Specifics of designing a technological component in an integrated methodological system of mathematical training of future engineers

Introduction. The article deals with the recent trend in the higher technical education. The new training course focuses on the integration model of mathematical training. The aim of article is to study the specific aspects of designing methodological system of technological component based on integration of bachelor's degree mathematical and engineering training. Materials and Methods. Scientific works on methodology of engineering, researches on theory of mathematical engineering education, and special normative documents were used as theoretical framework of the study. Historical, pedagogical, and experimental-inductive methods, dialogical understanding, visualisation, pedagogical integration, structuring and generalisation constituted methodological basis of the study. Results. The method of integrating the course of mathematics into the system of engineering education is described and substantiated. This method combines formal and informal approaches in teaching-learning process. It contains the experimental-inductive method and rational logic based on the visualization of learning. These new approaches were approved at Penza Technological University and Penza State University. They demonstrated their effectiveness in the educational process. The teaching of mathematics in technical universities should be carried out with account to the integration model of the educational process. It is relevant to harmonise the methodology of mathematics with the methodology of engineering. The authors propose to structure the applied approaches and to identify the integrative directions of methodological work aimed at separate engineering specialities. At the same time, known methodological positions receive a new qualitative interpretation. Discussion and Conclusions. Scholars in the field of vocational education and subject methodologies, teachers of mathematics in engineering specialities of universities, and teachers of mathematics of profile classes constitute the target group of the article.