Isomorphism as generalization tool (in combinatorics)

The article deals with constructing the discovery of the number of combinations. It stems from the approach of genetic constructivism, which works with the generic model theory, and its research goal was to develop the stages of isolated models, particularly using the phenomenon of isomorphism. Children aged 11–13 participated in the experiment during their mathematics club, in which they worked in groups at first and together at the blackboard afterwards. The results come from analyzing the experiment protocol and a video recording of part of the experiment. In this study, the authors focus primarily on a detailed analysis of individual sub-phases of isolated models under the generic model theory. The experiment highlights the importance of isomorphism as a generalization tool. The authors have identified the obstacles on the way to advanced sub-phases of isolated models. Another contribution is the division of the fourth sub-phase into two separate sub-phases, which has been achieved using the method of atomic analysis.