The method of visual presentation of educational information for solving problems of mathematics and informatics is effective for the development of algorithmic, logical and computational thinking of schoolchildren. Technical progress, informatization of education, the emergence of modern software for visualization of information change the activities of teachers who need to master new technologies of information visualization for use in the classroom and in work with gifted children. Visual models for presenting educational information and methods of their processing with the use of computer programs are also relevant in extracurricular activities, allowing to develop the intellectual abilities of schoolchildren. Teachers are required to teach children to create projects in which visibility is a necessary component and must be represented by an electronic product created using modern information visualization tools. The article proposes a variant of the advanced training course for teachers of mathematics and informatics on teaching methods for visualization of solving problems using graphs and the free software “Graphoanalyzator”. The relevance of the course is due to the need to form the competency to carry out targeted work with gifted children in the use of software for creating and processing graphs based on the graph visualization program “Graphoanalyzator”. The authors believe that the training of teachers on this course will contribute to the formation of their skills to solve problems of mathematical modeling in informatics and mathematics, to apply information technologies to solve pedagogical problems in the context of informatization of education.