teacher intervention, constructivism, teaching mathematics, genetic constructivism

Our undergoing research in action started half a year ago and focuses on pupils as well as teachers. The proposed article focuses on the teacher (author), whose main goal is to transform from transmissive education style to a constructivist one ? specifically, the genetic constructivism. We focus on the changes that take place in the pedagogical views of the teacher. The 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 and the presented study analyzes the part in which the teacher tries to lead pupils to discover the formula for n choose 2. The tool for this consists of five exercises with gradually increasing difficulty, beginning with the discovery of the relation for the number of 2-combinations from five elements in five different semantic contexts. 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 this study, we focused on analyzing the behavior of the teacher in terms of his intervention in the research process of the pupil. The goal is to determine what are the consequences of this intervention for pupils and on the other hand, what are the consequences for students the fact, when teacher?s intervention to a pupil solution is missing. The study includes several illustrations.