On the role of visualization in teaching mathematics (using an example of the concept of function)

In the teaching community, there is an ongoing discussion about the difference between visual and analytical thinking and the issues of psychological-pedagogical argumentation of the concept of visual teaching mathematics. Following the discussion, this paper is aimed to identify visual images understanding. The research objective is to identify the role of images in the formation of mathematical concepts (using an example of the concept of function). The novelty of the work is that an image is considered not as a result but as a condition for mathematical concept understanding. The authors used theoretical and experimental methods of study (the analysis of psychological and pedagogical sources, testing, and survey). To achieve the goal, special examinational questions were developed. The authors identified the role of influence of using images and concepts initially existing in the student’s mind on the efficiency of understanding the essence of a mathematical concept. The study revealed that students who have the skills of both visual and analytical thinking demonstrate the best results of understanding mathematical concepts. The research shows that visual and analytical types of thinking not always comply with each other, therefore, methodologically verified teaching mathematical concepts and relations should be proportionally balanced. The prevalence of any type of thinking by the students is individual. The essential prerequisite for successful application of visual teaching methods is to take into account the initial images, ideas, and associations of students in teaching. Visualization is an important method of learning mathematics; however, understanding mathematical concepts does not suppose isomorphism between understanding of a concept and its image.