DEVELOPMENT OF STUDENTS’ COGNITIVE ACTIVITY AT THE LESSONS OF HIGHER MATHEMATICS

The task of modern engineering education is to train an engineer capable to solve professional problems creatively, quickly acquiring new knowledge and being able to apply them in order to solve new non-standard situations. Training of such specialists is possible only if heuristic skills are formed in the process of training students. The greatest effect of the task is achieved during Maths classes. In the article some features and ways of development of students' abilities due to heuristic methods of teaching higher mathematics are considered. The analysis of the latest research and publications on the problem related to the formation and realization of heuristic ideas within Mathematics teaching has been carried out. It showed that today the issues regarding the methods aimed at forming profession-oriented heuristic activity of future engineers at Math classes are insufficiently studied. The aim of our research is to create and theoretically substantiate the system of the most effective methods aimed at developing students' heuristic skills during the classes of Higher Mathematics. The etymology of the word «heuristics» as well as its modern interpretation are represented in the article. These heuristic teaching methods are considered: the research method, the method of heuristic questions, the method of «brainstorming». Their role in the formation of students' abilities to assimilate information, expand and evaluate it to use the methods of cognitive and creative activities are revealed. A plan for the study of the object by students is presented, which is set forth by the well-known Russian teacher A. V. Khutorskoy. Some recommendations facilitating the solution of the problems using the method of heuristic questions by the well-known American mathematician and teacher George Polya are considered. According to the Russian researcher A. V. Khutorskoy, the rules specifying the application of the «brainstorming» method as well as its purpose are given. The conditions for using these heuristic teaching methods are indicated. The advantages and disadvantages of each of the listed methods are considered, including the advantages and disadvantages of heuristic training. An experimental study was conducted on the basis of the Department of Higher Mathematics of the Faculty of Computer Systems and Automation of Odessa National Academy of Food Technologies. The results of the research confirmed the success of using heuristic methods in Higher Mathematics classes. Conclusions are made about the expediency of using this or that heuristic method in studying various sections of Higher Mathematics. The prospects of further research are seen in the studies devoted to the definition of additional criteria for the effectiveness of the use of these teaching methods.