Abstract:

Modern mathematics teaching methods use a number of elements based on heuristic approaches to education. The main goal is that the student is not only the recipient of new knowledge, but that he also participates in the discovery of new knowledge. Therefore, the student should not only learn from the teaching process the required knowledge to learn, but he also should learn a number of skills, collectively referred to as school competencies, which may be useful in other areas of education and further professional practice. The aim of teaching mathematics in high school is for the student to acquire not only the required knowledge, but to learn independence at work and to acquire the skill to solve problems. This article seeks to show how problematic tasks can be applied in the teaching of mathematics, with which students can learn these skills. It is explained here how a scientific-research method can be used in solving mathematical problems, with the help of which the student can independently discover new contexts, knowledge and learn on his own. There are examples of suitable problems for teaching with a whole solution that can be included in teaching. Pupils' ability to solve problems independently can also influence their overall attitude towards mathematics and other professional practice. The article presents examples of several problems of various difficulties suitable for inclusion in mathematics teaching.

Keywords:

Heuristic, skills, competencies, results, skills, scientific-research method, solve, problem.