Mathematical analysis is one of the most difficult units both in the school course of mathematics and in the course of higher mathematics at the university. Therefore, the use of continuity in teaching is one of the conditions for the successful assimilation of the programme by students in the transition from school to university.

The authors of the article study the issue of applying innovative forms and methods of training pre-service mathematics teachers to teach students differential and integral calculus, which is closely related to the continuity in teaching between the levels of secondary and higher education. The article shows a brief review of the literature in recent years on teaching differential and integral calculus, continuity in teaching mathematics at school and university. A comparison of the content of the school course of algebra and the beginnings of analysis and university courses included in the module Introduction to Mathematical Analysis and Integral Calculus (on the example of M. Auezov SKU) is proposed.