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• Normalization based on dependency diagram

  121-132

  Márta Czenky

  Views:

  153

  Normalization is an important database planning method, although the understanding and application of this method brings up the utmost problem during data modelling. That is why we were looking for alternative normalization methods, from which the normalization with dependency diagram proved to be the most efficient. This was also confirmed by the statistical estimation of the carried out survey.

• On the legacy of G. Pólya: some new (old) aspects of mathematical problem solving and relations to teaching

  169-189

  Bernd Zimmermann

  Views:

  114

  In this article are given some new aspects of mathematical problem solving. A framework is presented by three main resources: (1) Pólya's studies about mathematical heuristics are augmented by information drawn from a study of the history of mathematical problem solving. (2) Connections are presented between mathematical problem solving and mathematical beliefs. (3) Experience with a special program for mathematical talented students is sketched. On this background a new textbook-series has been developed and some teaching examples are taken from this context. An outlook is given on some new research on teaching of problem solving, including possible relations to modern brain research.

• Mathematics teachers' reasons to use (or not) intentional errors

  263-282

  Riikka Palkki

  Peter Hästö

  Views:

  255

  Mathematics teachers can make use of both spontaneously arising and intentionally planted errors. Open questions about both types of errors were answered by 23 Finnish middle-school teachers. Their reasons to use or not to use errors were analyzed qualitatively. Seven categories were found: Activation and discussion, Analyzing skills, Correcting misconceptions, Learning to live with errors, (Mis)remembering errors, (Mis)understanding error and Time. Compared to earlier results, the teachers placed substantially less emphasis on affective issues, whereas the answers yielded new distinctions in cognitive dimensions. In particular, teachers' inclination to see errors as distractions could be divided into two aspects: students misunderstanding an error in the first place or student forgetting that an error was erroneous. Furthermore, the content analysis revealed generally positive beliefs towards using errors but some reservations about using intentional errors. Teachers viewed intentional errors mainly positively as possibilities for discussion, analysis and learning to live with mistakes.

• 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:

  164

  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.