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• Proof without words: Knopp series for (pi)

  451-452

  Ángel Plaza

  Views:

  30

  There are many expressions for number π as infinite series or infinite product (see for example [1, 2, 3]). In [1] the following series for number π is attributed to K. Knopp:...

• Summe einer unendlichen geometrischen Reihe im Mathematikunterricht

  229-240

  Ján Gunčaga

  Views:

  23

  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.

• Improper integrals, an excursion to classical calculus

  303-317

  Herbert Zeitler

  Views:

  28

  The aim of this paper is to show in what way we investigated improper integrals in the classroom. It was very important to calculate explicitly a lot of examples. Doing so, a criterion was developed. With step curves and infinite series we had a quick look at the mathematical background. The shot in the universe showed that improper integrals are needed in physics.

• Heads or Tails gambling — what can be learned about probability?

  15-41

  Attila Máder

  Views:

  23

  During the teaching of probability theory, a problem may appear whose solution requires the use of methods that are unfamiliar to secondary school students. In this paper, examples of methods that can resolve this difficulties are demonstrated, which could in future allow school students to tackle and solve a wide variety of problems involving probability.