Zugänge zur Normalverteilung und ihre fachdidaktische Analyse
The thesis wants to point out the purpose of introducing the Normal Distribution in a way that is based on understanding and developing ideas as opposed to an introduction that is based on pure definition and information about features of the Normal Distribution. Therefore a variety of possible approaches are illustrated in the first part of the paper. They are based on different starting points and use different stochastic and mathematical methods to deduce the density function of the Normal Distribution. For that reason there are differences among the various approaches described, on the one hand regarding the degrees of difficulty, and on the other hand regarding their use in different states of training. The second part of the thesis deals with the didactic analysis of the approaches to the Normal Distribution discussed above. To give an idea of the use in different teaching situations, each approach is characterized concerning its essential ideas, the mathematical qualifications demanded, generalization, etc. Practical suggestions are meant to explain how to realize the findings in lessons. The presentation both of teaching method and organisation is made with reference to methodical and didactic principles, which are discussed in a separate chapter. Alternative suggestions for teaching help to make adaptions to practical teaching situations. Considering current discussions about teaching mathematics, it is also explained how further qualifications – the critical reconsideration of one's own results or ways of solving a problem, for example – can be taught simultaneously when teaching such an essential mathematical matter as the Normal Distribution.