Abstract:

Although mathematics education has always been considered an important part of the educational systems of all countries, it does not guarantee the development of all skills (competences) that today’s pupils will need in adult life. Several recent PISA researches focused on the mathematical literacy showed that pupils of OECD countries handle algorithmic mathematical tasks, but the problem of many countries' pupils is such mathematical tasks as non-standard, problematic, with cross-curricular connections and requiring creative solutions. While non-standard tasks often have a divergent character as well as many naturally divergent situations that pupils solve in practical life – from building relationships, through solving school or work tasks to everyday tasks such as dressing, leisure time, etc. – in this contrast, convergent tasks dominate mathematics education (90-95% in traditional textbooks).

One of the reasons for the failure of many pupils in problematic mathematical problems is the approach of pupils to mathematics, which is rather negative in some countries. This fact is often associated with an overall low willingness of pupils to solve these problematic tasks. Fortunately, nowadays the focus is not only on developing financial literacy but primarily on the ability to solve these non-standard tasks and problems in which elements and concepts are interconnected not only from mathematics but from different fields, requiring different representations and different solutions. This kind of variable approaches is mainly created by the teacher in special educational situations that represent a specific time and place constraint in which a pupil is exposed to the teacher’s influences, having their specific learning objective, to which the pupil responds in some way.

This paper presents the results of qualitative research focused on the analysis of solving non-standard tasks and problems by pupils in mathematics education in the Czech Republic as an educational situation. The research is carried out through a case study, using anonymous interviews with mathematics teachers and pupils, analyzing pupils' working documents (exercise books, notes), participating in the observation of the teaching and learning process, and a non-standardized didactic test. The research is carried out in parallel at two primary schools in two classes, at the second stage (lower secondary school). The data are qualitatively and quantitatively processed using tables and graphs. The research conclusions aim to contribute to the understanding of the importance of non-standard tasks and problems in mathematics in primary education and to the approach of pupils and teachers to this issue.

Keywords:

primary education, mathematics education, educational situation, non-standard tasks, case study