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• Approximated Poncelet configurations

  163-176

  Örs Nagy

  Szilárd András

  Views:

  8

  In this short note we present the approximate construction of closed Poncelet configurations using the simulation of a mathematical pendulum. Although the idea goes back to the work of Jacobi ([17]), only the use of modern computer technologies assures the success of the construction. We present also some remarks on using such problems in project based university courses and we present a Matlab program able to produce animated Poncelet configurations with given period. In the same spirit we construct Steiner configurations and we give a few teaching oriented remarks on the Poncelet grid theorem.

• Teaching probability using graph representations

  103-122

  Gabriella Zsombori

  Szilárd András

  Views:

  11

  The main objective of this paper is to present an elementary approach to classical probability theory, based on a Van Hiele type framework, using graph representation and counting techniques, highly suitable for teaching in lower and upper secondary schools. The main advantage of this approach is that it is not based on set theoretical, or combinatorial knowledge, hence it is more suitable for beginners and facilitates the transitions from level 0 to level 3. We also mention a few teaching experiences on different levels (lower secondary school, upper secondary school, teacher training, professional development, university students) based on this approach.

• Teaching centroids in theory and in practice

  67-88

  Szilárd András

  Csaba Tamási

  Views:

  9

  The main aim of this paper is to present an inquiry-based professional development activity about the teaching of centroids and to highlight some common misconceptions related to centroids. The second aim is to emphasize a major hindering factor in planning inquiry based teaching/learning activities connected with abstract mathematical notions. Our basic problem was to determine the centroid of simple systems such as: systems of collinear points, arbitrary system of points, polygons, polygonal shapes. The only inconvenience was that we needed practical activities where students could validate their findings and calculations with simple tools. At this point we faced the following situation: we have an abstract definition for the centroid of a finite system of points, while in practice we don't even have such systems. The same is valid for geometric objects like triangles, polygons. In practice we have triangular objects, polygonal shapes (domains) and not triangles, polygons. Thus in practice for validating the centroid of a system formed by 4,5,... points we also need the centroid of a polygonal shape, formed by an infinite number of points. We could use, of course, basic definitions, but our intention was to organize inquiry based learning activities, where students can understand fundamental concepts and properties before defining them.