Prädikative versus funktionale Denkvorgänge beim Konstruieren von Algorithmen

Seen from a historical point of view, two approaches to the formation of mathematical knowledge can be distinguished: classical Greek substantiated inferential knowledge and ancient oriental functional knowledge. As might have been expected, both approaches are not equally well-suited to develop and handle particular concepts. Bateson’s analysis of the term «switch» exposes only fundamental functional features but no predicative ones. Consequently, there is a special demand for functional cognitive activities when solving problems that involve the use and control of the functioning of switching constituents. Within the framework of the DFG-project “Individual differences in the cognition of mathematical concept formation”, the ability of subjects to construct machines that carry out organisational or computational tasks with the help of given mechanical switches and additional connective building blocks have been tested. The construction procedures show pronounced differences. Furthermore, the case or difficulty to get involved with the planning and realisation of the process are reflected in the verbal protocols of the subjects. Their mental attitude corresponds nicely to their behaviour when working on logical problems as they appear in the QuaDiPF-tasks. For the machines see also: http://www.ikm.uos.de/oktivitaeten/dl/dynamic_labyrinths/dynamic-labyrinths.html