Abstrakt
The poster presents the results of researches that have recently enriched the Theory of generic model (Hejný, 2012). The theory models the process of gaining knowledge in mathematics and comes out of the ideas of Piaget's genetic epistemology and his description of cognitive development through developmental stages (Piaget & Garcia, 1989).
The Theory of generic models (TGM) has been gradually developed by M. Hejný in cooperation with several research teams since mid-20th century.
In our research. TGM is used as the basis for analysis and interpretation of pupils' thinking processes.
During in-depth analyses of several pupils' cognitive processes and their comparisons the first author discovered that sometimes there are two more steps in the cognitive process that has not yet been described. Pupils were solving a problem leading to the discovery of the relationship between two series of numbers and to generalization.
The poster presents four pupils' solutions. The pupils' thinking processes are interpreted with TGM at the background.