Teaching ways of compiling tasks as the fundamentals of the development of professional competence of future mathematics teachers
Based on the analysis of pedagogical experience, the authors showed that in order to master the method of solving a problem effectively, students need to master the methods of creating problems solved by this method. In addition, the system of mathematics education at school requires future teachers to master the methods of compiling tasks, which makes it possible to formulate a large and diverse range of tasks that enable the teacher to realize various educational goals. The research analyzed the ways of compiling the problems; according to the authors, the most effective ones for the training future mathematics teachers are sorted out. Three of the selected ways are discussed in detail: the bringing in a parameter when solving a problem and its further specification when creating a set of problems with predictable properties of solutions; compiling tasks with a given solution method in general terms; the formulation of questions to the so-called open problem and the ways of composing open problems. We have presents the methods of teaching students the selected ways of compiling mathematical problems in the study of various disciplines. Future teachers of mathematics mastering these skills allows one to perform the necessary multivariate test examination of students' knowledge on the topic being studied, using electronic means and Internet resources, preventing students from finding the answer on the Internet. The experimental research made it possible to conclude that the training future mathematics teachers to apply these methods of compiling mathematical problems practically forms a complex of universal and professional competences, creating the basis for the formation and development of their professional competence.