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• Veranschaulichung der Lehrstoffstruktur durch Galois-Graphen

  217-229

  László Fatalin

  Views:

  19

  In this article we compare the process diagram with the Galois-graph, the two hierarchical descriptions of the curriculum's construction from the point of didactics. We present the concrete example through the structure of convex quadrangles. As a result of the analysis it is proved that the process diagram is suitable for describing the activity of pupils, still the Galois-graph is the adequate model of the net of knowledge. The analysis also points out that in teaching of convex quadrangles the constructions of curriculum based only on property of symmetry and only on metrical property are coherent. Generalizing concept is prosperous if the pupils' existing net of knowledge lives on, at most it is amplified and completed. Teaching of convex quadrangles in Hungarian education adopts this principle.

• Über den Vergleich des mathematischen bzw. mathematikdidaktischen Vektorbegriffs durch den Galois-Graphen

  1-12

  László Fatalin

  Views:

  21

  In this article we show how to apply the method of Galois-graph – one of the means of the formal concept-analysis in order to coordinate the mathematical and didactical requirements. As an example we have chosen the concept of the "vector". As a result of the analysis it is proved that, in elaborating the right vector concept the geometric and algebraic foundations are both needed. The analysis also points out that the geometric model, based on the concept of the "directed segment" is unnecessarily overemphasized in the East-European education.