an important role in various domains of science, where knowledge has to be organized into hierarchy (biology, chemistry, etc.) In the computer science the languages of classes are often studied without mathematical aspects of the classification. In this paper the author has the goal to propose an introduction to the classification through the notion of lattices.We are convinced that the study of classification allows students to enlarge their knowledge on the object oriented modelling and programming.

• Dressed up problems - the danger of picking the inappropriate dress

  77-94

  Anna Muzsnay

  Csaba Szabó

  Views:

  14

  Modelling and dressed-up problems play an inevitably unavoidable role in mathematics education. In this study we would like to point out how dangerous is it to dress up mathematical problems. We go back to the principle of De Lange: The problem designer is not only dressing up the problem, but he is the solution designer, as well. We show three examples selected from Hungarian high school textbooks where the intended solution does not solve the problem, because the dressing changes the context and changes the problem itself.

• Teaching reliability theory with the Computer Algebra System Maxima

  45-75

  Attila Csenki

  Views:

  31

  The use of the Computer Algebra System Maxima as a teaching aid in an MSc module in Reliability Theory is described here. Extracts from student handouts are used to show how the ideas in Reliability Theory are developed and how they are intertwined with their applications implemented in Maxima. Three themes from the lectures are used to illustrate this: (1) Normal Approximations, (2) Markov Modelling, (3) Laplace Transform Techniques.
  It is argued that Maxima is a good tool for the task, since: it is fairly easy to learn & use; it is well documented; it has extensive facilities; it is available for any operating system; and, finally, it can be freely downloaded from the Web. Maxima proves to be a useful tool even for Reliability research for certain tasks. This latter feature provides a seamless link from teaching to research – an important feature in postgraduate education.