Analysis of the Expectations and Compatibility of the Participants in the Educational Process in the Realization of Problems in Mathematics

Abstract

There is no universal solution for successful math education. Many roads lead to this goal, some of which are radically different from others. Perhaps attention should be paid to more training in problem-solving; less arrogance and more understanding; learning in context; accounting not only the results, but also the necessary strategies and learning processes. Everyone has to solve problems in their life. The ability to cope with them is a necessity to be successful and competitive in today's society.This article examines the essence of problem education, its characteristics and conditions for the application in mathematics education. Different ways and means have been outlined to help solve a problematic situation during the lesson. Different levels of feasibility of the conditions also determine different levels of implementation of the problem approach. In problematic training, the teacher puts the students in a problematic situation and directs them towards solving it. Looking at it from different perspectives, even if they are wrong, this is extremely useful for understanding all logical links between objects. Any false hypothesis is correlated with new facts or arguments that lead to its rejection. The students, alone or with the help of the teacher, seek and discover the truth, the solution, the fact. The teacher, who has pre-prepared problems and facts, "directs" the process of discovering the new knowledge. With learning through discovery, students do not receive knowledge, but learn about the process of reaching it, and achieve creative goals in learning. Drawn to the discovery of the unknown knowledge, they become active participants in the learning process. The new knowledge they find is memorized more durably because the result has not been just announced to them, instead they have been involved in the search for the logical connectivity and validity of mathematics. They learn to look for different solutions to the problem and to not to be afraid if they get the wrong one. The exhaustion of all possible choices and choosing the right, through indisputable arguments, is a skill that will be extremely necessary in their life.For this research it was conducted a study on "Problem Mathematics Training - Expectations and Results". An analysis of the survey results was made by the participants in the educational process in mathematics - teachers and students with whom the problem education was conducted. The positive results by problem solving make a big impression- greater student activity, increased motivation to learn, problem solving skills, better teamwork. Students realize that math is necessary in life, it has become more interesting to them in class, they are challenged to solve problems and are satisfied with the new knowledge they have discovered. A significant part of the teachers are pleased with the use of problematic math education, but they also point out the problems they have encountered - lack of appropriate tasks in textbooks, methodological development and guidance, more time necessary to prepare the lesson itself.