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• Visualisation in geometry education as a tool for teaching with better understanding

  337-346

  Ján Gunčaga

  László Budai

  Tibor Kenderessy

  Views:

  153

  In primary and secondary geometry education, some problems exist with pupils’ space thinking and understanding of geometric notions. Visualisation plays an important role in geometry education, and the development of pupils’ visualisation skills can support their spatial imagination. The authors present their own thoughts on the potential of including visualisation in geometry education, based on the analysis of the Hungarian National Core Curriculum and Slovak National Curriculum. Tasks for visualisation are also found in international studies, for example the Programme for International Student Assessment (PISA). Augmented reality (AR) and other information and communication technology (ICT) tools bring new possibilities to develop geometric thinking and space imagination, and they also support mathematics education with better understanding.

  Subject Classification: 97U10, 97G10

• Summe einer unendlichen geometrischen Reihe im Mathematikunterricht

  229-240

  Ján Gunčaga

  Views:

  21

  This article deals with sums of infinite geometric series. We focus on the understanding of the notion by pupils at secondary school through generic and universal models. In the first part we survey this notion in the Czech and Slovak curriculum. We describe the process of gaining knowledge as a sequence of five stages. In the second part we show one possible approach how to introduce the notion "sum of the infinite geometric series" through this process. We illustrate this on some examples for pupils. At the end we formulate some pedagogical recommendation for teachers.

• Das Konzept des Analysisunterrichts von Professor Igor Kluvánek – einige Ergebnisse der qualitativen Forschung

  349-361

  Ján Gunčaga

  Views:

  24

  A renowned Slovak mathematician Professor Igor Kluvanek (1931-1993) during his affiliation with the University of Adelaide in Australia (1968-1990) has worked out a unique course of mathematical analysis for future high school teachers of mathematics. The course has been tested in its conceptual form but, as a whole, it still awaits its publication in the form of a monograph. Along these lines, our aim is to present the way he has introduced some key notions of differential calculus and to discuss its advantages. Central is the continuity of a function via which the limit and the derivative of a function at a point is defined.