Abstract:

This study stems from the on-going discussion about the quality of teaching of mathematics in schools as indicated by declining results of Czech pupils in TIMSS and PISA studies in the past years. The contribution by McKinsey (2010) concludes that “…it is necessary to change the attitude and behavior of people – in this case teachers.” After over 40 years of research of mathematical education at the Department of Mathematics and Mathematical Education of the Faculty of Education of the Charles University, it seems that the main shortcoming lies in the fact that the education is focused on reproduction and imitation in combination with low representation of creative activities of pupils in the class. This shortcoming has been felt for a longer period of time and many documents of the Ministry of Education, as well as various studies, draw attention to the need to increase creativity in mathematical education.

The VOBS method is a creative method of teaching mathematics. This teaching method represents an education style based on constructivism. The constructivist teaching method plays multiple roles in modern didactics of mathematics specified by adjectives. In order to distinguish this style elaborated by professor Hejný (2012), it was named after its specific property – Scheme-oriented education.

In 2014, an experiment was conducted with pupils on the second stage of elementary school during which the pupils were asked to solve tasks from different areas of combinatorics. The education consisted of 5 lessons in a group of no more than 10 pupils and the teacher tried to follow the scheme-oriented education method. The pupils focused on easier combinatoric tasks, closer to their current skill levels. For the whole duration of the class, the teacher tried to leave the discovery of all solutions to these tasks to the pupils and only entered the discussion as a moderator.

The results of this experiment indicated that pupils enjoyed this form of mathematical education much more. The pupils themselves discovered solutions of specific tasks, as well as general solutions. They were able to deduce not only generic procedural models of situations, but also abstract knowledge that is usually discovered only in later stages of education. The study also included an analysis of the teacher’s behavior. We can draw multiple conclusions and questions from this analysis and especially evaluate how difficult it is to change one’s teaching methods, as the specific teacher only worked with this method for a relatively short period of time.

Keywords:

Mathematical education, scheme-oriented education, combinatorics, constructivist teaching.