The Role of the Integrated Image of the Problem Solving Method in the Realization of the Mathematics Teaching Continuity

In the article we investigated the problem of forming in students' minds an integrated image of the way of solving mathematical problems. There were considered the possibilities of realization of intrasubject integration in the process of studying math. The methodical conditions under which due to the integrated image of the method of solving the problem the realization of the continuity of teaching mathematical disciplines during the transition from school to university was revealed. We have chosen the method of completing the square to describe the authors' methods of teaching math. Curricula and school textbooks currently in force in Ukraine were analyzed. We also considered universities' curricula of Mathematical Analysis. An experimental study with students on the formation of an integrated image of the method of solving problems, which showed positive dynamics and proved the effectiveness of the developed methodology. It was concluded that the formation of an integrated image of the method of solving problems during a long study of mathematics was possible with the correct choice of problems that are solved in a given way; application of the system of didactic principles, in particular systematicity, consistency and perspective; constant generalization and systematization of knowledge, skills and abilities of students.