Predicative versus functional thinking processes while constructing algorithms. 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 ease 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/aktivitaeten/dl/dynamic_labyrinths/dynamiclabyrinths.html Kurzreferat: In der Entwicklungsgeschichte mathematischen Wissens werden mit dem Begründungs-und Rezeptewissen zwei unterschiedliche Ansätze ausgemacht. Wie zu erwarten, ist die Art dieser beiden Herangehensweisen nicht immer gleichermaßen geeignet, um eine tragende begriffliche Vorstellung zu entwickeln. Eine Analyse von Bateson deckt beim Begriff »Schalter« fundamentale funktionale Charakteristikanicht aber prädikative -auf. Damit einher geht eine besondere Anforderung an kognitives funktionales Zurechtlegen bei Problemen, die die Nutzung und Regelung von Schalterfunktionen verlangen. Im Rahmen des DFG-Projektes "Individuelle Unterschiede in der Kognition mathematischer Begriffsbildung" wird die Fähigkeit von Versuchspersonen untersucht, mit mechanisch gegebenen Schaltern und verbindenden Bauteilen Maschinen zu konstruieren, die zur Ausführung von Organisations-bzw. Berechnungsaufgaben genutzt werden können. Es zeigen sich während des Konstruktionsprozesses der Maschinen auffällige Unterschiede, zudem spiegeln die sprachlichen Ausdrucksformen die Leichtigkeit oder Schwierigkeit wider, sich auf das Planen und Realisieren von Abläufen einzulassen. Die kognitive Haltung der Versuchspersonen beim Erfinden der Maschinen passt zu ihrem Verhalten beim Bearbeiten von Logikrätseln im QuaDiPFAufgabenformat. Zu den Maschinen s. auch:

Accuracy scores across the ten training blocks of the gifted, college, and grade 7/8 groups Response times across the ten training blocks Response times across the ten training blocks of the gifted, college, and grade 7/8 groups Slopes across the ten training blocks Slopes across the ten training blocks of the gifted, college, and grade 7/8 groups Accuracy scores of the gifted, college, and grade 7/8 groups for final training, retest, and transfer blocks Response times of the gifted, college, and grade 7/8 groups for final training, retest, and transfer blocks Slopes of the gifted, college, and grade 7/8 groups for final training, retest, and transfer blocks Plots of the power law having the same values for parameters b and c but different values for parameter a Plots of the power law having the same values for parameters a and c but different values for parameter b Plots of the power law having the same values for parameters a and b but different values for parameter c Accuracy scores for training, reversed, and new stages for both number and object stimuli Accuracy scores of the gifted and college groups for number and object stimuli Accuracy scores of the gifted and college groups for training, reversed, and new stages Accuracy scores of the gifted and college groups for the different stimulus-stage combinations Response times of the gifted and college groups for number and object stimuli Response times of the gifted and college groups for training, reversed, and new stages lOS Response times of the gifted and college groups for the different stimulus-stage combinations Rates of automatization for training, reversed, and new stages for number and object stimuli Rates of automatization of the gifted and college groups for number and object stimuli Rates of automatization of the gifted and college groups for training, reversed, and new stages Rates of automatization of the gifted and college groups for the different stimulus-stage combinations