Abstract:

Non-standard tasks are one of the basic components of mathematics education. Many experts agree that the core of key competencies for life and work in the future world is the ability to solve non-standard tasks and problems. In these tasks, pupils have to solve a mathematical problem and discover a way, a method of solution, because their previous experience does not allow solve the problem. The procedure for solving a task is usually unknown and the solver looks for the way to the result, often in an original way. Solving non-standard tasks therefore requires deep concentration, invention and time.

Usually, solutions and the creation of non-standard tasks are considered suitable for working with gifted pupils, because the tasks develop knowledge, metacognition and motivation. The degree of heuristics of non-standard tasks is a typical example when it is necessary to take into account not only the task itself, but also the competence of a solver.

In our paper we will focus on the theoretical defining of non-standard tasks and their inclusion in mathematics education in curricular documents, which is followed by an analysis of solutions of pupils in lower secondary mathematics education. The aim of the paper is to find out the ways of pupils' problem solving and to identify their problems in solving.

The analysis of pupils' problem solving is performed in the form of a case study, which includes the interviews, analysis of documents to characterize selected mathematical problems during solving, detection and identification of used procedures of solution and discovery of "special" performance of pupils.

Keywords:

Non-standard task, problem, lower secondary school, mathematics, pupil, identification, solving.