The new method of teaching the problems with a parameter was designed based on the identification of the reasons for the low success rate of the kids in solving the problems. In order to identify these causes and to find ways of their elimination, pedagogical research was carried out in two phases at selected universities of Slovakia (126 students) in 2016-2017. In the first stage the validity of the research hypothesis was confirmed, that the cause of the kids´ poor success in solving problems with the parameter is an algorithmic approach to their solution, a misunderstanding of the concept of a parameter and a formal determination of solvability conditions. Based on this, a new method of teaching the tasks with a parameter was developed. Its main idea is focusing on understanding the term parameter and showing its creative use in solving multiple tasks. In the second stage of the research, the success of the new teaching method was also verified experimentally. The results of the experiment confirmed the success of the students in solving the problems with the parameter, confirming that the basis of the success in solving the problems is the understanding of the term parameter and the ability to find their own solution to the task. It has turned out that the transition from the method of solving equations with a parameter by algorithms to the solution method by understanding the basic concepts and possibilities of their use is one of the methods to improve the teaching of mathematics.