Combinatorics, organization principles, combinatorial task

Our undergoing research in action started two year ago and focuses on pupils as well as teachers. The proposed article focuses on the pupils and their ability to solve combinatorial tasks. We are interested how the ability of students to organize objects affects the solving combinatorial problems. ?Combinatorial thinking is based on the ability to organize the elements of the set into transparent charts, graphs, diagrams, and lists? (Hejný, 1989). Despite the fact that the teachers try to explain combinatorial thinking to the upper primary school pupils and the secondary school pupils, the teaching process tends to follow the pattern of solving tasks according to a particular algorithm: pupils choose the right formula, solve the tasks and deliver the answer. The experiment builds on the results of the studying the organizational principles through the use of the preschool pupil (Krpec, 2014). This experiment took place during a mathematics teaching club attended by 5 to 10 pupils aged 11?13 studying at Secondary Grammar School of Prof. Otto Wichterle (Ostrava, Czech Republic). The curriculum focused on combinatorics, specifically on determining the combination of the second class of the five elements and variations of the second class of five elements. The experiment has been video-recorded and supplied with teacher?s personal notes. The recording was transcribed in writing and analyzed by the author. In the analysis we focused the organizational principles that students used to solve combinatorial tasks. Research has shown that students who have a problem with the organization objects usually have trouble to solve problem tasks of combinatorial type.