Many schoolchildren experience significant difficulties in teaching mathematics. The search for ways to solve this problem has actualized the appeal to the theory of cognitive load, which relates to the field of educational psychology and educational design. The purpose of this study is the theoretical substantiation, development and testing of methods aimed at reducing the cognitive load of schoolchildren when teaching mathematics. The implementation of the designated goal was carried out on the basis of the analysis of scientific literature, synthesis of the information obtained, study and generalization of pedagogical experience, a pedagogical experiment, the results of which were processed using the Mann-Whitney U-criterion. The study revealed the features of how the effects of cognitive load can be taken into account in the methods and techniques of teaching mathematics to schoolchildren. A method of proven geometric construction has been developed, which, along with other methods and techniques aimed at reducing the cognitive load of students, was tested when teaching geometry to schoolchildren in the 8th grade. The results of the pedagogical experiment indicate a positive impact of the introduction of ideas of the theory of cognitive load on the educational results of students. In conclusion, based on the completed study, methodological recommendations are proposed.