The problem of teaching mathematics in modern Ukrainian schools is general, but it has become more difficult for students with a non-mathematical background. Despite numerous studies of this problem, no specific recommendations have been made. Therefore, to develop and implement an experimental method of teaching mathematics aimed at activating the cognitive activity of non-mathematical specialties pupils. The goal was solved by conducting a questionnaire among students and teachers, which allowed us to reveal and deepen the aspects of the specified problem. Two groups were created: experimental and control. The experimental group studied according to the new model of education, and the control group - according to traditional methods of teaching mathematics. The study revealed a complex of interrelated problems, both for teachers and students. Among the problems, the lack of motivational mechanisms and a complex pedagogical approach to explaining mathematics and the limited amount of teaching mathematics to students with a non-mathematical background are of primary importance. The results of the study indicate the need to introduce the specifics of conducting classes, which would focus on understanding the subject through imaginative thinking. The need to develop textbooks and manuals, which would focus on a more in-depth and understandable teaching of the subject with exercises and tasks for humanitarian areas, has been proven. At the same time, such measures became urgent due to the introduction of quarantine measures of the Covid-2019 pandemic.