In: Recherches en didactique des mathématiques, Jg. 7 (1986) ; Nr. 3, S. 5-49
Zeitschriftenaufsatz / Fach: Mathematik
Fakultät für Mathematik » Didaktik der Mathematik
The paper analyzes the historical development of stochastical independence from an epistemological point of view with the intention of obtaining an educational perspective for this concept. In the historical development, a conversion of the concept's content and of the mathematical definition can be noted. At the beginning, immediately concrete representations about dependencies resp. independencies of real facts were associated with this concept, whereas the concept was formally defined, mathematically, by the multiplication formula. This process should not be interpreted as a total detachment of a mathematical concept from real references. This opens, in principle, a variety of possible references to applications, which, however, are no longer simultaneously realized in the scientific research of the discipline. As opposed to that, developing the concept in mathematics instruction should be organized by establishing a permanent relationship between representations of content (object) and mathematical definition (signs, formulas). In this respect, the concept of stochastical independence is an important example for analyzing the transition from an empirical to a theoretical understanding of the object.