Mathematics is an exact science, it is the embodiment of order and logic. Without it, the development of technology and the knowledge of nature would be impossible. It helps us to understand the world around us, to learn more about its laws. An understanding of mathematics is crucial both for humanity in general and for individual intellectual development. This understanding needs to be seen with reference to the idea of intellectual tolerance within the education process. In learning mathematics this means finding ways to overcome stereotypical thinking when searching for solutions to mathematical problems. Students with low level intellectual tolerance avoid applying new methods and only use known methods. So the teaching of mathematics should be directed to enabling students to break free from stereotypical conservatism. This can be achieved by using carefully selected strategies and methods-helping students become aware of different perspectives with regard to a studied fact or phenomenon. These strategies, such as the development of the skills to modify activity in changing situations, or to find concise and mathematically beautiful solutions, all enhance of students’ development. In this paper the author discusses the components of thinking within mathematical activity, and outlines a model of the formation of intellectual tolerance. The author also outlines methodological approaches in secondary school mathematics teaching which are designed to develop this intellectual tolerance.