Abstract:

The aim of secondary school mathematics teaching is, in addition to acquiring the pupil's common knowledge and skills, to teach the student independence in learning and the ability to solve problems. This article wants to show how problematic tasks can be used in teaching mathematics to help pupils learn these skills. It also shows how a method of exploration can be used to solve mathematical problems by which pupils can discover new contexts, knowledge, and learn themselves. Examples of problem-solving are demonstrated here on specific examples. The aim is to show how these heuristic methods can be used in teaching mathematics. The ability of pupils to solve problems independently can also influence their overall relationship to mathematics and their further school and professional practice. The modern concept of teaching mathematics requires the acquisition of skills that are useful for the further development of the pupil and his / her practice and are referred to as pupil competence. One of the pupil's competences, which is characterized by the National Institute for Education, is the development of pupil's competence to solve problems. This article shows that solving problém develop the competence to solve problems.

Keywords:

Problem, exploration, heuristic methods, strategy, experimentation, proof, hypothesis.