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• Supporting the theory of math didactic using knowledge-measuring questions and analysis of the solutions

  1-16

  Sándor Kántor

  Péter Fejes-Tóth

  Views:

  8

  New or rediscovered results presented in this paper are the results of the analysis of the problem sets used in the two-tier system secondary school final examination in mathematics, a system that was introduced in Hungary in 2005.
  Many of the revealed problem arise in connection with misunderstanding the text of the problems. Causes of misinterpretation can be either that the text is lacking some important information, or that it should be interpreted not in word-to-word manner.
  Theses and their argumentations presented here refer partly on the new types of problems (tests, non-standard mathematical contents), and partly on improvement of learning-teaching process in topics of equations and approximations.

• Teaching reliability theory with the Computer Algebra System Maxima

  45-75

  Attila Csenki

  Views:

  8

  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.

• Constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of CAS

  363-376

  Muharrem Aktümen

  Tolga Kabaca

  Views:

  9

  Calculus concepts should have been taught in a carefully designed learning environment, because these concepts constitute a very important base for almost all applied sciences. The integral, one of the fundamental concepts of Calculus, has a wide application area. This paper focuses on constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of a CAS.
  In this study, a semi-structured interview was carried out. In this interview, we tried to construct the disk method formula.
  The levels of constructing the disk method formula in this study are:
  • Introducing the concept: evaluating the volume of an Egyptian pyramid.
  • Evaluating the volume of a cone obtained by revolution (using Maple worksheet).
  • Designing their own ring and evaluating its price (using Maplet).
  In this study, the interview has been presented as a dialog between teacher and students. When we look at feedback from students, we see that such a teaching method effects students in a positive way and causes them to gain conceptual understanding directed towards the concepts of approximation and volume.